Abstract: In this paper, I show that exact area of circle = (π r2) = 17 - 8√3) r2. I found that the exact value of pi is = (17- 8√3).My findings are based on geometrical constructions, formula and proofs.
This pdf is free to download. This document is prepared by tutor Kundan sir from Vista's Learning.Keep learning CBSE Class 1 0 maths by signing up in Vista's Learning portal here
https://v-learning.in/live-course/1114/ncert-solutions-for-maths-chapter-2-polynomials-part-8-vistas-learning
Pre-calculus 1, 2 and Calculus I (exam notes)William Faber
Notes I typed using Microsoft Word for pre-calculus and calculus exams. Most of the images were also created by me. I shared them with other students in my class to increase their chance of success as well. Upon completion of the courses I donated them to the math center to help other math students.
This pdf is free to download. This document is prepared by tutor Kundan sir from Vista's Learning.Keep learning CBSE Class 1 0 maths by signing up in Vista's Learning portal here
https://v-learning.in/live-course/1114/ncert-solutions-for-maths-chapter-2-polynomials-part-8-vistas-learning
Pre-calculus 1, 2 and Calculus I (exam notes)William Faber
Notes I typed using Microsoft Word for pre-calculus and calculus exams. Most of the images were also created by me. I shared them with other students in my class to increase their chance of success as well. Upon completion of the courses I donated them to the math center to help other math students.
EXPRESSÕES NUMÉRICAS CONTENDO ADIÇÃO E SUBTRAÇÃO E AS DEMAIS OPERAÇÕES. https://accbarroso60.wordpress.com/2011/02/24/expressoes-numericas-com-adicao-e-subtracao/?blogsub=confirming#subscribe-blog
Abstract: In this paper we prove some extension of the Eneström-Kakeya theorem by relaxing the hypothesis of this result in several ways and obtain zero-free regions for polynomials with restricted coefficients and there by present some interesting generalizations and extensions of the Enestrom-Kakeya Theorem.
Integrating Traditional and Social Media WebinarCapstrat
TV. Digital. Radio. Social. All great media channels, and opportunities, to reach audiences. But how do they fit together? Join Jay Dolan, Senior Social Media Strategist, and Maria Walker, Media Supervisor, as they share 10 tips for integration.
Making visible the invisible. Metrical patterns, contrafacture and compilatio...Gimena Del Rio Riande
1. “Making visible the invisible. Metrical patterns, contrafacture and compilation in a Medieval Castilian Songbook”, en el Panel New Developments on Quantitative Metrics, DH2015, Global Digital Humanities, University of Western Sydney, del 29 de junio al 3 de julio de 2015 (con Elena González-Blanco).
Generalized Family of Efficient Estimators of Population Median Using Two-Pha...inventionjournals
ABSTRACT : For estimating the population median of variable under study, a generalized family of efficient
estimators has been proposed by using prior information of population parameters based upon auxiliary
variables under two-phase simple random sampling design. The comparison of proposed family of estimators
has been made with the existing ones with respect to their mean square errors and biases. It has been shown
that efficient estimators can be obtained from the family under the given practical situations which will have
smaller mean square error than the linear regression type estimator, Singh et al estimator (2006), Gupta et al
(2008) estimator and Jhajj et al estimator (2014). Effort has been made to illustrate the results numerically as
well as graphically by taking some empirical populations considered in the literature which also show that bias
of efficient estimators obtained from the proposed family of estimators is smaller than other considered
estimators.
EXPRESSÕES NUMÉRICAS CONTENDO ADIÇÃO E SUBTRAÇÃO E AS DEMAIS OPERAÇÕES. https://accbarroso60.wordpress.com/2011/02/24/expressoes-numericas-com-adicao-e-subtracao/?blogsub=confirming#subscribe-blog
Abstract: In this paper we prove some extension of the Eneström-Kakeya theorem by relaxing the hypothesis of this result in several ways and obtain zero-free regions for polynomials with restricted coefficients and there by present some interesting generalizations and extensions of the Enestrom-Kakeya Theorem.
Integrating Traditional and Social Media WebinarCapstrat
TV. Digital. Radio. Social. All great media channels, and opportunities, to reach audiences. But how do they fit together? Join Jay Dolan, Senior Social Media Strategist, and Maria Walker, Media Supervisor, as they share 10 tips for integration.
Making visible the invisible. Metrical patterns, contrafacture and compilatio...Gimena Del Rio Riande
1. “Making visible the invisible. Metrical patterns, contrafacture and compilation in a Medieval Castilian Songbook”, en el Panel New Developments on Quantitative Metrics, DH2015, Global Digital Humanities, University of Western Sydney, del 29 de junio al 3 de julio de 2015 (con Elena González-Blanco).
Generalized Family of Efficient Estimators of Population Median Using Two-Pha...inventionjournals
ABSTRACT : For estimating the population median of variable under study, a generalized family of efficient
estimators has been proposed by using prior information of population parameters based upon auxiliary
variables under two-phase simple random sampling design. The comparison of proposed family of estimators
has been made with the existing ones with respect to their mean square errors and biases. It has been shown
that efficient estimators can be obtained from the family under the given practical situations which will have
smaller mean square error than the linear regression type estimator, Singh et al estimator (2006), Gupta et al
(2008) estimator and Jhajj et al estimator (2014). Effort has been made to illustrate the results numerically as
well as graphically by taking some empirical populations considered in the literature which also show that bias
of efficient estimators obtained from the proposed family of estimators is smaller than other considered
estimators.
Salah satu materi perkuliahan prodi pendidikan matematika mata kuliah teori himpunan dan logika matematika - Diagram Venn, Contoh Soal mengenai Diagram Venn
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
1. International Journal Of Mathematics And Statistics Invention (IJMSI)
E-ISSN: 2321 – 4767 P-ISSN: 2321 - 4759
www.Ijmsi.org || Volume 3 Issue 2 || February. 2015 || PP-35-38
www.ijmsi.org 35 | P a g e
Exact value of pi π = (17- 8√3)
Mr. Laxman S. Gogawale
Fulora co-operative society, Dhankawadi, Pune-411043 (India)
Abstract: In this paper, I show that exact area of circle = (π r2
) = 17 - 8√3) r2
. I found that the exact value of
pi is = (17- 8√3).My findings are based on geometrical constructions, formula and proofs.
I. INTRODUCTION
Is it possible or impossible?
100% exact value of pi, 100% exact area of circle, area of circle = area of square
Yes, it is Possible!
We know that, where C /D = A/R2
= approximate value of pi = 3.1415926535897…which is endless value.
C = circumference of circle, D = diameter of circle, A = area of circle, R = radius of circle,
If we calculate C / D we cannot measure end point of circumference. So it will give approximate results.
I started research to find exact area of circle using A /R2
method.
There are different proofs to find the old value of pi but no one get 100% exact answer.
Like using number series, Trigonometry, Dividing circle into infinite parts, as practically we can’t measure
endpoint etc. In order to find 100% exact area of circle I found the new method.
I have made number of proofs but here I am giving simple proof out of it.
Reason why I am 100% sure about my research is that I estimated pi value by number of different
algebraic methods. Why should we discuss pi is transcendental or algebraic? This is not important. But we are
more concentrated on calculating 100% exact answer which is most important.
New methods are also discovered .i.e. algebraic table method. By all the methods the answer remains same.
Basic Figure
Modified figure (1 & 2)
2. Exact value of pi π = (17- 8√3)
www.ijmsi.org 36 | P a g e
Fig. 1
fig. 2
From fig. 1 & 2
Note: let a, b, c & d each part shows area
Area of square = (12a + 12b + 12c + 4d) = (16a + 16b) = 4r2
(12a + 12b + 12c + 4d) – (16a + 16b) = 0
= (- 4a - 4b + 12c + 4d) = 0
i.e. (4a + 4b = 12c + 4d) (a + b) = (3c+d) equation no. 1
From fig. no. 2
16a = [2r × 2(√3/2) r] = (2√3) r2
a = (2√3) r2
/16 = (0.125√3) r2
16b = [2r – 2(√3/2) r] × 2r = (4 - 2√3) r2
b = (4 - 2√3) r2
/ 16 = (0.25 – 0.125√3) r2
Problems faced during the research of pi that:
How to estimate the exact values of part c & part d?
I found number of equations for calculating area of square = 4r2
.Few of them is mentioned in the following
table. On the basis of these equations I estimated the exact area of circle in following manner.
Area of inscribed dodecagon (12a + 12b) = 3r2
area of square = (12a + 12b + 12c + 4d) = 4r2
= area of circle – 12c = area of circle + 4d
I have geometric proofs for all of the following equations
S. r. no. Equations of area of square = 4r2
Equations total = … 4r2
1 12a + 12b + 12c + 4d =4r2
12a + 12b + 12c + 4d = 4r2
2 64b + 12c + 8d =4r2
12a + 76b + 24c + 12d = 2(4r2
)
3 4a + 100b – 18c = 4r2
16a + 176b + 6c + 12d = 3(4r2
)
4 -8a + 120b + 8d = 4r2
8a + 296b + 6c + 20d = 4(4r2
)
5 32a – 96b + 24c =4r2
40a + 200b + 30c + 20d = 5(4r2
)
6 20a – 12b + 6c = 4r2
60a + 188b + 36c + 20d = 6(4r2
)
7 96b – 6c + 4d = 4r2
60a + 284b + 30c + 24d = 7(4r2
)
3. Exact value of pi π = (17- 8√3)
www.ijmsi.org 37 | P a g e
8 48a – 208b + 48c = 4r2
108a + 76b + 78c + 24d = 8(4r2
)
9 24a – 40b + 12c = 4r2
132a + 36b + 90c + 24d = 9(4r2
)
10 128b – 24c = 4r2
132a + 164b + 66c + 24d = 10(4r2
)
11 -20a + 172b + 12d = 4r2
112a + 336b + 66c + 36d = 11(4r2
)
12 12a + 44b – 6c = 4r2
124a + 380b + 60c + 36d = 12(4r2
)
13 28a – 68b + 18c = 4r2
152a + 312b + 78c + 36d = 13(4r2
)
14 8a + 72b – 12c = 4r2
160a + 384b + 66c + 36d = 14(4r2
)
15 4a + 68b + 4d = 4r2
164a + 452b + 66c + 40d = 15(4r2
)
16 60a – 292b + 66c = 4r2
224a + 160b + 132c + 40d = 16(4r2
)
17 104a – 600b + 132c = 4r2
328a – 440b + 264c + 40d = 17(4r2
)
18 18a + 2b + 3c = 4r2
346a – 438b + 267c + 40d = 18(4r2
)
19 36a – 124b + 30c = 4r2
382a – 562b + 297c + 40d = 19(4r2
)
20 48c + 16d = 4r2
382a – 562b + 345c + 56d = 20(4r2
)
Total area of 20 square = 382a – 562b + 345c +56d = 20(4r2
)
In the following proof I used area of inscribed dodecagon.
How I am getting the values of c & d for that see the following examples
Area of square = (12a + 12b + 12c + 4d) main equation
(Area of 15 square – area of 10 square) = (164a + 452b + 66c + 40d) – 10(12a + 12b + 12c + 4d)
= area of 5 square = (164a + 452b + 66c + 40d) – (120a + 120b + 120c + 40d)
= 44a + 332b – 54c
= 44a + 332b + area of 4.5 inscribed dodecagon – area of 4.5 circle
= 44a + 332b + 4.5(3r2
) – area of 4.5 circle
Area of 5 square + area of 4.5 circle = 44a + 332b + 4.5(3r2
)
Area of 4.5 circle = 44(0.125√3) r2
+ 332(0.25 – 0.125√3) r2
+ 13.5r2
- area of 5 square
= (5.5√3) r2
+ (83 – 41.5√3) r2
+ 13.5r2
– 5(4r2
)
= (96.5 – 36√3) r2
– 20r2
= (76.5 – 36√3) r2
Area of circle = (76.5 – 36√3) r2
/4.5
= (17- 8√3) r2
One more example
(Area of 12 square – area of 9 square) = (124a + 380b + 60c + 36d) - 9(12a + 12b + 12c + 4d)
= area of 3 square = (124a + 380b + 60c + 36d) – (108a + 108b + 108c + 36d)
= (16a + 272b – 48c)
= 16a + 272b + area of 4 inscribed dodecagon – area of 4 circle
= 16a + 272b + 4(3r2
) – area of 4 circle
Area of 3 square + area of 4 circle = 16a + 272b + 4(3r2
)
Area of 4 circle = 16(0.125√3) r2
+ 272(0.25 – 0.125√3) r2
+ 12r2
- area of 3 square
= (2√3) r2
- (68 - 34√3) r2
+ 12r2
– 3(4r2
)
= (80 – 32√3) r2
– 12r2
= (68 – 32√3) r2
Area of circle = (68 – 32√3) r2
/4
= (17- 8√3) r2
Found the value of 3c & d
Area of square = 4r2
Area of circle = (17 - 8√3) r2
(Area of square – area of circle) = 4d)
= 4r2
– (17 - 8√3) r2
= (8√3 – 13) r2
d = (2√3 – 3.25) r2
4. Exact value of pi π = (17- 8√3)
www.ijmsi.org 38 | P a g e
Area of square = 16a+16b = 4r2
(a + b) = (3c+d) = (4r2
/16) = o.25r2
(a + b) – d = 3c
= [0.25 – (2√3 – 3.25)] r2
= 3c = (3.5 -2√3) r2
a = (0.125√3) r2
b = (0.25 – 0.125√3) r2
3c = (3.5 - 2√3) r2
d = (2√3 – 3.25) r2
By using value of (a, b, c & d) in the above equations we get same answer = 4r2
& total …4r2
I have prepared all examples of this type but answer remains same.
Conclusions:-
Exact area of circle = (17 - 8√3) r2
Exact value of pi π = (17 - 8√3)
REFERENCES
Exact area of equilateral triangle formula = (√3 ÷ 4) × side2
Basic Algebra & Geometry concept, History of pi (π) from internet
Complete thesis of my research titled as ‘‘Exact value of pi ’’ is being published in following journals:
IOSR(international journal of scientific research) journal of mathematics in May-June 2012.
IJERA(international journal of Engineering research and applications) in July-August 2013.
Soft copy of my thesis is now also available on internet and one can get it by making search with following key
words:
“Laxman Gogawale.
“Pi value Gogawale.