Zero originated in India, where it was treated as a number by the 9th century AD. The Indian scholar Pingala used binary numbers around the 5th-2nd century BC. In 498 AD, Indian mathematician Aryabhatta developed the place value system. The oldest text to use zero in this way dates to 458 AD. Special glyphs for the digits, including zero, appeared in India in 876 AD. Operations involving zero, such as multiplication and division, can be complex and paradoxical. Zero was an important mathematical concept developed in ancient India.
Zero originated from Sanskrit and was introduced to mathematics by Indian mathematicians around AD 650. It was initially not considered a number but rather an empty space. Mathematicians like Aryabhata and Brahmagupta helped establish zero as a placeholder in mathematics. The concept of zero spread from India to other parts of the world through Islamic mathematicians and scholars. It took some time for zero to gain widespread acceptance as a number, but it is now recognized as having unique properties and playing a vital role in mathematics and science.
The document summarizes the history and development of the concept of zero. It discusses how zero was conceptualized and used in different ancient civilizations like the Maya, Babylonians, Indians, and Chinese. Key developments include the Maya using zero as a placeholder in their calendar system, the Babylonians using a placeholder in their place value system without treating it as a number, Indians developing the concept of zero as a number in the 9th century, and Chinese using empty space in counting rods to represent zero. The document also outlines the importance of zero in developing the place value number system and its role in mathematics and measuring physical quantities.
The document discusses the history and importance of zero. It describes how zero emerged over thousands of years, starting with early cultures like the Egyptians, Greeks, Romans, and Babylonians making early uses of placeholders or empty values without a true numerical concept of zero. Zero was formally developed in India and spread through Arabic mathematicians. It was resisted in Europe but became widely used by the 1500s. Zero is now recognized as a crucial concept in mathematics and other fields as a placeholder, separator of positive and negative numbers, and allowing calculations and systems like computers.
0 represents the number and concept of nothing or empty. It is the additive identity element, meaning any number added to 0 equals the original number. 0 originated from Arabic and Indian languages, with India developing the concept of 0 as a number rather than just a placeholder. 0 plays a unique and important role in mathematics, physics, chemistry, and computer science as either the lowest possible value, an identity element for addition, or representing nothing/empty.
Nicely made Zero importance for class 9 feel free to take reference from it and link of the template is this https://poweredtemplate.com/02406/0/index.html
This document is a student project on the history and importance of zero in mathematics. It discusses that zero was invented in ancient India by the mathematician Aryabhatta in the 5th century AD. It originated separately in ancient Babylon and the Mayan civilization as well. The project acknowledges the help received from teachers. It explains key properties of zero like its role as a placeholder in place value systems. It outlines the rules developed by Brahmagupta and how zero was crucial for advancing mathematics and computation. Without zero, basic operations like addition and multiplication would be far more complex.
Zero originated in ancient India, Babylon, and the Mayan civilization. The concept of zero as a number was first attributed to India in the 9th century CE, where it was treated as any other number in calculations. The symbol and rules for using zero in arithmetic operations were further developed by Indian mathematicians like Aryabhata and Brahmagupta. Their work influenced Arabic mathematicians who helped spread the concept of zero to Europe. While other ancient cultures used placeholder symbols, it was in India that zero was first understood and used as a true number.
Zero originated in India, where it was treated as a number by the 9th century AD. The Indian scholar Pingala used binary numbers around the 5th-2nd century BC. In 498 AD, Indian mathematician Aryabhatta developed the place value system. The oldest text to use zero in this way dates to 458 AD. Special glyphs for the digits, including zero, appeared in India in 876 AD. Operations involving zero, such as multiplication and division, can be complex and paradoxical. Zero was an important mathematical concept developed in ancient India.
Zero originated from Sanskrit and was introduced to mathematics by Indian mathematicians around AD 650. It was initially not considered a number but rather an empty space. Mathematicians like Aryabhata and Brahmagupta helped establish zero as a placeholder in mathematics. The concept of zero spread from India to other parts of the world through Islamic mathematicians and scholars. It took some time for zero to gain widespread acceptance as a number, but it is now recognized as having unique properties and playing a vital role in mathematics and science.
The document summarizes the history and development of the concept of zero. It discusses how zero was conceptualized and used in different ancient civilizations like the Maya, Babylonians, Indians, and Chinese. Key developments include the Maya using zero as a placeholder in their calendar system, the Babylonians using a placeholder in their place value system without treating it as a number, Indians developing the concept of zero as a number in the 9th century, and Chinese using empty space in counting rods to represent zero. The document also outlines the importance of zero in developing the place value number system and its role in mathematics and measuring physical quantities.
The document discusses the history and importance of zero. It describes how zero emerged over thousands of years, starting with early cultures like the Egyptians, Greeks, Romans, and Babylonians making early uses of placeholders or empty values without a true numerical concept of zero. Zero was formally developed in India and spread through Arabic mathematicians. It was resisted in Europe but became widely used by the 1500s. Zero is now recognized as a crucial concept in mathematics and other fields as a placeholder, separator of positive and negative numbers, and allowing calculations and systems like computers.
0 represents the number and concept of nothing or empty. It is the additive identity element, meaning any number added to 0 equals the original number. 0 originated from Arabic and Indian languages, with India developing the concept of 0 as a number rather than just a placeholder. 0 plays a unique and important role in mathematics, physics, chemistry, and computer science as either the lowest possible value, an identity element for addition, or representing nothing/empty.
Nicely made Zero importance for class 9 feel free to take reference from it and link of the template is this https://poweredtemplate.com/02406/0/index.html
This document is a student project on the history and importance of zero in mathematics. It discusses that zero was invented in ancient India by the mathematician Aryabhatta in the 5th century AD. It originated separately in ancient Babylon and the Mayan civilization as well. The project acknowledges the help received from teachers. It explains key properties of zero like its role as a placeholder in place value systems. It outlines the rules developed by Brahmagupta and how zero was crucial for advancing mathematics and computation. Without zero, basic operations like addition and multiplication would be far more complex.
Zero originated in ancient India, Babylon, and the Mayan civilization. The concept of zero as a number was first attributed to India in the 9th century CE, where it was treated as any other number in calculations. The symbol and rules for using zero in arithmetic operations were further developed by Indian mathematicians like Aryabhata and Brahmagupta. Their work influenced Arabic mathematicians who helped spread the concept of zero to Europe. While other ancient cultures used placeholder symbols, it was in India that zero was first understood and used as a true number.
- Zero originated as a placeholder in ancient Babylonian and Indian mathematics to represent empty value positions in their place value number systems. The Babylonians used a space or punctuation mark while Indians used a word meaning empty or void.
- The concept of zero as an actual number was developed in India by the 9th century AD where it was fully integrated into their mathematical system. This decimal system with a symbol for zero reached Europe in the 11th century via Arabic mathematicians.
- Fibonacci was instrumental in introducing the Hindu-Arabic numeral system, including the concept of zero as a number, to European mathematics in the 13th century. This system became prevalent and replaced previous numeral systems across Europe.
This document provides a summary of the history and development of the concept of zero. It discusses how zero originated in ancient India, Babylon, and the Mayan civilization, with the Hindus and Arabics in India generally considered the first to use it as a number. It describes how Aryabhatta is credited with inventing the number zero and establishing it as part of a decimal system. The document also covers how zero spread to other languages and cultures, the rules and equations developed by Brahmagupta and Bhaskar regarding its mathematical properties, and how zero enabled the development of modern binary systems and computing.
The document discusses the history and evolution of different number systems used by humans over time, from ancient Babylonian and Egyptian numerals to modern Hindu-Arabic numerals. It explains key concepts like natural numbers, integers, rational numbers, irrational numbers, real numbers, imaginary numbers, and complex numbers. The concept of zero, which represents nothing, was an important development that allowed for more advanced mathematics. Number systems provide a consistent way to represent quantities and solve problems.
The document discusses the history and development of number systems. It describes how ancient cultures like the Sumerians, Egyptians, Greeks, Romans, and Indians all developed early number systems to suit their needs. The most commonly used system today, the Hindu-Arabic numeral system, can be traced back to developments in India in the 5th century where place-value notation and the concept of zero were introduced. This system was then adopted and modified by Arabs and Europeans.
The document provides an overview of number systems used by different civilizations and an introduction to basic number concepts:
- It discusses ancient number systems including the Egyptian base-12 and Babylonian base-60 systems, as well as modern systems like binary and decimal.
- Basic number types are defined such as integers, rational numbers, irrational numbers, and real numbers. Fractions and decimal expansions are also introduced.
- Famous mathematicians who contributed to the study and development of number systems throughout history are acknowledged.
The document discusses the history and development of Hindu-Arabic numerals. It originated in India in around 300 BC and was developed by a mathematician named al-Binuri. These numerals evolved and spread to the Middle East and Europe through Arab traders in the 10th century. Leonardo Fibonacci helped popularize the use of Hindu-Arabic numerals in Europe in the early 13th century through his book Liber Abaci, as they were more efficient than traditional Roman numerals. Today, the Hindu-Arabic numeral system with 10 symbols (0-9) is the most widely used numeral system globally.
This document provides an overview of different number systems and concepts in mathematics related to numbers. It defines real numbers, rational numbers, integers, whole numbers, and natural numbers. It discusses that rational numbers can be divided into integers, whole numbers, and natural numbers. Irrational numbers are also introduced. Important mathematicians who contributed to the study and understanding of numbers are referenced, including Pythagoras, Archimedes, Aryabhatta, Dedekind, Cantor, Babylonians, and Euclid.
The document provides an overview of number systems throughout history. It discusses how ancient civilizations like the Egyptians and Babylonians experimented with different bases like base-12 and base-60 systems. It then covers the decimal system and describes number types like rational, irrational, integer, natural numbers and their properties. The document also discusses concepts like fractions in ancient Egypt, binary numbers and the expansion of numbers into terminating, non-terminating recurring and non-recurring decimals.
- The document discusses the origins and development of the number zero and the decimal numeral system. It originated in ancient India, where zero was used as a place-holder in the decimal system by 3000 BC. This system was later adopted by Arab mathematicians and brought to Europe, revolutionizing mathematics. Key figures who helped develop and popularize the system included Brahmagupta, Al-Khowarizmi, and Fibonacci. Today this decimal numeral system is known as the Hindu-Arabic system.
Indian mathematicians and their contribution to the field of mathematicsBalabhaskar Ashok Kumar
- Mathematics originated in India as early as 200 BC during the Shulba period, where the Sulba Sutras were developed as part of the Indus Valley civilization.
- During the "golden age" of Indian mathematics between 500-1000 AD, great mathematicians like Aryabhata, Brahmagupta, Bhaskara I, Mahavira, and Bhaskara II made significant contributions and advances in many areas of mathematics. Their work spread throughout Asia and influenced mathematics in the Middle East and Europe.
- Aryabhata, in particular, made early approximations of pi and proposed that it is irrational. He also discussed sine, verses, and solutions to indeterminate equations in his
Zero is a number that represents nothing or empty space. It was invented in ancient India and was an important development that allowed more advanced mathematics. Zero holds a central role and is the identity element in addition. It allows place-value systems like binary to function and is essential for computer science. Zero's existence was initially debated but is now widely used and crucial for science, mathematics, banking, and many other aspects of modern life.
Importance of mathematics in our daily lifeHarsh Rajput
The document discusses the history and origins of mathematics. It notes that mathematics originated from practical needs like measurement and counting, with early forms found on notched bones and cave walls. Over thousands of years, mathematics has developed from attempts to describe the natural world and arrive at logical truths. Today, mathematics is highly specialized but also applied in diverse fields from politics to traffic analysis. The document also provides examples of how concepts in commercial mathematics, algebra, statistics, geometry are useful in daily life.
Applications of mathematics in our daily lifeAbhinav Somani
The document discusses the history of mathematics. It states that the study of mathematics as its own field began in ancient Greece with Pythagoras, who coined the term "mathematics." Greek mathematics refined methods and expanded subject matter. Beginning in the 16th century Renaissance, new mathematical developments interacting with scientific discoveries occurred at an increasing pace. The document also notes that mathematics has been used since ancient times, with early uses including building the pyramids in Egypt.
Indian mathematicians made many important contributions throughout history. Some key figures introduced the decimal number system and concept of zero, including Aryabhata. Brahmagupta was the first to treat zero as a number. Later mathematicians such as Ramanujan, Mahalanobis, Rao, and Kaprekar made advances in areas like statistics, number theory, and linear programming. Overall, Indian mathematicians have significantly influenced mathematics globally with pioneering concepts and solutions that have shaped the field.
The document summarizes the early mathematical system developed by the Sumerians in Mesopotamia between the Tigris and Euphrates Rivers. Key points:
- The Sumerians developed one of the earliest known writing systems, cuneiform script, which enabled recording of early mathematics on clay tablets.
- They used a sexagesimal (base-60) numeric system combined with a place-value notation, which was superior to later Greek and Roman systems for calculating fractions and powers.
- Much of what is known about early Mesopotamian mathematics comes from clay tablets dating to the Old Babylonian period from around 1800-1600 BCE. These included table texts and problem texts.
The document provides an overview of the history and development of the concept of zero. It discusses how zero emerged as a distinct numerical concept over centuries, originating from its use as a placeholder in places value systems before being abstracted as an independent number. Key points covered include the influence of Indian and Arabic mathematicians in developing rules for zero and negative numbers, allowing for the development of algebra, as well as how different cultures and religions approached the concepts of nothingness and infinity that zero represents.
Mathematics is the foundation of modern science and technology. It is the language in which scientific concepts are expressed and without mathematics, no technological developments can occur. Mathematics is used extensively in physics, chemistry, astronomy and other sciences. It involves concepts like calculus, vectors, matrices, and differential equations which allow scientists and engineers to model real-world phenomena, make predictions, and solve problems across many domains.
Mathematics has evolved from simple counting and measurement used by early humans to the complex discipline it is today. Key developments include the establishment of number systems and algebra in ancient Mesopotamia and Egypt, advances in geometry and logic by ancient Greeks, transmission of knowledge to other ancient cultures like China and India, and the establishment of concepts like calculus and logarithms in Europe during the 16th-18th centuries. The 19th-20th centuries saw unprecedented growth in mathematical concepts and ideas through the work of mathematicians around the world, including Indians like Ramanujan who made seminal contributions despite facing disadvantages.
This document discusses the history of Indian mathematics through several prominent mathematicians such as Aryabhata, Bhaskaracharya, Varaha Mihira, and Srinivasa Ramanujan. It notes that while attitudes are slowly changing, Indian mathematical contributions remain neglected or attributed to other cultures. The document aims to address this neglect by discussing several influential Indian mathematicians and their achievements, as well as examining why Indian works were neglected and why this represents an injustice.
The document discusses ineffective and toxic grading practices such as using zeroes for missing work, averaging grades over time, and single assignments that heavily impact grades. It advocates for alternative practices like allowing students to make up missing work, using students' best work to represent their learning, and using incompletes rather than zeroes. The document argues these approaches more accurately reflect student learning and motivate students rather than punish them. It also discusses how improving grading policies can lead to better student outcomes, discipline, and faculty morale in schools.
- Zero originated as a placeholder in ancient Babylonian and Indian mathematics to represent empty value positions in their place value number systems. The Babylonians used a space or punctuation mark while Indians used a word meaning empty or void.
- The concept of zero as an actual number was developed in India by the 9th century AD where it was fully integrated into their mathematical system. This decimal system with a symbol for zero reached Europe in the 11th century via Arabic mathematicians.
- Fibonacci was instrumental in introducing the Hindu-Arabic numeral system, including the concept of zero as a number, to European mathematics in the 13th century. This system became prevalent and replaced previous numeral systems across Europe.
This document provides a summary of the history and development of the concept of zero. It discusses how zero originated in ancient India, Babylon, and the Mayan civilization, with the Hindus and Arabics in India generally considered the first to use it as a number. It describes how Aryabhatta is credited with inventing the number zero and establishing it as part of a decimal system. The document also covers how zero spread to other languages and cultures, the rules and equations developed by Brahmagupta and Bhaskar regarding its mathematical properties, and how zero enabled the development of modern binary systems and computing.
The document discusses the history and evolution of different number systems used by humans over time, from ancient Babylonian and Egyptian numerals to modern Hindu-Arabic numerals. It explains key concepts like natural numbers, integers, rational numbers, irrational numbers, real numbers, imaginary numbers, and complex numbers. The concept of zero, which represents nothing, was an important development that allowed for more advanced mathematics. Number systems provide a consistent way to represent quantities and solve problems.
The document discusses the history and development of number systems. It describes how ancient cultures like the Sumerians, Egyptians, Greeks, Romans, and Indians all developed early number systems to suit their needs. The most commonly used system today, the Hindu-Arabic numeral system, can be traced back to developments in India in the 5th century where place-value notation and the concept of zero were introduced. This system was then adopted and modified by Arabs and Europeans.
The document provides an overview of number systems used by different civilizations and an introduction to basic number concepts:
- It discusses ancient number systems including the Egyptian base-12 and Babylonian base-60 systems, as well as modern systems like binary and decimal.
- Basic number types are defined such as integers, rational numbers, irrational numbers, and real numbers. Fractions and decimal expansions are also introduced.
- Famous mathematicians who contributed to the study and development of number systems throughout history are acknowledged.
The document discusses the history and development of Hindu-Arabic numerals. It originated in India in around 300 BC and was developed by a mathematician named al-Binuri. These numerals evolved and spread to the Middle East and Europe through Arab traders in the 10th century. Leonardo Fibonacci helped popularize the use of Hindu-Arabic numerals in Europe in the early 13th century through his book Liber Abaci, as they were more efficient than traditional Roman numerals. Today, the Hindu-Arabic numeral system with 10 symbols (0-9) is the most widely used numeral system globally.
This document provides an overview of different number systems and concepts in mathematics related to numbers. It defines real numbers, rational numbers, integers, whole numbers, and natural numbers. It discusses that rational numbers can be divided into integers, whole numbers, and natural numbers. Irrational numbers are also introduced. Important mathematicians who contributed to the study and understanding of numbers are referenced, including Pythagoras, Archimedes, Aryabhatta, Dedekind, Cantor, Babylonians, and Euclid.
The document provides an overview of number systems throughout history. It discusses how ancient civilizations like the Egyptians and Babylonians experimented with different bases like base-12 and base-60 systems. It then covers the decimal system and describes number types like rational, irrational, integer, natural numbers and their properties. The document also discusses concepts like fractions in ancient Egypt, binary numbers and the expansion of numbers into terminating, non-terminating recurring and non-recurring decimals.
- The document discusses the origins and development of the number zero and the decimal numeral system. It originated in ancient India, where zero was used as a place-holder in the decimal system by 3000 BC. This system was later adopted by Arab mathematicians and brought to Europe, revolutionizing mathematics. Key figures who helped develop and popularize the system included Brahmagupta, Al-Khowarizmi, and Fibonacci. Today this decimal numeral system is known as the Hindu-Arabic system.
Indian mathematicians and their contribution to the field of mathematicsBalabhaskar Ashok Kumar
- Mathematics originated in India as early as 200 BC during the Shulba period, where the Sulba Sutras were developed as part of the Indus Valley civilization.
- During the "golden age" of Indian mathematics between 500-1000 AD, great mathematicians like Aryabhata, Brahmagupta, Bhaskara I, Mahavira, and Bhaskara II made significant contributions and advances in many areas of mathematics. Their work spread throughout Asia and influenced mathematics in the Middle East and Europe.
- Aryabhata, in particular, made early approximations of pi and proposed that it is irrational. He also discussed sine, verses, and solutions to indeterminate equations in his
Zero is a number that represents nothing or empty space. It was invented in ancient India and was an important development that allowed more advanced mathematics. Zero holds a central role and is the identity element in addition. It allows place-value systems like binary to function and is essential for computer science. Zero's existence was initially debated but is now widely used and crucial for science, mathematics, banking, and many other aspects of modern life.
Importance of mathematics in our daily lifeHarsh Rajput
The document discusses the history and origins of mathematics. It notes that mathematics originated from practical needs like measurement and counting, with early forms found on notched bones and cave walls. Over thousands of years, mathematics has developed from attempts to describe the natural world and arrive at logical truths. Today, mathematics is highly specialized but also applied in diverse fields from politics to traffic analysis. The document also provides examples of how concepts in commercial mathematics, algebra, statistics, geometry are useful in daily life.
Applications of mathematics in our daily lifeAbhinav Somani
The document discusses the history of mathematics. It states that the study of mathematics as its own field began in ancient Greece with Pythagoras, who coined the term "mathematics." Greek mathematics refined methods and expanded subject matter. Beginning in the 16th century Renaissance, new mathematical developments interacting with scientific discoveries occurred at an increasing pace. The document also notes that mathematics has been used since ancient times, with early uses including building the pyramids in Egypt.
Indian mathematicians made many important contributions throughout history. Some key figures introduced the decimal number system and concept of zero, including Aryabhata. Brahmagupta was the first to treat zero as a number. Later mathematicians such as Ramanujan, Mahalanobis, Rao, and Kaprekar made advances in areas like statistics, number theory, and linear programming. Overall, Indian mathematicians have significantly influenced mathematics globally with pioneering concepts and solutions that have shaped the field.
The document summarizes the early mathematical system developed by the Sumerians in Mesopotamia between the Tigris and Euphrates Rivers. Key points:
- The Sumerians developed one of the earliest known writing systems, cuneiform script, which enabled recording of early mathematics on clay tablets.
- They used a sexagesimal (base-60) numeric system combined with a place-value notation, which was superior to later Greek and Roman systems for calculating fractions and powers.
- Much of what is known about early Mesopotamian mathematics comes from clay tablets dating to the Old Babylonian period from around 1800-1600 BCE. These included table texts and problem texts.
The document provides an overview of the history and development of the concept of zero. It discusses how zero emerged as a distinct numerical concept over centuries, originating from its use as a placeholder in places value systems before being abstracted as an independent number. Key points covered include the influence of Indian and Arabic mathematicians in developing rules for zero and negative numbers, allowing for the development of algebra, as well as how different cultures and religions approached the concepts of nothingness and infinity that zero represents.
Mathematics is the foundation of modern science and technology. It is the language in which scientific concepts are expressed and without mathematics, no technological developments can occur. Mathematics is used extensively in physics, chemistry, astronomy and other sciences. It involves concepts like calculus, vectors, matrices, and differential equations which allow scientists and engineers to model real-world phenomena, make predictions, and solve problems across many domains.
Mathematics has evolved from simple counting and measurement used by early humans to the complex discipline it is today. Key developments include the establishment of number systems and algebra in ancient Mesopotamia and Egypt, advances in geometry and logic by ancient Greeks, transmission of knowledge to other ancient cultures like China and India, and the establishment of concepts like calculus and logarithms in Europe during the 16th-18th centuries. The 19th-20th centuries saw unprecedented growth in mathematical concepts and ideas through the work of mathematicians around the world, including Indians like Ramanujan who made seminal contributions despite facing disadvantages.
This document discusses the history of Indian mathematics through several prominent mathematicians such as Aryabhata, Bhaskaracharya, Varaha Mihira, and Srinivasa Ramanujan. It notes that while attitudes are slowly changing, Indian mathematical contributions remain neglected or attributed to other cultures. The document aims to address this neglect by discussing several influential Indian mathematicians and their achievements, as well as examining why Indian works were neglected and why this represents an injustice.
The document discusses ineffective and toxic grading practices such as using zeroes for missing work, averaging grades over time, and single assignments that heavily impact grades. It advocates for alternative practices like allowing students to make up missing work, using students' best work to represent their learning, and using incompletes rather than zeroes. The document argues these approaches more accurately reflect student learning and motivate students rather than punish them. It also discusses how improving grading policies can lead to better student outcomes, discipline, and faculty morale in schools.
How To Rock Your Content Curation StrategyPic Presents
A succesful content marketing strategy needs a healthy blend of both content creation and content curation. This presentation highlights a content curation strategy and then discovers 20 top content curation tools and tips.
- The document discusses how computers use negative exponents to process fractions and percentages during photo processing, which allows apps like Photoshop to shrink photos.
- It explains that negative exponents represent fractions, with the item with the negative exponent moving to the denominator when written as a fraction. This allows computers to perform mathematical operations involving fractions.
- Examples are provided of how negative exponents simplify to fractions through the rule of a-m = 1/am, with the item in the exponent moving between the numerator and denominator.
Machine learning models are trained on past data with known outcomes to predict unknown future outcomes. The document compares several machine learning algorithms on a medical dataset to predict kidney disease:
- ZeroR classified 28.2% correctly by always predicting stage 3 disease.
- Naive Bayes classified 56.6% correctly using attribute probabilities.
- OneR classified 80.2% correctly with a single rule based on serum creatinine levels.
- J4.5 decision tree classified the highest at 88.4% correctly by recursively splitting data into subgroups based on attribute information gains.
- Aryabhata was an Indian mathematician and astronomer born in 476 CE in Taregana, Bihar. He authored several texts on mathematics and astronomy, with his magnum opus being the Aryabhatiya.
- The Aryabhatiya covered topics in algebra, arithmetic, plane trigonometry, and spherical trigonometry. It also included continued fractions, quadratic equations, and a table of sines.
- While Aryabhata did not use a symbol for zero, it is believed knowledge of the place-value system and zero was implicit in his mathematics. He made several accurate estimations for astronomical values like the solar sidereal rotation and length
This document provides an overview of Naive Bayes classification. It begins with background on classification methods, then covers Bayes' theorem and how it relates to Bayesian and maximum likelihood classification. The document introduces Naive Bayes classification, which makes a strong independence assumption to simplify probability calculations. It discusses algorithms for discrete and continuous features, and addresses common issues like dealing with zero probabilities. The document concludes by outlining some applications of Naive Bayes classification and its advantages of simplicity and effectiveness for many problems.
This is a brief, I mean brief, introduction to mathematics that I used this year. I also introduced the different types of Geometry, and steps to solving a geometry problem.
HISTORY OF MATHEMATICS SLIDE PRESENTATION;ResmiResmi Nair
The document provides a historical overview of the development of mathematics from ancient to modern times. It covers major periods and developments, including ancient numeration systems; Greek logic, philosophy, and Euclidean geometry; the Hindu-Arabic numeral system and algebraic advances by Islamic mathematicians; the transmission and spread of knowledge in Europe during 1000-1500 AD; and key figures and discoveries in the early modern period such as logarithms, analytic geometry, and calculus developed by Newton, Leibniz, and Euler. The document uses examples of important works, thinkers, and mathematical concepts to illustrate the evolution of mathematics across civilizations over thousands of years.
Peter Wang, a physics graduate and CTO/co-founder of Continuum Analytics, shares thoughts on startups based on his experience. He discusses focusing deeply on one topic rather than many, framing risk and credit in terms of human dynamics rather than money, learning from others more knowledgeable, and prioritizing relationships and understanding people over technical details or social validation. The document emphasizes purpose, communication, and focusing on the interactions that matter most.
The document provides guidance on making ideas stick through simple, memorable messaging. It discusses focusing on the core idea and compact delivery. Unexpected elements can grab attention if they surprise without losing the connection to the core. Concrete language uses specifics, names and examples to make abstract concepts tangible. Credibility comes from authority, testimonials and compelling details. Emotional appeals tap into what people care about. Stories engage audiences and help them visualize ideas.
This document provides advice and insights from various sources on how to build creativity as a habit. It discusses reframing how we think about creativity, establishing rituals and habits to support creativity like taking walks, keeping notebooks, and meditating. It also addresses dealing with failure and getting unstuck creatively, suggesting strategies like powering through or strategically procrastinating to overcome creative blocks. The overall message is that creativity can be cultivated by incorporating various practices into one's routine.
This document introduces speech act theory, which holds that when people use language they are not just conveying information but performing actions like commands, promises, threats, etc. It discusses three types of speech acts:
1) Locutionary act - the basic meaning and words alone without context.
2) Illocutionary act - the action performed by an utterance, like a command or promise, which can be implicit or explicit.
3) Perlocutionary act - the effect on the listener, which may be intended or unintended, like actually following a command or feeling insulted.
Truth values are less important than appropriateness - whether an utterance fits the context of the situation
This document provides an overview of the number zero, including:
- Zero represents a count or amount of null size and plays a central role in mathematics as the additive identity.
- The concept of zero has evolved over time, from a placeholder used by ancient Babylonians to its formal definition in Brahmagupta's writings in the 7th century.
- Zero is now fundamental in fields like physics, where it represents the lowest possible value of some physical quantities, and computer science, where most modern programming languages use zero-based numbering.
Exploring Communication with the Perplexing Other - When Introverts and Extra...Leslie Boyter
This document discusses communication challenges between introverts and extraverts. It aims to provide understanding of personality types, appreciate the strengths each type brings, and offer tools to prevent small misunderstandings from escalating. The webinar covers introversion and extraversion, how tensions can snowball if not addressed, and strategies like perspective-taking, checking intentions, and verifying impact to improve understanding between personality types. Overall, the webinar argues improved communication across types can foster better collaboration.
The document provides guidance on how to conduct a civilized debate. It discusses what a debate is, including that it is a discussion where different opinions are expressed on a topic. Debates can be formal organized events or informal discussions. Examples are given. The document also discusses why debates are important, as they help people develop skills in thinking logically, being critical thinkers, and expressing disagreements civilly. Language for stating opinions, disagreeing, attempting to persuade others, and agreeing is presented to help people debate respectfully. Finally, sample debates are provided to demonstrate proper debating techniques.
Achievement First is a growing network of non-profit, high-performing, college-preparatory, K to 12 public charter schools in Connecticut, New York and Rhode Island. The mission of Achievement First is to deliver on the promise of equal educational opportunity for all of America's children. We believe that all children, regardless of race or economic status, can succeed if they have access to a great education. Achievement First schools provide all of our students with the academic and character skills they need to graduate from top colleges, to succeed in a competitive world and to serve as the next generation of leaders in our communities.
Achievement First was established in 2003 by the founders of Amistad Academy, a nationally acclaimed public charter school in New Haven, CT. Amistad Academy, which was founded in 1999 to prove that urban students can achieve at the same high levels as their suburban peers, enabled its students to achieve at such extraordinarily high levels that the founders were asked to use Amistad Academy's knowledge and best practices to have a greater impact. Achievement First has grown into a network that includes 25 public charter schools in five cities.
Achievement First will continue to create public charter schools that close the achievement gap, while also looking to partner with other like-minded, reform-oriented organizations and traditional school districts to maximize our collective impact. Our theory of change is that by creating the equivalent of an urban public school "district," Achievement First can serve as proof that closing the achievement gap is possible at district scale and inspire broader reform. Achievement First is focused on continuing to close the achievement gap and serving as an example for other public charter schools and traditional public school districts. We will continue our work until every child is given access to a great education and enjoys the real freedom that flows from that opportunity.
This presentation is an interactive lesson about the left and right brain and how to exercise our creative brain with some games and a creative writing activity. In additional, the participants will learn adjectives using to describe personality traits.
Ravi Amba+pudi presented on innovation to Young Scholars at Greene Scholar's Program and other forums. The document discusses what innovation is, providing examples of famous innovators like Edison and Jobs. It explores where great ideas come from, noting they often start by looking for problems to solve, asking questions, challenging norms, taking risks, embracing serendipity, learning from history, and working with others. Great ideas can create change and improve lives in both big and small ways.
This document discusses various aspects of communication and conversation. It defines key concepts like monologues, dialogues, and deixis. It explains Grice's Cooperative Principle and Maxims of Quantity, Quality, Relation, and Manner. While these maxims outline ideal conversational behavior, the document notes we often violate them through implicature to communicate implied meanings and intentions. Overall, the document provides an overview of principles and theories of human communication and conversation.
This document explores the relationship between numerology and names. Numerology is the belief that numbers are related to events, names, and other phenomena. Various numerology systems assign numerical values to letters in order to calculate numbers related to people's names and birth dates. For example, one system sums the numerical values of the letters in a name to determine characteristics about that person. Numerologists have observed potential characteristics associated with different single-digit numbers that can be derived from names and birth dates.
Think out of_the_box_(power_point_show)Priti Mudgal
This document discusses thinking outside the box and creative thinking. It suggests that the box, which represents conformity and limitation, is made up of six sides: limiting assumptions, addiction to the status quo, hyper-rationality, tunnel vision, intolerance for ambiguity, and no intrinsic motivation. It encourages the reader to identify which side most limits their thinking and commit to an action to go beyond that limitation when working on a new project. The document provides advice from creative thinkers on championing new ideas and expressing one's original thoughts. The overall message is to get out of habitual thinking patterns and fully commit to creative pursuits.
This document discusses thinking outside the box and creative thinking. It suggests that the box, which represents conformity and limitation, is made up of six sides: limiting assumptions, addiction to the status quo, hyper-rationality, tunnel vision, intolerance for ambiguity, and no intrinsic motivation. It encourages the reader to identify which side most limits their thinking and commit to an action to go beyond that limitation when working on their most inspiring new idea or project. The document provides quotes and questions to help motivate creative thinking and getting ideas started.
The document discusses designing interactive learning spaces in libraries. It recommends adding color, art, open modular areas, and movable furniture to encourage creativity, discovery, collaboration, interaction, and innovation. The key is to provide tools and technology like 3D printers, robotics kits, and programming devices to allow patrons to learn through hands-on making and invention. Community involvement is important, with patrons able to teach skills and staff providing coaching. The goal is to create safe spaces for exploration and failure that spark new ideas and opportunities.
This document provides a series of nonsensical definitions or examples for letters of the alphabet. Some key points include:
- Letter A defines various types of alignments and categories things as good, evil, or neutral.
- Letter C discusses annual pilgrimages and filters those viewed as ashamed.
- Letter D distinguishes between things that change time, extend time, or maximize time.
- The document continues in this absurdist vein by providing random associations for most other letters as well.
The document discusses thinking outside the box and creative thinking. It suggests that the box, which represents conformity and limiting habits, is made up of six sides: limiting assumptions, addiction to the status quo, hyper-rationality, tunnel vision, intolerance for ambiguity, and no intrinsic motivation. It encourages the reader to identify which side most limits their thinking and to take action to expand beyond that boundary in their work. The document provides quotes and questions to inspire creative approaches.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Liberal Approach to the Study of Indian Politics.pdf
Zero
1. Zero: 0
“In the history of culture, the discovery of zero will always
stand out as one of the greatest single achievements of the
human race.” Tobias Danzig
WITHOUT ZERO:
• THERE WOULD BE NO CALCULUS.
• NO FINANCIAL MATHEMATICS.
• NO ALGEBRA
• NO ABILITY TO DO CALCULATIONS QUICKLY.
• NO COMPUTERS.
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2. ZERO IS A SPECIAL NUMBER
• IF WE ADD ZERO TO ANY NUMBER THE RESULT IS THE
ORIGINAL NUMBER. A + 0 = A
•(THE SAME IS TRUE FOR SUBTRACTION). A – 0 = A
• IF YOU MULTIPLY ANY NUMBER BY ZERO THE PRODUCT
IS ZERO. A x 0 = 0
•IF YOU RAISE ANY NON-ZERO NUMBER TO THE POWER
OF ZERO, THE RESULTING NUMBER IS 1: Aº = 1
• IF YOU DIVIDE ZERO BY ANY NON-ZERO NUMBER, THE
QUOTIENT IS ZERO. 0 ÷ A = 0
• ANY NUMBER DIVIDED BY ZERO IS UNDEFINED. A ÷ 0 is
UNDEFINED
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3. Error: Division by Zero
The error here is the division by (a-b) which is ZERO which is an
operation that is inadmissible in mathematics.
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4. A Brief History of ZERO
•The Maya civilization (2000 B.C. – 900 A.D.) in what is now
Mexico used the concept of zero as a PLACEHOLDER: that is, 705
is a way bigger number than 75. (Like using a comma in written
language.) The Babylonians used it similarly in the 7th century
B.C.
• The 7th century Indian mathematician Brahmagupta treated zero
as a “number” and not just as a place-holder. He elaborated the
rules mentioned on page 2 of this presentation.
• The Hindu-Arabic numbering system that included zero in the
way that was used in the West by Leonardo of Pisa – Fibonacci -
in his Book of Counting, published in 1202.
• Zero gained a central place in the number system soon
afterwards, with it literally separating the positive numbers from
the negative ones as in the number line.
• In the decimal system, zero serves as a place holder which
enables us to use both huge numbers and microscopic figures.
• Hence the sheer beauty and usefulness of zero which could lend
its use to science in its wonderfully succinct scientific notation.
5/13/2014 4
5. ZERO IS NOT NOTHING
• LATIN: “cifra” = zero; FRENCH: “chiffre”
• In English we use the word “nought” to mean
zero, a derivation from the word “nothing.”
• However, Nought is really a mathematical
misnomer (that is, a wrong name), for it would
be wrong to think of zero as nothing.
• 0 is certainly SOMETHING: it is a powerful
symbol, 0, that gives our modern notation
extraordinary power.
5/13/2014 5
6. Zero as Central Point or Start Point
• In the Real Number System, 0 is the only number
that is neither negative nor positive.
• It holds the unique position, almost the Still Point
to use Eastern Philosophy, between the positive
numbers and the negative ones.
• This position makes 0 the natural starting point or
origin on many scales such as on the axes of
Cartesian Geometry or Co-ordinate Geometry, or on
the many scales used in scientific measurement from
Temperature to Air Pressure to Acidity/Basicity etc
65/13/2014
7. A Little Bit of Religion (Theology)
• The mainline Christian religions believe that God created the world
out of NOTHING. But there are other viewpoints among different
religions that God could have created the world from pre-existing
matter (chaos) etc. This contradicts mainline science on the origins
of the Universe.
• Creation out of nothing, or creation ex nihilo, is the belief
that God created the world out of nothing, ex nihilo being Latin for
"from nothing." This view does not contradict THE BIG BANG
THEORY of the origin of the Universe. So this view can be
reconciled with the teachings of science.
• Scientists say that there was no time or space, therefore literally
nothing, there before the great explosion of THE BIG BANG.
• For believers “creation out of nothing” is a religious tenet that
shows both the power and mystery of God.
5/13/2014 7
8. A Little Bit of Philosophy (Wondering)1
• Asking the Big Questions of Life.
• “Why is there Something rather than Nothing?” – a question
asked by the philosopher Martin Heidegger (1889-1976).
• What is some-thing? What is no-thing?
• Some mathematicians have said that zero is not “nothing” as it
is a very important symbol and indeed a number very necessary
to all modern calculations. However, philosophers would say
that this is true to some extent only, as zero as a symbol
represents “nothing” and that it is important to ask the question
as to what that nothing is.
• Did I come from Nothing into life and then do I return into
Nothing?
• Is there a spiritual world there beyond the visible world? Or just
Nothing?
• Or again, good philosophers of mathematics ask what are
numbers anyway?
5/13/2014 8
9. A Little Bit of Philosophy (Wondering) 2
• Does a hole exist in itself? Is it some-thing or no-thing?
• Do letters that are engraved in or cut into solid stone exist in
themselves? Something made out of Nothing!
• Does the year ZERO, 0, exist? The Year 1 B.C. is actually
followed by the year 1 A.D.
• Does the floor Zero exist? We call the ground floor no. 1.
• What is absolute ZERO? Ask a Chemistry student.
• Tacticians speak about zeroing in on a target.
• A zero-sum game is one where the loss of one player is
balanced by the gain of another or others .e.g., poker where
what the winner wins equals what the losers lost.
• Is the Stock Market a Zero-Sum game?
5/13/2014 9
10. Some Final Thoughts
• How tiny are you in comparison to the size of the universe? How big
is the universe in comparison to you? Is your size actually
approaching zero.
• Limits are important in algebra and in differentiation: We speak of
the limits of certain expressions in x as x approaches ZERO or
INFINITY etc. The mathematical principle is that x or y or whatever
letter you choose may approach either 0 or Infinity, but never get
there. In mathematical terms division by ZERO and INFINITY is
undefined.
• Limits are always about approaching ZERO or INFINITY but never
getting there.
• Maybe the Mystery of God is like the Mystery of Zero or the Mystery
of Infinity – we can never really understand it in this life – we cannot
simply get there through human reasoning.
• Let the Wonder of ZERO, 0, begin!!
5/13/2014 10