This ppt slide is all about number system. here we learn-
To represent numbers
To know about different system
How number system works
The study of numbers is not only related to computers. We apply numbers everyday, and knowing how numbers work, will give us an insight of how computers manipulate and store numbers.
The document discusses different numeration systems used in various cultures and time periods around the world. It begins by explaining that the appropriate numbering system depends on the application. It then provides details on tally systems, the Hindu-Arabic numeral system, and various place-value systems including binary, decimal, and other bases. It also discusses the evolution of the concept of real numbers to include integers, rational numbers, and irrational numbers.
The document provides an overview of number systems used by different civilizations. It discusses ancient number systems including the Egyptian use of base-12 and Babylonian use of base-60. The decimal system is introduced as the most common modern system using base-10. Other number systems mentioned include binary, Mayan vigesimal, and fractions in ancient Egypt. Real numbers are defined as including integers, rational numbers like fractions, and irrational numbers like pi. Terminating, non-terminating recurring, and non-terminating non-recurring decimals are also briefly explained.
Mathematics for Primary School Teachers. Unit 2: NumerationSaide OER Africa
Mathematics for Primary School Teachers has been digitally published by Saide, with the Wits School of Education. It is a revised version of a course originally written for the Bureau for In-service Teacher Development (Bited) at the then Johannesburg College of Education (now Wits School of Education).
The course is for primary school teachers (Foundation and Intermediate Phase) and consists of six content units on the topics of geometry, numeration, operations, fractions, statistics and measurement. Though they do not cover the entire curriculum, the six units cover content from all five mathematics content areas represented in the curriculum.
The document provides an overview of the history and types of number systems. It discusses how ancient civilizations like the Egyptians, Babylonians, and Mayans developed different base number systems based on counting fingers and toes. It then explains the modern decimal number system and provides examples of different types of numbers like rational, irrational, integer, natural numbers. The document also briefly touches on concepts like terminating and recurring decimals as well as scientists who contributed to the study of number systems.
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 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.
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.
The document discusses different numeration systems used in various cultures and time periods around the world. It begins by explaining that the appropriate numbering system depends on the application. It then provides details on tally systems, the Hindu-Arabic numeral system, and various place-value systems including binary, decimal, and other bases. It also discusses the evolution of the concept of real numbers to include integers, rational numbers, and irrational numbers.
The document provides an overview of number systems used by different civilizations. It discusses ancient number systems including the Egyptian use of base-12 and Babylonian use of base-60. The decimal system is introduced as the most common modern system using base-10. Other number systems mentioned include binary, Mayan vigesimal, and fractions in ancient Egypt. Real numbers are defined as including integers, rational numbers like fractions, and irrational numbers like pi. Terminating, non-terminating recurring, and non-terminating non-recurring decimals are also briefly explained.
Mathematics for Primary School Teachers. Unit 2: NumerationSaide OER Africa
Mathematics for Primary School Teachers has been digitally published by Saide, with the Wits School of Education. It is a revised version of a course originally written for the Bureau for In-service Teacher Development (Bited) at the then Johannesburg College of Education (now Wits School of Education).
The course is for primary school teachers (Foundation and Intermediate Phase) and consists of six content units on the topics of geometry, numeration, operations, fractions, statistics and measurement. Though they do not cover the entire curriculum, the six units cover content from all five mathematics content areas represented in the curriculum.
The document provides an overview of the history and types of number systems. It discusses how ancient civilizations like the Egyptians, Babylonians, and Mayans developed different base number systems based on counting fingers and toes. It then explains the modern decimal number system and provides examples of different types of numbers like rational, irrational, integer, natural numbers. The document also briefly touches on concepts like terminating and recurring decimals as well as scientists who contributed to the study of number systems.
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 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.
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.
- 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 contains information about different types of numbers including rational numbers, irrational numbers, integers, natural numbers, and real numbers. It discusses how rational numbers can be expressed as fractions with integer numerators and non-zero denominators, and how irrational numbers cannot be expressed as fractions. It also contains examples of terminating and non-terminating decimals. Additionally, it discusses number lines and includes an example of marking distances on a number line.
This document provides an overview of a maths project on number systems. It discusses different types of numbers including real numbers, rational numbers, irrational numbers and integers. Rational numbers are divided into fractions and integers. Integers are divided into negatives and whole numbers, with whole numbers further divided into zero and natural numbers. Irrational numbers cannot be represented as fractions, while rational numbers can. The document also covers decimal expansions, representing real numbers on a number line, laws of exponents and the process of rationalization.
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 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.
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.
This document provides an overview of different types of real numbers:
- Rational numbers can be written as fractions p/q where p and q are integers. Their decimals are terminating or repeating.
- Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimals.
- Real numbers include all rational and irrational numbers and can be represented on the real number line. The document discusses properties and operations of real numbers.
The concept of zero evolved over centuries, starting from the Babylonians using a placeholder space or symbol in their numeral system, to the Indians in the 9th century treating zero as a number. Zero is the absence of quantity and is represented by the digit 0, which was distinguished from the letter O over time. Natural numbers are conventionally defined as either positive integers or non-negative integers including zero.
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.
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.
Mathematical concepts and their applications: Number systemJesstern Rays
The document discusses various number systems including binary and hexadecimal used in computing. It explains how binary represents numbers as 1s and 0s and is used in electronics like transistors and to represent text, images, and more. Hexadecimal is also introduced which uses 16 symbols to efficiently represent more characters using fewer bits than binary. Color codes in computing are represented using hexadecimal values for red, green, and blue components.
The document discusses different number systems used in mathematics. It begins by explaining that a number system is defined by its base, or the number of unique symbols used to represent numbers. The most common system is decimal, which uses base-10. Other discussed systems include binary, octal, hexadecimal, and those used historically by cultures like the Babylonians. Rational and irrational numbers are also defined. Rational numbers can be written as fractions of integers, while irrational numbers cannot.
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.
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.
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.
2.1 lbd numbers and their practical applicationsRaechel Lim
The document discusses the history and development of numbers and numerical systems. It begins with early counting methods using tallies and evolved to include the Egyptian, Babylonian, Roman, and Hindu-Arabic systems. The modern number system is then built up from the natural numbers to integers to rational numbers to real numbers, which include irrational numbers. Imaginary and complex numbers were later introduced to solve problems involving square roots of negative numbers. Place value systems and the ability to represent zero were important developments.
Mathematics has been an important part of the human search for understanding for over two thousand years. Mathematical discoveries have come from attempts to describe the natural world and from logical reasoning. In recent centuries, mathematics has also been successfully applied to other human endeavors such as politics, archaeology, traffic analysis, and sustainable forestry management. Today, mathematical thinking is more valuable than ever before and is an essential part of a liberal education.
The document provides an overview of different number systems including decimal, binary, Mayan, natural numbers, integers, rational numbers, and irrational numbers. It discusses key concepts like place value, bases, rationalization, and successive magnification on the number line. The document was written by a student as part of a school project on mathematical numbers and systems.
This document provides an overview of the early development of number concepts and arithmetic. It discusses primitive counting methods using tally marks and how this led to more advanced systems like Roman numerals and the Hindu-Arabic number system. Key points covered include:
- Primitive counting involved using tally marks or objects to represent quantities, showing the earliest abstraction of numbers.
- Roman numerals and other early systems represented improvements but were still cumbersome for arithmetic.
- The Hindu-Arabic system introduced the place-value concept, allowing representation of any number using just 10 symbols.
- Early cultures also developed methods for addition, subtraction, multiplication and division, starting from concrete processes and advancing to more abstract algorithms and memorization of tables.
EDMA163 Exploring Mathematics And Numeracy.docx4934bk
The document discusses the history of numbers and numerical systems in ancient Egypt. It describes how the Egyptians developed hieroglyphic and hieratic numerical systems based on symbols to represent numbers. The hieroglyphic system used symbols like gods and animals to represent values and was a base-10 place value system. Fractions were also represented. The hieratic system compactly wrote numbers and had over 25 discovered equations. Mathematics played a key role in Egyptian culture and civilization, aiding construction of structures like pyramids. The numerical systems evolved over time and help understand the foundations of modern mathematics.
- 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 contains information about different types of numbers including rational numbers, irrational numbers, integers, natural numbers, and real numbers. It discusses how rational numbers can be expressed as fractions with integer numerators and non-zero denominators, and how irrational numbers cannot be expressed as fractions. It also contains examples of terminating and non-terminating decimals. Additionally, it discusses number lines and includes an example of marking distances on a number line.
This document provides an overview of a maths project on number systems. It discusses different types of numbers including real numbers, rational numbers, irrational numbers and integers. Rational numbers are divided into fractions and integers. Integers are divided into negatives and whole numbers, with whole numbers further divided into zero and natural numbers. Irrational numbers cannot be represented as fractions, while rational numbers can. The document also covers decimal expansions, representing real numbers on a number line, laws of exponents and the process of rationalization.
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 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.
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.
This document provides an overview of different types of real numbers:
- Rational numbers can be written as fractions p/q where p and q are integers. Their decimals are terminating or repeating.
- Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimals.
- Real numbers include all rational and irrational numbers and can be represented on the real number line. The document discusses properties and operations of real numbers.
The concept of zero evolved over centuries, starting from the Babylonians using a placeholder space or symbol in their numeral system, to the Indians in the 9th century treating zero as a number. Zero is the absence of quantity and is represented by the digit 0, which was distinguished from the letter O over time. Natural numbers are conventionally defined as either positive integers or non-negative integers including zero.
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.
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.
Mathematical concepts and their applications: Number systemJesstern Rays
The document discusses various number systems including binary and hexadecimal used in computing. It explains how binary represents numbers as 1s and 0s and is used in electronics like transistors and to represent text, images, and more. Hexadecimal is also introduced which uses 16 symbols to efficiently represent more characters using fewer bits than binary. Color codes in computing are represented using hexadecimal values for red, green, and blue components.
The document discusses different number systems used in mathematics. It begins by explaining that a number system is defined by its base, or the number of unique symbols used to represent numbers. The most common system is decimal, which uses base-10. Other discussed systems include binary, octal, hexadecimal, and those used historically by cultures like the Babylonians. Rational and irrational numbers are also defined. Rational numbers can be written as fractions of integers, while irrational numbers cannot.
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.
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.
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.
2.1 lbd numbers and their practical applicationsRaechel Lim
The document discusses the history and development of numbers and numerical systems. It begins with early counting methods using tallies and evolved to include the Egyptian, Babylonian, Roman, and Hindu-Arabic systems. The modern number system is then built up from the natural numbers to integers to rational numbers to real numbers, which include irrational numbers. Imaginary and complex numbers were later introduced to solve problems involving square roots of negative numbers. Place value systems and the ability to represent zero were important developments.
Mathematics has been an important part of the human search for understanding for over two thousand years. Mathematical discoveries have come from attempts to describe the natural world and from logical reasoning. In recent centuries, mathematics has also been successfully applied to other human endeavors such as politics, archaeology, traffic analysis, and sustainable forestry management. Today, mathematical thinking is more valuable than ever before and is an essential part of a liberal education.
The document provides an overview of different number systems including decimal, binary, Mayan, natural numbers, integers, rational numbers, and irrational numbers. It discusses key concepts like place value, bases, rationalization, and successive magnification on the number line. The document was written by a student as part of a school project on mathematical numbers and systems.
This document provides an overview of the early development of number concepts and arithmetic. It discusses primitive counting methods using tally marks and how this led to more advanced systems like Roman numerals and the Hindu-Arabic number system. Key points covered include:
- Primitive counting involved using tally marks or objects to represent quantities, showing the earliest abstraction of numbers.
- Roman numerals and other early systems represented improvements but were still cumbersome for arithmetic.
- The Hindu-Arabic system introduced the place-value concept, allowing representation of any number using just 10 symbols.
- Early cultures also developed methods for addition, subtraction, multiplication and division, starting from concrete processes and advancing to more abstract algorithms and memorization of tables.
EDMA163 Exploring Mathematics And Numeracy.docx4934bk
The document discusses the history of numbers and numerical systems in ancient Egypt. It describes how the Egyptians developed hieroglyphic and hieratic numerical systems based on symbols to represent numbers. The hieroglyphic system used symbols like gods and animals to represent values and was a base-10 place value system. Fractions were also represented. The hieratic system compactly wrote numbers and had over 25 discovered equations. Mathematics played a key role in Egyptian culture and civilization, aiding construction of structures like pyramids. The numerical systems evolved over time and help understand the foundations of modern mathematics.
The Mesopotamian culture is often called Babylonian, after the lar.docxoreo10
The Mesopotamian culture is often called Babylonian, after the large metropolis of that name. We could “babble on”1 and on about their many fine achievements in architecture, irrigation, and commerce, but it is their mathematics that is truly remarkable, dwarfing that of other contemporary civilizations. One might not be impressed by their use of a vertical mark for “one” and a horizontal mark for “ten” – ten being a common unit in the mathematics of many societies, including Egypt, China, Rome, and our own society today. On the other hand, they were the first to employ a “positional” system which, except for minor changes, survives to this day!
1The authors would like to apologize for the easy pun, but we couldn’t resist.
Let’s remind ourselves how our current number system works. It does not suffice to say that it is based on grouping by tens. The Egyptians did this – yet we have left them in the dust by taking a giant step forward to the “position system.” We require only ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Nevertheless, we can handle numbers of any size without the need to define a new symbol. This is because the value of a number is determined not just by the symbol. We must note the positionof the symbol as well. The two 3’s in the number 373 represent different quantities. You would rather have three hundred dollars than three dollars, right? To summarize, our number system employs a mere ten symbols, whose values depend on their position in the number. Moving one digit to the left multiplies its place value by ten, while moving to the right (not surprisingly) divides its place value by ten.
Observe, by the way, that this is true on both sides of the decimal point! In the number 3.1416, the 1 near the 6 is worth only one hundredth of the 1 near the 3. There is no number in the entire universe that is too large or too small for our clever (ten-digit!) number system (of Hindu-Arabic origin, by the way). We call our system the decimal system, because ten is the base.
The Babylonians used instead the sexagesimal system because they chose 60 as their base. While we are not sure why, we are fairly certain they did not have 60 fingers. One theory (which is very popular) is that 60 has a multitude of factors, that is, many numbers go into 60. Put another way, $60 can be divided without coin among 2, 3, 4, 5, 6, 10, 12, 15, 20, or 30 people. We shall follow the common practice of using commas to separate groups. Thus (3, 50)60 shall mean 3 sixties and 50 ones for a total of 230. What does (2, 3, 50)60 mean? Well in our position system, 357 means 3 hundreds, 5 tens, and 7 ones, right? Each column is ten times more valuable than its neighbor. In the same way, each column to the left in the Babylonian system is sixty times bigger! In the number (2, 3, 50)60, the 2 represents 2 3600’s – because 60 × 60 = 3600. The next column to the left would represent 60 × 3600 or 216000.
The Babylonians only used two symbols: a vertical mark for 1 and ...
This document discusses the history and development of numeral systems. It begins by explaining the key aspects of a numeral system and some of the earliest systems used, such as unary notation. It then describes the development of place-value systems, including the Hindu-Arabic decimal system. Various base systems are covered, such as base-2 (binary), base-5, base-8, base-10, base-12, base-20, and base-60. The document also discusses weighted and non-weighted binary coding systems, including excess-3 code and gray code. The history of binary numbers is outlined, from early concepts developed by ancient Indian and Chinese mathematicians to its modern implementation in digital circuits.
This document discusses the history and development of various types of numbers. It covers natural numbers, numerals and numeral systems, negative numbers, rational numbers such as fractions, irrational numbers like square roots, infinity and infinitesimals, and complex numbers involving square roots of negative numbers. Key developments include the earliest use of tally marks and place value systems, the recognition of negative numbers in China and India, proofs of irrational numbers, and the first references to infinite quantities and complex numbers.
The document discusses several ancient numeration systems including the Egyptian, Babylonian, Roman, Mayan, and Hindu-Arabic systems. It provides examples of how each system represented numbers from 1 to 10. The Egyptian system used pictographs for the first nine numbers and logographs for higher numbers. The Babylonian system used a base-60 place value system with symbols for 1 and 10, requiring context to distinguish numbers. The Roman system used additive and subtractive principles with symbols for 1, 5, 10, 50, 100, 500, and 1000. The Mayan system was a base-20 place value system using dots, bars, and shells to represent numbers up to 19.
The document provides a history of mathematics from ancient civilizations to modern times. It discusses how mathematics originated in ancient Babylon and Egypt around 3000 BC, with the Egyptians having an advanced decimal number system and knowledge of geometry. It also describes the Babylonian sexagesimal system of representing numbers. Key figures discussed include Pythagoras, whose theorem is summarized, and Carl Gauss, a mathematical genius whose contributions transformed number theory and other fields in the 19th century. The document concludes by outlining the fundamental purposes and objectives of teaching mathematics.
The history of algebra began thousands of years ago and has progressed through different civilizations. Ancient Egyptians, Babylonians, Greeks, Indians, Arabs, and Europeans all made contributions. Quadratic equations in particular date back to ancient Babylonians around 1800 BC. Key developments include factoring, completing the square, and the quadratic formula. Today, quadratic equations are used in many areas of real life like physics, engineering, and finance.
This document is a term paper submitted by Zulfikar Pasha Dipto on the mystery of zero. It includes an acknowledgement, abstract, table of contents, and introduction section. The acknowledgement thanks various individuals for their support and guidance. The abstract provides a brief overview of the history and development of zero in different cultures from 700 BC to 1600 AD. The introduction discusses how zero was originally viewed as an empty space rather than a number, and how its usage and acceptance evolved over time in cultures like the Babylonians, Greeks, Indians, and others.
This document discusses numerology and symbolism from multiple perspectives. It covers:
1. Two layers of numerology - physics of frequencies and group mind/matrix of meaning.
2. Pythagoras' theory of the music of the spheres and how mathematical ratios relate to cosmic objects.
3. How Freemasonry uses gematria, a system where letters correspond to numbers, to encode messages numerically and through symbols. Examples are given.
4. Lists of gematria ciphers in Latin, English, Greek and Hebrew along with the numerical values they assign letters. Master numbers and their meanings are also listed.
For over 2000 years, mathematics has evolved from practical applications to a field of rigorous inquiry and back again. Early civilizations developed basic arithmetic and geometry to solve practical problems. The Greeks were first to study mathematics with a philosophical spirit, seeking inherent truths. Their work in geometry, algebra, and other areas remains valid today. Over centuries, mathematics spread across cultures through trade, exploration, and scholarship. It has grown increasingly specialized while also finding new applications, aided by computers. Today, mathematics is more valuable than ever as a way of understanding both natural and human systems through abstraction and modeling.
JOURNEY OF MATHS OVER A PERIOD OF TIME..................................Pratik Sidhu
DESCRIBES IN DETAIL ANCIENT AGE ,MEDIEVAL AND PRESENT AGE OF MATHS AND ALSO THE FAMOUS MATHEMATICIANS.REALLY AN AMAZING ONE WITH ANIMATED SLIDE DESIGND..............
This document discusses the difference between arithmetic and algebra. It begins by defining algebra as a way of thinking logically about numbers rather than performing calculations with specific numbers. Algebra involves introducing variables to represent unknowns and using logic to determine their values, while arithmetic uses numbers to perform calculations. The document then traces the origins and evolution of arithmetic from counting to modern symbolic notation, and explains how algebra emerged separately in ancient Babylonia through solving geometric problems using general patterns and unknown values. It emphasizes that algebra requires a different type of thinking than arithmetic.
The document provides information about the history of mathematics in Egypt. It discusses how the Egyptian system of arithmetic was based on iterative symbols representing successive powers of ten. It describes the Egyptian methods for addition, subtraction, multiplication and division. It notes that early Egyptians calculated areas and volumes but did not deal with theorems or proofs. It lists several important Egyptian mathematical texts from around 1850 BC. It then provides brief biographies of prominent Egyptian and Greek mathematicians including Claudius Ptolemy, Al-Khwarizmi, and Ibn Yunus who made significant contributions to mathematics and astronomy.
The document is a student paper on the history of mathematics. It covers the development of mathematics from prehistoric times through modern eras in different regions, including Prehistoric, Babylonian, Egyptian, Greek, Chinese, Indian, Islamic, Medieval European, Renaissance, and Modern mathematics. Key developments discussed include the earliest numerical notations and mathematical objects from prehistoric times, the sexagesimal numeral system of Babylonian mathematics, Egyptian contributions preserved in papyri, Greek advances in logic and deductive reasoning, China's place-value decimal system, and the flowering of mathematics during the Islamic Golden Age.
This document provides an overview of the history of mathematics from prehistoric times through modern times. It discusses early developments in places like Babylonia, Egypt, Greece, China, and India. Key contributions included early number systems, arithmetic operations, and early geometry concepts in places like ancient Mesopotamia and Egypt. Greek mathematics made large advances through rigorous deductive reasoning and the foundations of logic. Places like China and India also made important contributions, with China developing a very advanced decimal place-value system called rod numerals. The document outlines the major developments in mathematics across different time periods and civilizations.
This is a BSc final Project book on Student portal system application which is mobile based on android application. it will help students to write the project book in a proper way.
This is a final project presentation on student portal system application which is a mobile based software on android platform. It gives a project presentation idea with a standard format of sequence.
Smart Notice Board with android app via BluetoothS.M. Fazla Rabbi
This a project of Microprocessor, Microcontroller & Assembly Language Subject (CSE-305) of Dhaka International University.
This presentation made by-S.M. Fazla Rabbi. It is a project based submission.
How to make a project in arduino, is clearly describe here.
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How to Download & Install Module From the Odoo App Store in Odoo 17Celine George
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
Artificial Intelligence (AI) has revolutionized the creation of images and videos, enabling the generation of highly realistic and imaginative visual content. Utilizing advanced techniques like Generative Adversarial Networks (GANs) and neural style transfer, AI can transform simple sketches into detailed artwork or blend various styles into unique visual masterpieces. GANs, in particular, function by pitting two neural networks against each other, resulting in the production of remarkably lifelike images. AI's ability to analyze and learn from vast datasets allows it to create visuals that not only mimic human creativity but also push the boundaries of artistic expression, making it a powerful tool in digital media and entertainment industries.
8+8+8 Rule Of Time Management For Better ProductivityRuchiRathor2
This is a great way to be more productive but a few things to
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Post init hook in the odoo 17 ERP ModuleCeline George
In Odoo, hooks are functions that are presented as a string in the __init__ file of a module. They are the functions that can execute before and after the existing code.
3. Acknowledgment
We would like to thank Mahabubur Rahman Sir for giving me an
opportunity to express such a important topic via mathematical
presentation. I am also thankful to our friends for their ideas and co-
operation they provided to me. I am grateful to all of them.
4. Who I am...
S.M. Fazla Rabbi
Roll No. 37
Batch E-53
Department of CSE
9. Introduction
A number system defines a set of values used to represent a quantity.
We talk about the number of people attending school, number of
modules taken per student etc.
Quantifying items and values in relation to each other is helpful for us
to make sense of our environment.
The study of numbers is not only related to computers. We apply
numbers everyday, and knowing how numbers work, will give us an
insight of how computers manipulate and store numbers.
10. Brief Introduction About Numbers
A number is a mathematical object used in counting
and measuring. It is used in counting and measuring.
Numerals are often used for labels, for ordering serial
numbers, and for codes like ISBNs. In mathematics,
the definition of number has been extended over the
years to include such numbers as zero, negative
numbers, rational numbers, irrational numbers, and
complex numbers.
11. The history of number system
Modern Number System came
from different civilizations
12. The history of number system
The Ancient Egyptians
The Ancient Egyptians experimented with duo-decimal
(base-12) system in which they counted finger-joints
instead of finger . Each of our finger has three joints. In
addition to their base-twelve system, the Egyptians also
experimented with a sort –of-base-ten system. In this
system , the number 1 through 9 were drawn using the
appropriate number of vertical lines.
A human hand palm was the way
of counting used by the
Egyptians…
13. The history of number system
The Ancient Babylonians
Babylonians, were famous for their astrological observations
and calculations, and used a sexagesimal (base-60)
numbering system. In addition to using base sixty, the
babylonians also made use of six and ten as sub-bases. The
babylonians sexagesimal system which first appeared around
1900 to 1800 BC, is also credited with being the first known
place-value of a particular digit depends on both the digit
itself and its position within the number . This as an
extremely important development, because – prior to place-
value system – people were obliged to use different symbol to
represent different power of a base.
14. The history of number system
Aztecs, Eskimos, And Indian Merchants
Other cultures such as the Aztecs, developed vigesimal (base-
20) systems because they counted using both finger and toes.
The Ainu of Japan and the Eskimos of Greenland are two of
the peoples who make use of vigesimal systems of present day
. Another system that is relatively easy to understand is
quinary (base-5), which uses five digit : 0, 1, 2, 3, and 4. The
system is particularly interesting , in that a quinary finger-
counting scheme is still in use today by Indian merchant
near Bombay . This allow them to perform calculations on one
hand while serving their customers with the other.
Aztecs were the ethnic
group of Mexico
15. The history of number system
Mayan number system
This system is unique to our current decimal system, as
our current decimal system uses base -10 whereas, the
Mayan Number System uses base- 20.
The Mayan system used a combination of two symbols.
A dot (.) was used to represent the units and a dash (-)
was used to represent five. The Mayan's wrote their
numbers vertically as opposed to horizontally with the
lowest denomination on the bottom.
Several numbers according to Mayan
Number System
16. Binary number system
The binary numeral system, or base-2 number system,
represents numeric values using two symbols, 0 and 1. More
specifically, the usual base-2 system is a positional notation
with a radix of 2. Owing to its straight forward implementation
in digital electronic circuitry using logic gates, the binary
system is used internally by all modern computers. Counting in
binary is similar to counting in any other number system.
Beginning with a single digit, counting proceeds through each
symbol, in increasing order. Decimal counting uses the symbols
0 through 9, while binary only uses the symbols 0 and 1.
The history of number system
17. The history of number system
Fractions and Ancient Egypt
Ancient Egyptians had an understanding of fractions, however they
did not write simple fractions as 3/5 or 4/9 because of restrictions
in notation. The Egyptian scribe wrote fractions with the
numerator of 1. They used the hieroglyph “an open mouth" above
the number to indicate its reciprocal. The number 5, written, as a
fraction 1/5 would be written as . . .There are some exceptions.
There was a special hieroglyph for 2/3, , and some evidence that
3/4 also had a special hieroglyph. All other fractions were written
as the sum of unit fractions. For example 3/8 was written as 1/4 +
1/8.
18. The history of number system
Finally, In the sections following this one, we will give a chronological survey of number
systems throughout our mathematical history. We begin with prehistoric number systems,
which—in a way—predate even counting. We then travel through the proverbial wormhole,
if you will, and arrive at about ~3000 B.C.E. where the Egyptians are ruling supreme. Not
alone though, as the Summerians are more or less side by side and show signs of a much
higher mathematical understanding (~3000 B.C.E.). As the Summerians more or less
become the Babylonians around 2000 B.C.E. The Chinese, working largely in isolation, are
next: ~2500 B.C.E. Greek mathematicians become a reckoned—in more than one sense of
the word—force around 500 B.C.E. The mathematically impaired Romans provide no real
mathematical interest, but rotationally they are of large interest (~0 C.E.). Four hundred
years later (~400 C.E.) and across the globe, the astrologists of the Mayan civilization are
making incredible computations using, what seems to be, a number system developed in
isolation. The Hindus make achievements during a long period of time. Perhaps the most
important ones to us around 300 B.C.E. to 400 C.E. Then again, we make a rather big jump in
history and arrive in modern times, where we discuss computers and number systems.
19. Classification of Number System
Number Systems
Complex
Real
Rational
Imaginary
Irrational
Positive
Integer
Negative Zero Whole/ Non-negative
Natural
Composite
Fraction
Odd
Even
Prime
Terminating and
Repeating
NoTerminating and No
Repeating
21. Prime & Composite
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors
other than 1 and itself.
There are hints in the surviving records of the ancient Egyptians that they had some knowledge of prime
numbers: the Egyptian fraction expansions in the Rhind papyrus, for instance, have quite different forms for
primes and for composites. However, the earliest surviving records of the explicit study of prime numbers come
from the Ancient Greeks. Euclid's Elements (circa 300 BC) contain important theorems about primes
Example: 5 can only be divided evenly by 1 or 5, so it is a prime number.
When a number can be divided up evenly it is a Composite Number. Ex- 4,6,8,9….
Composite
History
Definition
Definition
22. Integer
An integer is a number that can be written without a fractional component . For example, 21, 4,
0, and −2048 are integers, while 9.75, 5 1⁄2, and √2 are not. Integer is denoted as Z.
Z= {……,-3,-2,-1,0,1,2,3,…..}
Whole/ Non-
negative
Odd
Even
Positive {1,2,3,…….}
Negative {….,-3,-2,-1,}
Zero { 0 }
{0,1,2,3,…….}
{2,4,6,8……}
Any integer that can be divided exactly by 2 is an even number.The last digit is 0, 2, 4, 6 or 8
Example: −24, 0, 6 and 38 are all even numbers.
{1,3,5,7,……}
Any integer that can be divided exactly by 2 is an even number.The last digit is 0, 2, 4, 6 or 8 .
Example: −3, 1, 7 and 35 are all odd numbers.
Zero’s origin>>4000 yrs Mesopotamia-Sumerian ”space”>>> third
century B.C. in ancient Babylon zero symbol >> 350 A.D.Mayans
calender.>>>seventh century A.D. in India mathematician
Brahmagupta >>>Middle East 773 A.D Mohammed ibn-Musa al-
Khowarizmi It was al-Khowarizmi who first synthesized Indian
arithmetic and showed how the zero could function in algebraic
equations.
23. Fraction
This is a type of a rational number. Fractions are written as two numbers, the numerator and the
denominator ,with a dividing bar between them. In the fraction m/n ‘m’ represents equal parts, where
‘n’ equal parts of that size make up one whole.
If the absolute value of m is greater than n ,then the absolute value of the fraction is greater than
1.Fractions can be greater than , less than ,or equal to1 and can also be positive ,negative , or zero.
24. Real
In mathematics, a real number is a value that represents a quantity along a line. The adjective real in this
context was introduced in the 17th century by René Descartes, who distinguished between real
and imaginary roots of polynomials. Julius Wilhelm Richard Dedekind was a German mathematician who
made important contributions to abstract algebra (particularly ring theory), algebraic number theory and
the foundations of the real numbers. The Real Numbers had no name before Imaginary Numbers were
thought of. Mathematician got called "Real" because they were not Imaginary.
Rules
* Real Numbers are measurable.The sets of real number, are those numbers
That can be mapped on a number line.
* Real Numbers have a concrete value
* Real Numbers can be manipulated, all can rewritten as a decimal
In mathematics, a real number is a value that represents a
quantity along a continuous line. The real numbers include
all the rational numbers, such as the integer −5 and
the fraction 4/3, and all the irrational numbers such as
√2 (1.41421356… the square root of two, an
irrational algebraic number) and π (3.14159265…, a
transcendental number).
History
Definition
25. Rational & Irrational
In mathematics, a rational number is any number that can be expressed
as the quotient or fraction p/q of two integers, a numerator p and a non-
zero denominator q. Since q may be equal to 1, every integer is a rational
number. Rational numbers are usually denoted by a boldface Q, it was
thus denoted in 1895 by Giuseppe Peano. Example: ⅛, ⅔.
History
&
Definition
Characteristics
Definition
Characteristics
Terminating>>> ½ = 0.5
Repeating>>> 10/3 =3.333333
No terminating & No repeating >>> √2= 1.4142135624 ………
The numbers cannot be written as a ratio of two integers are
called Irrational Numbers. Example: π (Pi) is a famous irrational
number. π = 3.1415926535897932384626433832795... (and more)
26. Imaginary
An imaginary number is a complex number that can be written as a real
number multiplied by the imaginary unit i, which is defined by its property i2 =
−1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number,
and its square is −25. Zero is considered to be both real and imaginary.
Greek mathematician and engineer Heron of Alexandria is noted as the first to have
conceived these numbers,Rafael Bombelli first set down the rules for multiplication of
complex numbers in 1572. The concept had appeared in print earlier, for instance in work
by Gerolamo Cardano.
Imaginary numbers can be very useful for solving engineering problems. On example is
if you have a pendulum swinging, it starts to slow down and eventually stop. If you want
to work out the motion of the pendulum over a certain time (ie derive a formula) then
the best way to do it is to use complex numbers.
History
Definition
Uses
27. Complex
A complex number is a number that can be expressed in the form a + bi,
where a and b are real numbers, and i is the imaginary unit (which satisfies
the equation i2 = −1). In this expression, a is called the real part of the
complex number, and b is called the imaginary part. If z=a+bi, then we
write {Re} (z)=a and {Im} (z)=b .
For example, −3.5 + 2i is a complex number.
The Italian mathematician Gerolamo Cardano is the first person known to have introduced complex
numbers. He called them "fictitious" during his attempts to find solutions to cubic equations in the 16th
century.
Complex numbers are the building blocks of more intricate math, such as
algebra. They can be applied to many aspects of real life, especially in
electronics and electromagnetism.
History
Definition
Uses
28. Other Types
There are different kind of other numbers too. It includes
hyper-real numbers,
hyper-complex numbers,
p-adic numbers,
surreal numbers etc.
These numbers are rarely used in our day-to-day life.
Therefore, we need not know about them in detail.
29. In Short
Natural, N={1,2,3,4,5……..}
Integer, I={-3,-2,-1,0,1,2,3}
Real, R=[-∞, +∞]
Rational, Q= {
𝑝
𝑞
, 𝑝, 𝑞 ∈ 𝐼, 𝑞 ≠ 0} ex.
1
2
=0.5 (Terminating),
10
3
=3.333333 (repeating)
Irrational, Qi={√2, √3, √5, √7} ex. 2 = 1.4142135624 (no terminating & no repeating)
Complex, Z= x+iy, x,y ∈ 𝑅 where, x= real part and iy= Imaginary part…we can say
All real number are Subset of complex number.
Imaginary, i = Square root of negative number. Ex. −1, −2, −3….Where i exist.
30. 1) Binary Number System
A Binary number system has only two digits that are 0 and 1. Every number (value) represents
with 0 and 1 in this number system. The base of binary number system is 2, because it has only
two digits.
2) Octal number system
Octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with
0,1,2,3,4,5,6 and 7 in this number system. The base of octal number system is 8, because it has
only 8 digits.
3) Decimal number system
Decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with
0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal number system is 10, because it
has only 10 digits.
4) Hexadecimal number system
A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F. Every
number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The
base of hexadecimal number system is 16, because it has 16 alphanumeric values. Here A is 10, B
is 11, C is 12, D is 13, E is 14 and F is 15.
Most popular number
systems
Used
In
Computer
System
And
Mathematics
Also
31. S o m e
R e f e r e n c e s
Work behind
en.wikipedia.org
www.archimedes-lab.org
www.math.chalmers.se www.slideshare.net
www.google.com
translate.google.com
www.mathsisfun.com www.youtube.com
www.purple-math.com
www.whatis.techtarget.com www.basic-mathematics.com