Vedic Mathematics is a system of mathematics that allows problems to be solved quickly and efficiently. It is based on the work of Sri Bharathi Krishna Thirthaji Maharaja (1884 – 1964), who devised the system from a close study of the Vedas. The Vedas are ancient scriptures of India that deal with many subjects. It is based on 16 sutras (aphorisms) from the Vedas that provide a principle or a rule of working to solve a problem. These sutras may be ancient in origin, but are still relevant to modern day mathematics.
Welcome to the wonderful world of "Vedic" mathematics, a science that its founder claims was lost due to the advent of modern mathematics. Vedic mathematics is said by its founder to be a gift given to this world by the ancient sages of India, though there is no historical evidence whatsoever for this claim. It is a system for limited arithmetic and polynomial calculation which is simpler and more enjoyable than the equivalent algorithms of modern mathematics.
Here are some interesting maths quizzes. Find out the answers of these quizzes and see how genius you are....all the best!!!
Pls do visit, www. mathemagix.co.in for maths shortcuts, formulas, symbols, quizzes, facts
A Vedic Maths is the name given to the ancient system of Indian Mathematics which was rediscovered from the Vedas/sutras between 1911 and 1918 by Sri Bharati Krisna Tirthaji (1884-1960).
According to his research, maths is based on 16 SUTRAS or word-formulae. These formulae describe the way the mind works naturally and are therefore a great help in directing the students to the appropriate solution. This unifying quality is very satisfying,; it makes maths easy, enjoyable and encourages innovation.
Many times, you will find yourself in a situation where you need to or rather you want to quickly multiply or divide complicated numbers. And given the traditional methods of learning mathematics, you may not be able to do so. Moreover, with the growing dependence on calculators is slowly crippling you.
Welcome to the wonderful world of "Vedic" mathematics, a science that its founder claims was lost due to the advent of modern mathematics. Vedic mathematics is said by its founder to be a gift given to this world by the ancient sages of India, though there is no historical evidence whatsoever for this claim. It is a system for limited arithmetic and polynomial calculation which is simpler and more enjoyable than the equivalent algorithms of modern mathematics.
Here are some interesting maths quizzes. Find out the answers of these quizzes and see how genius you are....all the best!!!
Pls do visit, www. mathemagix.co.in for maths shortcuts, formulas, symbols, quizzes, facts
A Vedic Maths is the name given to the ancient system of Indian Mathematics which was rediscovered from the Vedas/sutras between 1911 and 1918 by Sri Bharati Krisna Tirthaji (1884-1960).
According to his research, maths is based on 16 SUTRAS or word-formulae. These formulae describe the way the mind works naturally and are therefore a great help in directing the students to the appropriate solution. This unifying quality is very satisfying,; it makes maths easy, enjoyable and encourages innovation.
Many times, you will find yourself in a situation where you need to or rather you want to quickly multiply or divide complicated numbers. And given the traditional methods of learning mathematics, you may not be able to do so. Moreover, with the growing dependence on calculators is slowly crippling you.
The paper presents the advantages of the Vedic Mathematics approach and highlights the unique qualities of this sutra based Mathematics develoed in ancient India
India's pursuit of climate targets, including net-zero emissions by 2070, hinges on integrating renewable energy. The power sector's heavy reliance on fossil fuels necessitates a significant shift towards renewables. With a rising demand for electricity, effective demand-side management strategies are vital to ensure grid stability. Time-of-use (ToU) tariffs, recognized globally, play a crucial role in this strategy, offering a more accurate reflection of electricity costs compared to flat rates.
This report focuses on evaluating the impact of various ToU tariff designs on grid management parameters for Tamil Nadu in 2024. The objective is to assess how static ToU tariffs prompt consumers to shift or reduce electricity usage, facilitating greater renewable energy integration. The study considers 27 ToU tariff designs, assuming 17% wind energy and 11% solar energy. Notably, findings are specific to Tamil Nadu's energy demand pattern, peaking in early afternoon hours in April.
Results emphasize the importance of defining peak and off-peak time slots optimally to reduce peak loads and curtailment of renewables. Shifting peak hours from 6:00h-10:00h and 18:00h-22:00h to 5:00h-7:00h and 17:00h-23:00h improves key parameters, including a reduction in peak load instances on the gross and net load. Introducing a tariff rebate during solar energy generation hours (solar sponge) from 10:00h to 16:00h effectively reduces peak load magnitudes and encourages load distribution throughout the day, enhancing grid stability. Adjusting peak hour tariffs and shifting peak hours has a noticeable impact on load distribution and peak load occurrences.
The study indicates that a 25% increase in peak-hour tariffs outperforms a more aggressive 40% increase, which may create new peak load instances. Simulated off-peak rebates of 5% and 10% during late night and early morning hours have negligible effects.
Overall, these findings underscore the potential benefits of implementing ToU tariffs for all consumer categories, including reduced peak loads, load range occurrences, and ramping requirements. Careful consideration of peak hour tariffs and adjustments to peak hours can further optimise load distribution and maximise the efficiency of the power grid. To meet its RPO and its climate change objectives Tamil Nadu will have to accelerate the deployment of renewable energy generation. In order to manage the variable nature of wind and solar energy generation and of demand the grid management will require a higher degree of demand and generation flexibility services.
Auroville Consulting (AVC) published its annual sustainability report for the financial year 2022-23.
This year we intensified this practice along with the digital footprint through network usage and website hosting, understanding the impact of our recently installed HVAC system, and emissions avoided through providing e-bikes to all our team members. We have achieved a net zero emission balance for FY 2022-23. This was made possible through planned interventions and implementation of good practices to reduce gross emissions, followed by investment in long term effective carbon positive projects. Some key highlights:
● 92% of this year’s gross emissions were offset by planting trees and the remaining 8% was offset by excess solar generation, making AVC a carbon net-zero organisation.
● 100% of electricity demand was supplied by renewable energy through rooftop solar.
● 25.58 kWh of electricity was consumed per square meter of office space, which is 75% lower than the benchmark of Bureau of Energy Efficiency (BEE) for an office building in a warm and humid climate (Benchmark: 101 kWh/sq. m/yr).
● From March 2022 onwards, the organisation has been providing electric two-wheelers to all its full-time team members for their daily commute to and from office and for their own personal use, along with a charging facility supplied by an additional installed capacity of rooftop solar. This initiative resulted in :
o An emission reduction of 2,584 kg CO2e for their daily commute to and from office, which is an 88% decrease in comparison to the previous year, and
o An emission reduction of 6,309 kgCO2e, which was achieved by converting the personal commute of our team members to e-vehicles and charging them through renewable energy. This is a value higher than the total gross emissions of the organisation..
● 98% of the operational expenditure was made in local areas, with 91% inside Auroville; and the remaining 2% in Pondicherry and Tamil Nadu – preventing unnecessary emissions and stimulating the local economy.
Rajapalayam is the taluk headquarters of Rajapalayam Taluk, and an important town in the district of Virudhunagar within the State of Tamil Nadu. Rajapalayam LPA, which includes Rajapalayam town, 15 surrounding revenue villages and 2 reserved forests, has a total population of 2.16 lakh, as per the 2011 Census. In 2023, a master plan was formulated for Rajapalayam LPA, the master plan has a planning period till 2041. The master plan was meant to foster sustainable urban development, responsible land-use and resource efficiency and is expected to propel the town on a pathway towards decarbonization and inclusive growth. Rajapalayam is the first town in Tamil Nadu that has aspired to announce a GHG emission reduction target, it aims at achieving net zero emissions by the year 2041.
It is in this context that an emissions inventory for the town has been developed. The purpose of this GHG emissions inventory is to report on the sources and magnitude of GHG emissions. While this inventory provides us a broad understanding of today’s emissions, consecutive reports on a yearly or bi-yearly basis can help improve the quality of the data and understand the progress of the activities undertaken by the LPA to reduce their impact on the surrounding environment.
ELECTRICITY SUBSIDY AND A JUST ENERGY TRANSITION IN TAMIL NADUAurovilleConsulting
To address climate change, to promote adaptation and resilience, to eliminate energy poverty, and to ensure a just energy transition, countries and states will have to mobilise substantial financial resources. A recent study estimated that India will need to invest a 900 billion USD over the next 30 years to ensure a ‘just energy transition’ (Bushan 2023). While developed countries have pledged to provide climate finance to developing countries, these pledges have not been fulfilled, or are very slow to arrive, or are insufficient. Developing countries will need to find additional and alternative resources to accelerate the decarbonization of its economies and to invest into climate adaptation. The United Nations (2022) has outlined a few interventions that can help in accelerating a just energy transition. These include:
to make renewable energy technologies a public good,
to shift energy subsidies from fossil fuels to renewable energy, and
to triple investments into renewables.
In 2009, G20 members committed to phasing out and rationalizing fossil fuel subsidies in the medium term (Reuters 2009). But as of 2022, fossil fuel subsidies have not been phased out, neither have they been reduced; instead, fossil fuel subsidies exceeded USD 1 trillion globally for the first time. This is largely due to governments’ increased subsidies to cushion consumers from rising energy prices (IISD 2023).
Energy subsidies are found in virtually every country. Justifications for their use range from social welfare protection, job creation, encouragement of renewable energy sources, promotion of economic development, to energy security. However, it may be worth examining some of the current energy subsidy schemes asking if and to what extent these subsidy schemes are contributing to a just energy transition and to what extent these subsidies align with the proposed three interventions by the UN.
Read the full report here: https://www.aurovilleconsulting.com/electricity-subsidy-and-a-just-energy-transition-in-tamil-nadu/
LAND SUITABILITY ASSESSMENT FOR STORMWATER MANAGEMENT, MAYILADUTHURAI DISTRIC...AurovilleConsulting
Land is a finite resource with competing and conflicting use. Unplanned and unscientific use of land can exacerbate climate change, and disasters like drought or floods. Judicious use of land resources is key in meeting the state’s social, economic, and environmental development goals. A comprehensive land suitability assessment can guide responsible and sustainable development practices and land-use policies.
Land and water are closely interlinked, as the availability and flow of freshwater depends on the land characteristics, such as its topography and composition, amongst other factors. Therefore, certain areas of lands naturally act as better sinks for capturing stormwater or surface run-off water from precipitation. Freshwater, on the other hand, is a critical resource, and the stress on freshwater resources is expected to increase with growing population, development, and climate change. According to India’s Composite Water Management Index (Niti Aayog, 2018), 600 million people in the country are suffering from an acute shortage of water. Read more in the report: https://www.aurovilleconsulting.com/land-suitability-assessment-for-stormwater-management-mayiladuthurai-district-tamil-nadu/
MAXIMISING THE BENEFITS OF DISTRIBUTED SOLAR ENERGY: AN EVALUATIONAurovilleConsulting
Tamil Nadu is making significant strides towards a sustainable energy future, supported by announcements of adding 20 GW of solar energy capacity and 10 GW of battery energy storage capacity by 2030. The state’s policy and regulatory frameworks, including the Tamil Nadu Solar Policy and the Generic Tariff Order, are driving the adoption of grid-connected distributed solar energy. As the adoption of distributed generation systems increases, the importance of smart grid integration becomes evident. Studies that provide an avoided cost assessment offer an opportunity to network operators to identify the most appropriate distribution network nodes and distributed renewable energy (DRE) capacities
This report focuses on evaluating the network and societal impacts of introducing distributed solar energy in the Karungalpalayam HT Feeder under the Erode substation. This analysis provides valuable insights into the distribution of active power and voltage, allowing operators to optimize network performance. The report utilized the Solva tool. Solva is a web-based tool with the aim to assist grid operators in assessing the network and societal value of distributed energy resources (VODER). Solva assesses both network benefits and societal benefits. Network benefits encompass the avoided costs associated with energy, distribution capacity, transmission capacity, and generation capacity. Simultaneously, societal benefits factor in the avoided costs of CO2 emissions, SO2 emissions, NO2 emissions, and PM2.5 emissions.
For the selected feeder a 4.50 MW solar energy system interconnected at the tail end of the feeder results in a VODER benefit of INR 12.84 per kWh. These benefit is subdivided into network benefitss and societal benefit. The societal benefits achieved from the integration contribute to 8.84 INR/kWh or 69% of the total benefit. Network benefits are found to be at 4.00 INR/kWh or 31%. With the integration of distributed solar energy, the distribution line losses show a reduction, particularly if interconnected at the middle end or tail end of the HT feeder. When the solar energy system is interconnected at the tail end or at the middle end of Karungalpalayam HT Feeder, a deferral of feeder upgradation is found.In particular to Karungalpalayam HT feeder, interconnecting the distributed solar energy system close to the point of consumption offers the highest benefits.
In 2022 a GHG emission baseline for Auroville was established. The inventory highlighted the overall emissions from the community. This report now intends to assess the sequestration capabilities of Auroville land under tree cover for a five-year period from February 2017 to February 2022. The tree cover in Auroville is a prime contributor to the community’s long-term vision of sustainable development. The overall tree cover includes the residential zones, industrial zones, parks, public spaces and the designated green belt area of Auroville developed and maintained by the Forest Group of Auroville.
The cumulative carbon stock for Auroville’s land under tree cover of 920 hectares for the time period from February 2017 to February 2022 was estimated at 34,778 tCO2e. This equals an average carbon stock addition of 6,956 tCO2e per year. The average carbon stock per hectare of forest land in Tamil Nadu was estimated at 87.26 tCO2e/year. The average carbon stock per hectare over five years for the Auroville forest was found to be 99.96 tCO2e/year which is 14.55% above the average.
As per the Auroville Greenhouse Gas Accounting Report, Auroville produced 8,298.54 tCO2e in FY 2018- 2019, this excludes emissions from agriculture, forestry and other land use (AFLOU) and industrial production and product use (IPPU). Auroville’s green cover sequestered 84% of its total emission or 6,956 tCO2e per year. The surplus CO2e emitted for FY 2018-19 therefore is 1,343 tCO2e or 16%. To offset this carbon an additional 19.82 hectare of land would need to be converted from moderately dense forest to very dense forest. This could also be achieved by installing a 1.19 MW solar energy capacity or by transitioning all units to low or zero emission transport solutions.
Consistent studies either on a yearly or bi-yearly basis can help improve accuracy of emissions tracking and sequestration numbers of the community and help set targets. This would lead to additional financing opportunities and access to voluntary mechanisms such as carbon financing to support existing forestry activities.
During the last COP events (COP 26 and COP 27) India stepped up its climate ambitions and announced a goal of reaching net-zero by the year 2070. More specifically its Nationally Determined Contributions (NDCs) includes to achieve about 50 percent cumulative electric power installed capacity from non-fossil fuel-based energy resources by 2030.
In December 2022 Tamil Nadu launched its own Climate Change Mission. Its goals include the development of strategies to cut emissions by using green and renewable energy. This complements an earlier announcement by the State Government, that it aims to add an additional 20 GW of solar energy by the year 2030.
More recently, in March 2023, the Tamil Nadu Governments announced that it will target that 50% of all energy will be sourced from renewable energy sources. If the state where to meet this target it would firmly establish itself as a climate leader on the national and international stage. Further, Tamil Nadu aspires to be a leading export state and as there is increasing international supply chain pressures for industries to reduce their carbon emissions accelerating the transition towards a renewable energy can help its industries to stay competitive in a decarbonizing world. An accelerated energy transition will also promote Tamil Nadu as an attractive location for industries.
In FY 2021-22 the total energy generated was 1,17,553 million units (MU). Renewable energy, this is solar, wind, bioenergy, and hydro, accounted for a 22% of the total energy generation in FY 2021-22. Coal power with a share of 70% is the single largest energy sources. This total energy generation can be subdivided into two parts, (i) energy procured by TANGEDCO and (ii) energy under Open Access. TANGEDCO accounted for 83% or 97,297 MU of energy in FY 2021-22. Whereas the remaining 17% of 20,266 MU are on account of Open Access.
Interestingly TANGEDO procured only 16% of its energy from renewables. Whereas 52% of all energy under Open Access is RE. 51% of all energy procured by TANGEDCO came from either TANGEDCO owned or Centra owned coal power plants. The actual share of coal power may be higher as there is 24% of energy that was sourced under the category ‘Short term and others’ and this may primarily be coal power.
To meet the 2030 RE target an additional 60,637 MU of RE will need to be generated in 2030. This represents approximately an addition of 28 GW of wind energy capacity or a 32 GW of solar energy capacity and means that in the next six years starting with FY 2023-24 approximately 4.80– 5.50 GW of renewable energy capacity needs to go on-grid. The average annual RE capacity addition in Tamil Nadu from 2018 to 2023 was 1.21 GW.
Meeting the 50% RE target will require a concerted effort by all major power sector institutions and players including the distribution licensee, the Electricity Regulatory Commission, the Energy Department, Independent Power producers and the consumers/prosumers.
In the face of the global climate crisis there is an increasing commitment to decarbonise the global economy. This is highlighted by a shift towards renewable energy sources, the energy transition. Energy transition is the process of reducing reliance on fossil fuel across the economy and moving toward greater use of cleaner energy sources such as renewables.
Globally, countries, including those in the European Union, are introducing legislative measures to accelerate the decarbonisation of its economies. In January 2021, the European Union (EU) introduced a Carbon Border Adjustment Mechanism (CBAM). CBAM is part of the EU’s efforts to reduce greenhouse gas emissions and achieve climate neutrality by 2050. It will put restrictions at the borders on goods produced with carbon and Greenhouse gas emissions (GHG)
While the carbon price will be levied from 2026 onwards, the reporting of emissions on imported goods has stated in January 2023. CBAM is initially focusing on some key sectors only, but is expected to expand over time. Sectors for which CBAM applies include:
Iron and steel, Cement, Chemicals, Aluminium, Paper, Glass, Fertilizers, Pulp and paper, Textiles,Ceramics,Basic metals
Other countries or regions that consider introducing similar mechanisms include: Canada, United Kingdom, United States, Japan and South Korea.
The EU is a key export market for India, it is India’s third largest trading partner. India’s exports to the EU were worth EUR 46.20 billion in 2021. Compliance of Indian companies with the EU CBAM will require monitoring, calculating and disclosure of the GHG emissions embedded in the products covered under CBAM.
Tamil Nadu has the second largest state economy in India. The Tamil Nadu Government has set a goal of becoming a USD 1 trillion economy by 2030. The state has a diversified manufacturing sector and features among the leaders in several industries like automobiles and auto components, engineering, pharmaceuticals, garments, textiles, leather, chemicals, plastics, etc.
The role of Micro, Small and Medium enterprises (MSMEs) in the economic and social development of the country is well established. Tamil Nadu has the third-largest number of MSMEs in the country with a share of 8% or about five million enterprises (MSME Department 2022). MSMEs form an important and growing segment of the state’s industrial sector, contributing 12.09% to the GSDP. However, the growth of the state’s MSME sector has been severely impacted by Covid and has been stagnant.
As Tamil Nadu aspires to be a leading export state in India at a time when more countries are proposing Carbon Border Adjustment Mechanism (CBAM) decarbonisation will become an imperative for export-oriented industries to stay completive. For the exported goods from Tamil Nadu to be compliant with regulations it is important to decarbonise the production. The decarbonization will also be paramount for the MSME sector.
LAND SUITABILITY ASSESSMENT FOR DISTRIBUTED SOLAR ENERGY, VILLUPURAM DISTRICTAurovilleConsulting
Land is a finite resource with competing and conflicting use. Unplanned and unscientific use of land can exacerbate climate change, and disasters like drought or floods. Judicious use of land resources is key in meeting the state’s social, economic, and environmental development goals. A comprehensive land suitability assessment can guide responsible and sustainable development practices and land-use policies.
As per its intended Nationally Determined Contribution under the United Nations Framework Convention on Climate Change, India is targeting 50% of its cumulative power generation capacity from non-fossil fuel-based energy resources by 2030. Tamil Nadu has announced that it aims at adding an additional 20 GW of solar energy capacity by the year 2030. This capacity addition is envisioned to be primarily achieved by distributed solar energy generation.
One of the key challenges in developing solar energy project is the identification of suitable lands and land acquisition. The complex land acquisition process can lead to project delays or even cancelation of proposed projects. Unused or fallow lands can be of particular interest for solar energy development. This method avoids the uptake of land under productive agricultural use. Local authorities can proactively facilitate solar energy development in the district by identifying unused lands and by undertaking a solar suitability assessment of these lands. This geospatial information if provided to solar developers and electricity distribution companies has the potential to spur local economic development and to create green jobs.
The objective of this report is to identify unused lands in Villupuram district and to evaluate to what extent these unused lands can be utilized to meet the state’s solar energy capacity addition target of 20 GW by the year 2030. Deploying 20 GW of ground mounted solar energy will require approximately 80,000 acres of land, this represents 0.25% of Tamil Nadu’s total geographical area (TGA).
Villupuram, district has a total geographical area of 3,907 km2 of which 1,092 km2 or 28% has been classified as unused or fallow lands. The district’s solar energy target has been set as a proportional share of the state’s solar energy capacity addition target of 20 GW by 2030. The district’s target is to add 0.62 GW of solar energy by 2030. This requires a land area of 2,465 acres. The land suitability analysis revealed that 92,149 acres of unused land have a technical potential for ground mounted solar energy development. These lands are distributed over 3,084 plots. The suitable lands identified can accommodate up to 23.04 GW of solar capacity, this would help achieving a whooping 3,738% of (or 37 times) the district’s solar capacity addition target.
THE SOLAR ENERGY-LAND NEXUS SUSTAINABLE LAND USE STRATEGY FOR SOLAR ENERGY IN...AurovilleConsulting
Energy generation can have intensive or extensive land use requirements, causing habitat and biodiversity loss in sensitive and diverse ecosystems globally or competing with other land use such as agriculture.
As a direct consequence of the Paris Climate Agreement, which requires global decarbonization, renewable energy sources will continue to expand, in particular solar and wind. The increasing land use for renewable energy generation systems and related infrastructure will become more relevant in the future. The extent to which the overall land use balance will be more favourable than for non-renewable sources depends on the mix of renewables, their siting and centralized or decentralized mode of deployment (UNEP, 2016). Innovative deployment of renewables can reduce land use pressures, as well as avoid landscape disturbances caused by fossil fuels and nuclear energy (Lovins, 2011).
While the use of fossil fuels is limited by the size of the resource (including future cost and the carbon dioxide (CO2 ) budget), renewable energy and in particular solar energy, is mostly restricted by land use allocation and by the availability or solar irradiation or adequate windspeeds.
Land or sea occupancy is one of the most visible impacts for any energy development. The relatively large land requirement for solar energy highlights the importance of good mitigation practices to help facilitate the transition into a renewable energy future. Fortunately, the abundance of solar energy means that, unlike other energy sources, there is often flexibility in project siting, allowing the integration of solar energy systems with buildings and infrastructure assets or the co-location of solar energy systems with agricultural practices or the use of wastelands.
Tamil Nadu has set a target of adding a 20 GW of solar energy by 2030. If this target is to be primarily met by ground-mounted solar plants a 405 km2 land area will be required. Considering the projected annual electrical energy demand of 4,89,395 MU by 2050 (Auroville Consulting 2022) the need to decarbonize the state’s power sector and the fact that solar is among the most cost -efficient energy sources today, the potential land-impact of solar is substantial. Meeting 50% of the projected electricity demand for 2050 would require 133 GW of solar capacity, and 2,691 km2 of land resources, which equals the total geographical area of Chengalpattu District or 2.07% of the state’s geographical area.
There are competing and often conflicting demands for land for economic, ecological, and social needs in the development sector. It will be critical to limit the conversion of agricultural lands for solar energy development.
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LAND SUITABILITY ASSESSMENT FOR FORESTATION, MAYILADUTHURAI DISTRICT, TAMIL NADUAurovilleConsulting
Land is a finite resource with competing and conflicting use. Unplanned and unscientific use of land can exacerbate climate change, and disasters like drought or floods. Judicious use of land resources is key in meeting the state’s social, economic and environmental development goals. A comprehensive land suitability assessment can guide responsible and sustainable development practices and land-use policies.
As per its intended Nationally Determined Contribution under the United Nations Framework Convention on Climate Change, India is targeting the creation of an additional carbon sink of 2.5 to 4 billion tonnes of CO2 by 2030 – through additional forest and tree cover of 25-30 million hectares. In this context, the State Government of Tamil Nadu has set a target to increase its percentage of tree cover from 23% to 33% by the year 2030.
A forestation land suitability assessment for the Mayiladuthurai district in Tamil Nadu, India was carried out using a geospatial digital tool LiLa (LifeLands). LiLa uses satellite imagery, AI & GIS mapping to create critical data-based insights and visualization that supports decision-making by providing detailed information. This includes geo-spatial and socio-economic data-layers to address the core aspects of sustainable land-use management. It identifies and evaluates unused lands for its potential in terms of solar energy, forestation and water management.
The objective of this report is to identify unused lands in Mayiladuthurai district and evaluate its potential for forestation initiatives that can contribute meeting the state’s tree-cover target of 33% by the year 2030.
Identified unused lands were evaluated based on multiple-criteria methodology including parameters pertaining to terrain suitability, existing road, rail and electrical transmission and distribution infrastructure, elevation, water potential and potential to create forest corridors. The lands are also further assessed based on their potential for competing climate action, such as areas that are suitable for water harvesting and solar energy generation.
The land use mapping indicates that 8% of the district’s geographical area is under tree cover. Agriculture land use is by far the most dominating land use category accounting for 63%. Identified unused lands account for an area of 118 km2 or 10% of the total geographical area. Out of the total identified unused lands 56% or 16,237 acres have been found to be suitable for forestation. If all the unused lands suitable for forestation were put under tree cover Mayiladuthurai district would increase its share of lands under tree cover from 8% to 13.5% creating a carbon stock of 0.55 million tonnes of carbon.
PATHWAYS TO DECARBONISATION – MODELLING TAMIL NADU’S POWER SECTOR DECARBONISA...AurovilleConsulting
Tamil Nadu’s electricity demand is expected to increase year on year, and so are the sector’s absolute carbon dioxide emissions. Considering India’s commitments under the United Nations Framework Climate Change Convention, and the recent announcement of targeting net zero carbon by 2070, Tamil Nadu will require a long-term strategy to reduce its emissions. This may start with establishing sector-specific emission inventories, followed by sector-specific emission target setting.
The power sector is deemed to be one of the sectors easiest to decarbonise. One of the first steps for putting in place a decarbonisation strategy is target setting. This report assumes a net-zero carbon target for the Tamil Nadu power sector by 2050. It applies the Sectoral Decarbonisation Approach (SDA) of the Science Based Target (SBT) model to simulate decarbonisation pathways that are in line with the goals of the Paris agreement – limiting global warming well below 2°C above pre-industrial levels (ETP B2DS) and pursuing efforts to limit warming to 1.5°C (SBT 1.5°C) respectively.
In this paper, we undertake the following steps:
1) Projecting the electricity generation for the upcoming years along with the corresponding emissions.
2) Setting targets for the emissions based on the Science Based Targets (SBT).
3) Comparing various scenario planning models for decarbonising the electricity sector of Tamil Nadu.
LAND SUITABILITY ASSESSMENT FOR DISTRIBUTED SOLAR ENERGY MAYILADUTHURAI DISTR...AurovilleConsulting
A land assessment for the Mayiladuthurai district in Tamil Nadu, India was carried out using a geospatial digital tool LiLa (LifeLands) developed in-house. LiLa uses satellite imagery, AI & GIS Mapping to create critical data-based insights and visualization that supports decision-making by providing detailed information. This includes geo-spatial and socio-economic data-layers to address the core aspects of sustainable land-use management. It identifies and evaluates unused lands for its potential in terms of solar energy, reforestation and water management.
The objective of this report is to identify unused lands for this district and evaluate to what extent these unused lands can be utilized to meet the state’s solar energy target of 20 GW by the year 2030. The lands were evaluated based on multiple levels of criteria that accounted for plot size, and their distance from evacuation infrastructure, roads, railways and waterbodies. The lands are also further assessed based on their potential for climate action, such as areas that are suitable for forestation and water harvesting.
The assessment indicated that a target of 0.29 GW of solar installation is achievable with lands that meet the technical criteria. Lands ranked medium can achieve a cumulative capacity of 0.46 GW with a total area of 1,860 acres. Lands ranked high with a total area 698 acres can achieve a capacity of 0.17 GW.
The prevalence of offshore wind is growing globally. According to the Global Wind Energy Council, the total installed capacity worldwide climbed to 57.2 GW at the end of 2021. Offshore wind technology has key advantages such as eliminating the need for large areas of land and harnessing energy from better wind conditions than onshore. Currently, India does not have any installed capacity. However, there has been a recent build-up in momentum. Tamil Nadu has been identified as one of the highest potential states for harnessing offshore wind energy in India. But the State faces technical, social, and financial barriers for phasing-in this new technology. In this regard, the Tamil Nadu Government can play a key role in unlocking this significant source of energy by (i) providing the overall infrastructure required, (ii) engaging with local stakeholders, and (iii) facilitating the clearance process for offshore wind projects, among others.
BATTERY ENERGY STORAGE SYSTEMS AS AN ALTERNATIVE TO DIESEL GENERATORS – A COM...AurovilleConsulting
Power demand across the country is growing, and meeting peak demand is becoming more challenging. In Tamil Nadu, frequent power outages are observed, especially during summer months. To reduce economic impacts of unreliable power supply, commercial and industrial (C&I) entities, undertake investments in power backup systems. The most commonly used systems are diesel generator sets (DG sets) and battery energy storage systems (BESS), also known as an uninterrupted power supply (UPS).
DG sets have been a convenient power backup option due to an established market, their reliability, affordability, and modularity. But they have a high environmental footprint, cause noise pollution and negatively impact human health. On the other hand, BESSs could operate on zero emissions, if charged from renewable energy sources, and with minimal noise pollution. And with no exhaust emissions, they are particularly helpful in urban areas.
The cost of batteries, especially those of lithium-ion (Li-ion) battery packs, have been observing a dramatic drop – of 89% over the years 2010-2020. And, apart from performing their primary function as a power backup, BESSs can also provide grid services such as load shifting, load following, peak load management, voltage, and frequency support and facilitate higher levels of renewable energy integration. Thus, BESSs contest DG sets economically and technically as an alternative type of back-up system.
This report compares the economic and environmental performance of a Li-ion-based BESS with a conventional DG set, as power backup solutions. The analysis indicated that the levelized cost of battery storage (LCOS) is dictated by the battery pack costs in the market, while the levelized cost of energy (LCOE) of the DG is sensitive to diesel prices. The cost analysis was carried over a range of hours of back-up required, and the results favour the Li-ion BESS as a back-up option, in terms of economic and environmental performance, especially when charged at solar tariff solar tariff.
We hope that this report will assist C&I entities in Tamil Nadu to make the most economic and environmentally sound investment in their power backup systems.
BRIEFING NOTE: ELECTRIFICATION OF TOP-PERFORMING INDUSTRIES IN TAMIL NADUAurovilleConsulting
Tamil Nadu is one of the most industrialised states in India and accounted for 9.47% of India’s GDP in FY 2020-21. Tamil Nadu aspires to be a leading export state in India at a time when more countries are proposing Carbon Border Adjustment Mechanism (CBAM). CBAM includes the introduction of a carbon price on certain products imported into the European Union (EU). This will put restrictions at the borders of the EU on goods produced with carbon and Greenhouse gas emissions (GHG). As per an assessment of the World Bank, many countries are considering setting a carbon price in the years to come. Tamil Nadu could be exporting its finished goods to a few of those countries in the future. For the exported goods from Tamil Nadu to be regulation-proof, it is important to decarbonise the production. The first step towards decarbonisation is the electrification of the processes in the industries. This briefing note explores the potential for the electrification of some of the processes in the top-performing (in terms of contribution to the State’s GDP) industrial sectors of Tamil Nadu.
The second phase of the Auroville Smart Mini Grid is also complete. Driven and conceived by Auroville Consulting it compromises 108 kW of distributed rooftop solar energy systems. The solar PV systems reduces Auroville’s electricity consumption from the TANGEDCO grid by an average of 1,57,680 kWh per year and reduces it’s dependency on TANGEDCO. This is another step forward towards self reliance and sustainability. The project includes an energy storage system with a capacity of 10 kWh, 20 smart energy meters with a remote reading facility and additions to the Auroville internal electricity distribution system. Further we were able to upgrade our internal HT and LT distribution infrastructure and started piloting an active demand response program for domestic air conditioners and for municipal water pumps. The project was lead by Auroville Consulting. Other Auroville units include Auroville Electrical Service, Sunlit Future & Aurinoco.
Inspired by the method of Environmental, Social, and Governance (ESG) reporting, this report attempts to consolidate data on the performance of Tamil Nadu Generation and Distribution Company (TANGEDCO). The aim of this work is to initiate and develop holistic benchmarks. These key performance indicators would help TANGEDCO to track its own performance. Apart from the KPIs, this report also highlights the importance of sharing data in a public domain for the civil society to access.
LEVELISED COST OF BTM STORAGE IN INDIA 2021 – A STATUS REPORTAurovilleConsulting
This status report aims to present a snapshot of the current cost of energy storage in India for behind-the-meter (BtM) applications, and project them over the next 10 years to analyse when energy storage will start seeing significant adoption. Based on a detailed cost model for solar PV and energy storage with 50+ parameters & data on battery energy storage systems (BESS) gathered from several vendors in India, we evaluate the levelized cost of solar plus energy storage and standalone energy storage.
Even though as of today, BtM energy storage is not feasible in a lot of cases, we find that this will change fast this decade. By 2025, it will be possible for non-residential consumers to integrate large amounts of battery storage to generate and consume their own energy, enabling a distributed energy future. Along with it, the utilities face an inevitable transition from their traditional roles to distribution system operators.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
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• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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3. ii
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All Things Vedic
Auroville Collaborative
Saracon, Auroville, TN 605111, INDIA.
Tel: +91-413-2622571
Web: www.allthingsvedic.in/addition
5. 4
Preface
Vedic Mathematics is a system of mathematics that allows
problems to be solved quickly and efficiently. It is based on the
work of Sri Bharathi Krishna Thirthaji Maharaja (1884 – 1964),
who devised the system from a close study of the Vedas. The
Vedas are ancient scriptures of India that deal with many
subjects. It is based on 16 sutras (aphorisms) from the Vedas
that provide a principle or a rule of working to solve a problem.
These sutras may be ancient in origin, but are still relevant to
modern day mathematics.
Vedic Math provides many different methods to solve any given
problem. The choice of method depends on the conditions that
the given problem satisfies. This is very much like planting a
tree – the choice of which tree to plant has to depend on the
nature of the soil and the environment. It is impossible to plant
the same tree everywhere without considering the
surroundings. Vedic math works in a similar manner.
Conventional mathematics generally provides a single method
to solve a mathematical problem. This method is applied
“blindly” whenever the student comes across the problem.
However, in vedic math, the student chooses which method to
employ. In multiplication, for instance, there are almost five
different methods that can be used, and the choice of method
depends entirely on what the student is comfortable with.
Learning such a system of mathematics at an early age can
greatly help in dispelling fears of mathematics in children and
can even make it more fun. Vedic math also allows us to
develop the ability of lateral thinking, enabling us be faster at
calculations and even to rely less on the calculator. ! !
This series of books is an attempt to present the material in a
modular fashion. Each book focusses on one specific arithmetic
operation - addition, subtraction, multiplication and division.
These books can be read in any order, but it is recommended
that addition and subtraction be read before multiplication and
division. This particular book is related to addition only, and
subsequent books will cover the other arithmetical operations.
Some of the vedic methods apply to specific sets of numbers,
while others are general methods and can be used in all cases.
How to use this book
Each chapter introduces one or two ideas, and takes you from
the simple to the more advanced methods. At times, you will be
posed a question, and I suggest that you pause, think and
arrive at an answer before continuing.
6. 5
Content has been optimized for the iPad. There are essentially
two kinds of interactivity available in the iPad version:
screencasts and buttons.
A screencast is a digital recording of computer screen output,
explaining the Vedic Math techniques, along with an audio
narration. Screencasts are natively available on an iPad, and in
some versions of the pdf. If the screencasts do not play on your
computer or tablet, these are also available on
www.youtube.com/VedicAddition for reference. At times, it is
easier to explain orally, than in written words. Hence, each
method is illustrated using a screencast, as well as a written
explanation.
Buttons are used to display the solutions to exercises. If the
buttons do not work in your version of this eBook, all solutions
are provided in Chapter 6 as well.
Note for the teacher
If you plan on using this material in your classes, I would
suggest a minimum of two hours on each chapter. Supplement
the exercises presented in this book with your own. Though not
essential, I would suggest that the students understand the
concept of negative sign, before being introduced to Vedic
Math.
Prerequisites
No prior knowledge of Vedic Math is necessary to read and
understand the material I have presented in this book. I start
with the basics, and proceed to the more advanced techniques
of Vedic Math. It will be helpful to know the addition tables till
20+20 to fully grasp the techniques presented in this book.
8. 7
Some notes
Patterns in numbers
Ever seen a pattern in nature, such as the recurring phases of
the moon, and wondered at the beauty of nature? These
patterns exist in numbers too. Patterns such as the Fibonacci
Numbers and the Golden Mean are well known examples.
Learning how to recognize these patterns and using them to
solve problems is what Vedic Math is all about.
Number line and negative numbers
The number line is a straight line with zero at the center and
extending to infinity on either side. Numbers to the left of zero
are negative while those to the right are positive. Zero, a
number discovered in ancient India, is neither positive nor
negative.
Negative numbers are used extensively in Vedic Mathematics.
You will notice that in the above diagram, the negative sign is
placed above the digit rather than to its left as in conventional
math e.g. -3 has been written as 3̅̅. Similarly, –9 will be written
9̅̅, -32 as 3̅̅2̅, –10 as either 1̅0̅ or 1̅0 (since 0̅ = 0).
Number tables
There are two kinds of number tables that are essential for
mathematics – addition & subtraction tables and multiplication
& division tables. Today, schools generally advocate addition
tables till 10 + 10, and multiplication tables until 12 x 12. For
Vedic Math, you only need to know the tables up to 5 x 5.
Tables of higher numbers are not required. However,
knowledge of tables till 20 x 20 and 16 x 16 will be useful.
Answers in parts
Answers are normally obtained in parts, namely, the left hand
side (LHS), middle (mid) and the right hand side (RHS). Each
of these are obtained using different methods. For example,
998 x 992 = 990 / 016
Here the answer to the problem 998 x 992 has been obtained
mentally in two steps – one giving the left hand side of the
answer (990) and the second giving the right hand side (016).
The method used will be discussed in a later chapter.
Bases
There are two kinds of Bases – Standard Base and Special
Base. Examples of standard bases are 10, 100, 1000, 10000
and so on i.e. numbers start with a 1 and followed by zeroes.
Multiplication and division with these numbers are very simple
– the decimal point is shifted, either to the right or to the left
0 1 2 33̅ 2̅ 1̅
9. 8
respectively. Vedic math also uses Special bases. These can
be any number, such as 50, 500, 5000, 25, 250, 2500 and so
on. More on this later.
Place value
Place-value notation, or positional-notation is a way of
representing numbers. The value of a digit, depends on its
place or position in the number. Beginning with the ones place
at the right, each place value is multiplied by increasing
powers of 10. Place value for the number 24.759 is shown
below
To the left of the decimal point, digits to the right have smaller
place value than those to the left by a factor of 10. However,
to the right of the decimal point, digits to the left have higher
place value than those to the right.
Columns
We will use the terms “Place value” and “Columns”
interchangeably. For instance, while adding the numbers, we
will refer to columns.
Direction
In conventional math, most arithmetic operations are
performed Right to Left, i.e. starting with the Units column,
and moving leftward to the Tens column, Hundreds column
and so on. For instance, while adding 2 numbers, the Units
column are added first, then the tens and so on. While
subtracting numbers, again the units column is subtracted
first, then the tens. Direction of operation is Right to Left.
In Vedic Math, arithmetical operations are performed Left to
Right. In so doing, digits with a higher Place Value are
processed first, and rightfully so, as they have a larger value.
2 4 . 7 5 9
4 5 7
9 8 6
+ 3 4 5
Units column
Tens columnHundreds column
Tens Units Decimal Tenths Hundredths Thousandths
10. 9
Carryover
Unlike conventional math, carryover in Vedic Math can be
made either to the left or to the right. When a digit is to be
carried over, it is written in small case. For instance, in the
following number, the ‘2’ is a carry-over which is added to the
5.
5 2 4 6 = 7 4 6
12. 11
Conventional method
Before we study the Vedic Math techniques of addition, let us
review the method most commonly used today. Add the
following numbers:
It is likely that you started the addition from the Units column.
The main elements in this method of addition are:
1. Addition starts with the rightmost column, usually the Units
column, unless there are decimals.
2. The carry over is added on top of the column to the left.
3. All the columns are added, and the answer is given from the
left.
Although the conventional method can be applied to all cases
of addition, it is not an efficient method.
1. Addition starts with the column of least importance i.e. the
Units column, and in cases with decimal figures, addition
starts with the decimal digits which have even lower place
value. In day-to-day situations, it is far more important to sum
the columns with the higher place value i.e. the hundreds
column, or the thousands column rather than the units
column.
2. Addition moves from the rightmost column to the left,
however the final answer is given starting with the leftmost
digit. This becomes a problem if a paper and pen are not
available, since you will need to remember the digits in
reverse order while giving the answer. This makes mental
addition cumbersome.
In the following chapters, you will learn the vedic techniques of
addition that will overcome the problems that arise with
conventional addition. With practice, you will perfect these new
techniques.
3
1
8
1
9
4 2 5
+ 6 7 0
1 4 8 4
Carryovers
Addition begins
with the units
column
3 8 9
4 2 5
+ 6 7 0
14. 13
Column-less addition
Add the following numbers in the method that you are familiar
with.
It is likely that you started adding from the Units column
(7+6+5), and then moved to the Tens column (5+8+9).
Sometimes, having to start from the units column may not be a
such a great idea. There may be cases where you need to start
from the Leftmost column (since that column has the highest
place value). In the following chapter, you will learn a method of
adding numbers from the Leftmost column. For now, let us see
if it is possible to add numbers starting from any column.
Example 1
Watch the screencast below to see the column-less method of
adding these numbers. This can also be viewed at http://
youtu.be/JmZQdFCLqvQ
Screencast 2.1 Column-less addition
4 5 7
9 8 6
+ 3 9 5
15. 14
Step 1: Numbers are added column by column, starting with
the column of your choice. Lets add numbers in Column 2, then
Column 1 and lastly Column 3.
Adding digits in Column 2, 5+8+9 gives 22, written as a ‘small
2’ and a ‘big 2’.
Adding digits in Column 1, 4+9+3 gives 16, written as a ‘small
1’ and a ‘big 6’.
Adding digits in Column 3, 7+6+5 gives 18, written as a ‘small
1’ and a ‘big 8’.
Step 2: All the small digits are carried over to the previous
column, 1 is carried over to the 2 giving 3, 2 and 6 give 8, and
the 1 is carried over 0 to give 1. The answer is 1838.
Example 2
In some cases, there will be multiple carryovers. Try adding the
following numbers using the column-less method.
You will see that you will need to carryover twice to arrive at the
final answer.
Column1 Column2 Column3
Step 1
Step 2
4 5 7
9 8 6
+ 3 9 5
16 2 2 18
1 8 3 8 2 6 7
7 7 8
+ 5 5 9
16. 15
Watch the screencast below to see the solution. This can also
be viewed at http://youtu.be/BvyKC3SEfog
Step 1: Numbers are added column by column, starting with
the column of your choice.
Adding digits in Column 2, 6+7+5 gives 18, written as a ‘small
1’ and a ‘big 8’. Adding digits in Column 1, 2+7+5 gives 14,
written as a ‘small 1’ and a ‘big 4’. Adding digits in Column 3,
7+8+9 gives 24, written as a ‘small 2’ and a ‘big 4’.
Step 2: All the small digits are carried over to the previous
column, 2 is carried over to the 8 giving 10. This is written as a
‘small 1’ and a ‘big 0’. The existing ‘1’ to the left of the 8 is
carried over to the Hundreds column giving 5, and the ‘1’ with
the ‘4’ is carried over to the Thousands column, 0+1 giving 1.
Step 3: The ‘small 1’ is carried over the 5, giving 6. The final
answer is 1606.
Screencast 2.2 Double carry-over Step 1
Column1 Column3Column2
Step 2
2 6 7
7 7 8
+ 5 5 9
1 4 18 2 4
1 5 10 4
1 6 0 4Step 3
18. 17
Two-Digit Method
In this chapter, you will learn a method of adding numbers
quickly and efficiently. You will see that numbers don’t have to
be added from the right to the left only, which is most likely what
you are accustomed to. Lets review two points from before.
Place value
Place-value notation, or positional-notation is a way of
representing numbers. The value of a digit, depends on its
place or position in the number. Beginning with the ones place
at the right, each place value is multiplied by increasing
powers of 10.
To the left of the decimal point, digits to the right have smaller
place value than those to the left by a factor of 10. However,
to the right of the decimal point, digits to the left have higher
place value than those to the right.
Direction
In conventional math, most arithmetic operations are
performed Right to Left, i.e. starting with the Units column,
and moving leftward to the Tens column, Hundreds column
and so on. For instance, while adding numbers, the Units
column are added first, then the Tens column, then the
Hundreds. While subtracting numbers, again the Units column
is subtracted first, then the Tens. Direction of operation is
Right to Left.
In Vedic Math, arithmetical operations are performed Left to
Right. Digits with a higher Place Value are processed first, and
rightfully so, as they have a larger value.
Let us examine this more closely with Addition. Add these two
sets of numbers.
It is likely that you added the above numbers from the Right to
the Left, i.e. starting with the Units column in both cases. Now
see if you can find a way to add these numbers from the Left to
the Right. i.e. start adding from the Hundreds column in both
cases!
2 5 6
+ 8 9 4
6 3 8
+ 1 9 4
19. 18
Example 1
In the following example, we add 769 and 583, from the Left to
Right i.e. we start with the Hundreds column, or the leftmost
column, and move column by column, to the right.
Watch the screencast below for an explanation. This can also
be viewed at http://youtu.be/qSd_glxGfDo
The process is broken down into 6 steps, shown in roman
numerals.
Step i: Start by adding the Hundreds column, 7+5 to get 12.
This is written as a 1 in the preceding column (thousands
column), and the 2 is carried over to the subsequent column
(tens column).
Step ii: The 2 and the 6 in the tens column are combined as
“26”. Add 26 and 8 to get 34.
Step iii: 34 written as a 3 in the preceding column (the
Hundreds column), and the 4 is carried over to the subsequent
column (Units column).
Step iv: The 4 and 9 are combined as 49. Add 49 and 3 to get
52
7 2
6 4
9
+ 5 8 3
1 3 5 2
Step i Step iii Step v Step vi
Step ii Step iv
Screencast 3.1 Adding 769 and 583
20. 19
Step v: 52 is written as 5 in the previous column (tens column),
and the 2 is carried over to the subsequent column.
Step vi: Since there is no column to the right of the units
column, the 2 from the 52 is written in the units column.
Read the above steps again carefully, and apply this method to
add the following 325 and 948. The steps are explained in the
next page, but spend a few minutes trying to figure this out
yourself, before continuing.
Hint: start writing your answer one column ahead.
Example 2
Were you able to add 325 and 948 from Left to Right? These
numbers are again added Left to Right i.e. we start with the
leftmost column, and move to the right. Watch the screencast
below for an explanation. This is also available at http://
youtu.be/3mNpth3NwQ0
3 2 5
+ 9 4 8
Screencast 3.2 Adding 325 and 948
21. 20
Here is the solution for this exercise:
Step i: Start by adding the hundreds column, 3+9 to get 12.
This is written as a 1 in the preceding column (Thousands
column), and the 2 is carried over to the subsequent column
(Tens column).
Step ii: The 2 that was carried over, and the 2 in the tens
column are combined as “22”. Add 22 and 4 to get 26.
Step iii: 26 written as a 2 in the preceding column (the
Hundreds column), and the 6 is carried over to the subsequent
column (Units column).
Step iv: The 6 and 5 are combined as 65. Add 65 and 8 to get
73
Step v: 73 is written as 7 in the previous column (Tens column),
and the 3 is carried over to the subsequent column.
Step vi: Since there is no column to the right of the units
column, the 3 is written in the units column.
Example 3
Try adding 4658 and 7589 using this method on your own now.
Make sure you add Left to Right.
The solution is explained in the next page, however, try to figure
this out before seeing the solution.
Step i Step iii Step v Step vi
Step ii Step iv
3 2
2 6
5
+ 9 4 8
1 2 7 3
4 6 5 8
+ 7 5 8 9
22. 21
Watch the screenshot below for the solution. This is also
available at http://youtu.be/GyRFgxb-gy8
Step i and ii: Start by adding the leftmost column, 4+7 to get
11. This is written as a 1 in the previous column, and 1 is
carried over to the subsequent column (Tens column).
Step iii: The 1 that was carried over, and the 6 in the tens
column are combined to get “16”. 16 and 5 are added to get 21.
Step iv: 21 written as a 2 in the preceding column, and the 1 is
carried over to the subsequent column.
Step v: The 1 and 5 are combined as 15. 15 and 8 are added
to get 23
Step vi: 23 is written as 2 in the previous column, and the 3 is
carried over to the subsequent column.
Step vii, viii, ix: 38 and 9 are added to get 47 the last two digits
in the answer.
Step ii Step iv Step vi Step viii
Step iii Step vStep i Step vii
Step ix
4 1
6 1
5 3
8
+ 7 5 8 9
1 2 2 4 7Screencast 3.3 Adding 4658 and 7589
23. 22
Exercises in Two-Digit Addition
Try the following exercises, starting from the leftmost column,
and move to the right. Answers are provided in Chapter 6.
Attempt the following mentally, i.e. keep the carryovers in your
mind, and write down only the digits of the final answer.
5 1 4 3
+ 2 6 2 9
4 3 5 8
+ 7 2 0 9
7 6 5 8
+ 1 2 7 9
3 0 2
5 7 3
4 2 6
+ 2 5 8
Click for solution
7 5 6
1 2 2
9 2 3
+ 4 0
Click for solution
Click for solution
Click for solution
3 0 9 2
+ 7 1 7 4
Click for solution
Click for solution
6 8 0 2
+ 5 4 1 6
Click for solution
9 3 2
+ 4 8 7 6
1245 + 3529 =
4427 + 1903 =
12.54 + 23.56 =
45.95 + 45.95 =
8.695 + 3.795 =
Click for solution
Click for solution
Click for solution
Click for solution
Click for solution
34.50 + 88.50 = Click for solution
Click for solution
24. 23
Why is this called the Two-digit Method?
You may have wondered why this technique is called the “Two-
Digit method” of addition. It is so called because any column
that is added, must yield 2, and only 2 digits. For example, in
the following, the hundreds column sums to 3, but should be
written as ‘03’, with the ‘0’ in the thousands place, and the ‘3’
carried over to the tens column. Again while adding the Units
column, 02+7 gives 9, but must be written as ‘09’. The answer
will be incorrect otherwise.
What would happen if the sum of any column results in 3 digits?
This will result in a Reverse carryover.
Example 1
Try the following for instance, using the Two-Digit method of
addition.
You will have three digits when you sum Column 2, but in the 2-
digit method, you must have two, and only two digits as you
sum each Column.
The final answer in this case is 1035. How would you handle
the three digits of Column 2 to arrive at this answer?
2 3
6 0
2
+ 1 4 7
0 4 0 9
2 5 7
3 4 2
+ 4 3 6
25. 24
Watch the screenshot below for an explanation, and solution of
this issue. This is also available at http://youtu.be/gREz1ilAMcY
The following explains this in detail.
Step 1: Adding digits in Column 1, we get 9, a single digit.
Hence, a zero is inserted in front of the 9, making it a ‘09’. ‘0’ is
written in the preceding column, and the ‘9’ is carried over to
the Tens column.
Adding digits in Column 2, we get 95+4+3=102, three digits,
written as a ‘small 1’ and ‘big 0’ in the Hundreds column, and ‘2’
is carried over to the Units column.
Adding digits in Column 3, 27+2+6 gives 35, written as 3 in the
tens column and 5 in the Units column.
Step 2: The ‘small 1’ in the Hundreds column needs to be
carried over to the Thousands column. 0+1=1, giving the final
answer as 1035. This is the Reverse Carryover since it moves
Screencast 3.4 Reverse Carryover
2 9
5 2
7
3 4 2
+ 4 3 6
0 10 3 5
1 0 3 5
26. 25
from the right to the left, i.e. in the reverse direction as
compared to the other carryovers (the ‘9’ was carried over from
the left to the right, and so was the ‘2’).
Example 2
Try another example involving Reverse Carryover.
Try solving this on your own, before viewing the screenshot
given in the next page. Here’s a hint: the Reverse Carryover in
the above example arises due to the Units column.
The final answer in this case is 1035. How would you handle
the three digits of Column 2 to arrive at this answer?
Watch the screenshot below for an explanation, and solution of
this issue. This is also available at http://youtu.be/
1pIpNeYS8Q0
1 6 6 2
4 3 5 8
+ 3 7 8 6
Screencast 3.5 Reverse carryover
27. 26
Step 1: Adding digits in Column 1, we get 8, a single digit.
Hence, a zero is inserted in front of the 8, making it a ’08’. ‘0’ is
written in the preceding column, and the ‘8’ is carried over to
the Hundreds column.
Adding digits in Column 2, we get 86+3+7=96, ‘9’ is written in
the preceding column, and the ‘6’ is carried over to the Tens
column.
Adding digits in Column 3, 66+5+8 gives 79, written as 7 in the
Hundreds column and 9 is carried over to the Units column.
Adding digits in Column 4, 92+8+6 gives 106. This is three
digits, and is written as a ‘small 1’ and ‘big 0’ in the Tens
column, and 6 in the Units column.
Step 2: The ‘small 1’ in the Tens column needs to be carried
over to the Hundreds column. 7+1=8, giving the final answer as
9806. This is the Reverse Carryover since the 1 is carried over
from the right to the left, i.e. in the reverse direction as
compared to the other carryovers (the ‘8’ was carried over from
the left to the right, and so were the ‘6’ and ‘9’).
Although this still works, the Reverse Carryover prevents us
from arriving at the final answer mentally, and hence, a paper
and pen become necessary.
The alternative is to use the Three-Digit method of addition.
How would that work? What would be the steps? Try the
following, and formulate a Three-Digit method of addition. The
goal is to sum these numbers mentally, and avoid the Reverse
Carryover.
1 8
6 6
6 9
2
4 3 5 8
+ 3 7 8 6
0 9 7 10 6
0 9 8 0 6
Step 1
Step 2
2 0 2
3 3 4
+ 5 6 7
29. 28
Three-Digit method
The Three-Digit method of addition is a variation of the Two-
Digit method. In some cases, the Two-Digit method leads to a
Reverse Carryover in the final step, which can be avoided using
this method.
Example 1
Let us revisit the question from the previous chapter. Were you
able to formulate the Three-Digit method for summing the
numbers below? The answer in this case is 1103. How can we
add these numbers, from left to right (starting with the
Hundreds column), and arrive at the answer mentally?
Watch the screencast below for an explanation of the Three-
Digit method. This can also be viewed at http://youtu.be/
9EdIMGNAJqc
Screencast 4.1 Three-Digit method
2 0 2
3 3 4
+ 5 6 7
30. 29
Here are the detailed steps for the Three-Digit method
Step i: Adding digits in Column 1, 2+3+5 gives ‘10’, a two digit
number. In this method, the sum of each column must be
written as 3 digits. Hence, a zero is inserted in front of the ‘10’,
making it a ‘010’.
Step ii: The ‘0’ from the ‘010’ is written in the column before the
preceding column (Hundred-thousands column), and the ’10’ is
carried over the existing ‘0’ in the Tens column, now read as
‘100’.
Step iii and iv: Adding digits in Column 2, we get
100+3+6=109, ‘1’ is written in the column before the preceding
column (the Thousands column), and the ’09’ is carried over to
the Units column.
Step v: Adding digits in Column 3, 92+4+7 gives 103, written
as ‘1’ in the Hundreds column, ‘0’ in the Tens column and ‘3’ in
the Units column, giving 1103 as the final answer.
Did you notice how the Three-Digit method helped us avoid the
Reverse Carryover? We were able to solve the addition moving
only from the left to the right.
Here is another example.
Example 2
Sum the following numbers using the Three-Digit method. The
answers are given in the next page, but try to solve this on your
own before continuing.
Hint: start writing your answer two columns ahead.
2 10
0 09
2
3 3 4
+ 5 6 7
0 1 1 0 3
Step i Step iii Step v
Step iv Step viStep ii
4 2 5 9
+ 8 7 9 3
31. 30
Watch the screencast below for the solution. This can also be
viewed at http://youtu.be/N_qd2Z4kZ6o
Here is the detailed solution.
Step i: Adding digits in Column 1, 4+8 gives ’12’, a two digit
number. In this method, the sum of each column must be
written as 3 digits. Hence, a zero is inserted in front of the ’12’,
making it a ‘012’.
Step ii and iii: The ‘0’ from the ‘012’ is written in the column
before the preceding column, and the ’12’ is carried over to the
Hundreds column, next to the the existing ‘2, making it ‘122’.
Step iii, iv and v: Adding digits in Column 2, we get 122+7
giving 129. ‘1’ is written in the column before the preceding
column, and the ‘29’ is carried over to the Tens column next to
the ‘5’.
Screencast 4.2 Three-Digit method
4 12
2 29
5 04
9
+ 8 7 9 3
0 1 3 0 5 2
Step iii Step vStep i
Step iv
Step vi
Step viiStep vStep ii
32. 31
Step v and vi: Adding digits in Column 3, 295+9 gives ‘304’,
written as ‘3’ in the Thousands column, and ’04’ is carried over
to the Units column.
Step vi and vii: Adding digits in the Units column, 49+3 gives
‘52’. This is a two digit number, but we are using the Three-Digit
method. Hence, a ‘0’ is inserted in front of the number, making
it ‘052’, written along the Hundreds, Tens and Units column.
The answer is 13052.
Now try both these examples with the Two-Digit method, and
see which method may be more efficient with practice.
Exercises in Three-Digit Addition
Try the following exercises using the Three-Digit method. Start
from the leftmost column, and move to the right. Write the sum
of each column as three digits by inserting a ‘0’ in case the sum
is two digits, and inserting two ‘0’s if it is a single digit. Answers
are provided in Chapter 6.
3 6 7
+ 4 3 7
Click for solution
1 4 5
+ 8 7 4
Click for solution
3 4 2 5
+ 8 2 7 8
Click for solution
1 3 0 4
+ 3 9 8
Click for solution
2 3 9
7 8 5
+ 2 3
Click for solution
2 5 7
1 2 8
+ 3 2 3
Click for solution
33. 32
Common errors
Here is a list of some common errors that we make while using
the Vedic Math methods. Check if any of these apply to you.
Are there any other kinds of errors that you seem to make
often? Share your comments.
Concluding remarks on the Three-Digit method
One question that is likely to arise is, how does one decide
when to use the Three-Digit method over the Two-Digit
method? The Two-Digit method is surely easier, as there are
fewer digits to work with, but it may result in a Reverse
Carryover in some cases. Can we know in advance whether a
sum will give a Reverse Carryover? If so, then we can use the
Three-Digit method from the start, rather than having to switch
from the Two-Digit to the Three-Digit method mid way.
The answer is ‘yes’, there is a way to determine if a sum will
result in a Reverse Carryover by examining the numbers to be
added. But try to figure this out yourself, and mail me your
answer. A hint: Read up on “Digital Roots” presented in the
Book on Vedic Subtraction.
Writing the sum of a column as a single digit in the Two-!
Digit method, or as two digits in the Three-Digit method.
Make sure that the sum of every column is written as 2 digits
in the Two-Digit method, and as 3 digits in the Three-Digit
method.
Starting the answer in the same column as the column which
is summed. This will give errors. The answer must be written
in the preceding column in the Two-Digit method, or the
column before the preceding column in the Three-Digit
method.
Making an error while summing a column. At times we sum 2
and 3 as 6. Check your calculations and search where you
may have gone wrong.
Mistaking the Column-less methods with the Two-Digit or
Three-Digit methods. Unlike the conventional system, where
there is only one method to remember, Vedic Math provides
several methods for each arithmetic operation. We must
understand each method clearly, and apply accordingly.
X
X
X
X
Summing digits across different columns, rather than across
a single column. This usually happens when the numbers
are not written in an organized manner, most common in real
world situations.
X
34. 33
Another question that is likely to arise is, how to choose among
the different Vedic Math techniques when faced with a problem.
You have learnt three methods of adding numbers - the
Column-less method, the Two-Digit method and the Three-Digit
method. Should you choose any of these methods for a
particular sum, or stick with the Conventional method? Or
chuck them all and pull out the calculator?
You will find the answer to this question yourself, when you
have given the Vedic Math techniques a fair share of practice,
and attention.
Attempt some real world problems using these methods in the
following chapter.
36. 35
Real world problems
One of the aims of this book is to make math easy to apply in
day-to-day situations when a calculator, or a paper and pen are
not available. This could be in the grocery store, or while paying
the bill in the restaurant, or while collecting change from the
pizza delivary guy. For the Vedic Math techniques to become
second nature, practice is necessary.
Answer the following real-world questions, using the techniques
you have learnt in the previous chapters. You will soon see, that
you don’t need to perform the entire addition, and from the
Units column as well, in most cases. Answers are provided in
Chapter 6.
Irresponsible clerk
John visited the medical diagnostic centre, and had a few x-
rays taken. While clearing the bill, the receptionist’s computer
crashed and she had the clerk make the bill manually. John has
a feeling the clerk has made an error while summing the
figures. Check to see if John is right!
Click for solution
37. 36
The Woodchucks
The Woodchucks may have won the 2014 wood chucking
competition. The Iron Ladies chucked 1500 kg, a record in
itself. The data entered by the referees is given below. Did the
Woodchucks win?
Concluding remarks
You have now completed learning Addition in Vedic Math. You
learnt the Column-less method which can be used to sum any
column independently of the other columns, as well as the Two-
Digit and Three-Digit methods with which you can sum
numbers from Left to Right.
All of these methods can be explained using Algebra. In fact
Algebra is the foundation on which Vedic Math can be built. If
you are familiar with Algebra, try proving the Vedic Math
techniques using Algebra.
Use these methods in your day to day situations, and you will
improve with practice. You will find that the other books in this
series, viz. Vedic Subtraction, Vedic Multiplication and Vedic
Division will assist you in doing other mental calculations in real
world situations.
Click for solution
41. 40
Answers to exercises in Chapter 4
Here are solutions to the exercises on Real World problems
Irresponsible clerk
The clerk has indeed made an error. Add the balance column
starting from the left. 2+2 gives 04, with the ‘4’ carried over to
the tens column. In the Tens column we see there is a 4 and 8,
which is greater than 10. Hence, the Hundreds digit now
becomes 5. However, the clerk has mentioned the Total
Balance as 443, which is a mistake.
The Woodchucks
Summing the Hundreds column, we get 14. The ‘4’ is carried
over tot he Tens column. Summing the Tens column, we get
42+7+4+1 which exceeds 50. Hence, it is clear the
Woodchucks have won!
43. xlii
References
Glover, J., T. (2002) “Vedic Mathematics For Schools, Book 1”,
Motilal Banarsidass Publishers Pvt. Ltd., New Delhi.
Glover, J., T. (2003) “Vedic Mathematics For Schools, Book 2”,
Motilal Banarsidass Publishers Pvt. Ltd., New Delhi.
Glover, J., T. (2003) “Vedic Mathematics For Schools, Book 3”,
Motilal Banarsidass Publishers Pvt. Ltd., New Delhi. 14
Gupta, A. (2006) “The Power of Vedic Maths – For Admission
Test, Professional & Competitive Examinations”, Jaico
Publishing House, India.
Jagadguru Swami Bharathi Krishna Thirthaji Maharaja (1992)
“Vedic Mathematics”, Motilal Banarsidass Publishers Pvt. Ltd.,
New Delhi.