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. Some of the key developments highlighted include the earliest numerical notations and arithmetic concepts in prehistoric times, the sexagesimal numeral system of the Babylonians, Egyptian contributions to geometry and fractions, Greek advances in logic and proof-based mathematics, China's place-value decimal system, and the introduction of algebra and Arabic numerals through Islamic mathematics.
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. The paper provides an overview of key mathematical concepts, texts, and figures from each historical period and location.
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..............
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.
History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
This document provides an overview of ancient mathematics in Babylon and Egypt. It describes how early mathematics developed out of practical needs in early civilizations along rivers like the Nile, Tigris, Euphrates, Indus, and Huangho. Archaeologists have uncovered hundreds of thousands of clay tablets in Mesopotamia containing early mathematical concepts. These include arithmetic, algebra, geometry, and early use of tables and formulas. Egyptian mathematics is also discussed and sources of early mathematical knowledge from Egypt are described, including papyri, monuments, and other inscriptions.
The history of mathematics began with early civilizations developing basic arithmetic and geometry. Some of the earliest and most influential mathematical texts came from ancient Mesopotamia, Egypt, China, and India. Greek mathematics built upon earlier traditions and introduced deductive reasoning and mathematical rigor. Key Greek mathematicians included Thales, Pythagoras, Plato, Euclid, Archimedes, and Apollonius, who made seminal contributions to geometry, number theory, and the early study of functions and calculus. Following this Golden Age of Greek mathematics, mathematical advances continued within the Islamic world and medieval Europe.
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 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. The paper provides an overview of key mathematical concepts, texts, and figures from each historical period and location.
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..............
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.
History of Math is a project in which students worked together in learning about historical development of mathematical ideas and theories. They were exploring about mathematical development from Sumer and Babylon till Modern age, and from Ancient Greek mathematicians till mathematicians of Modern age, and they wrote documents about their explorations. Also they had some activities in which they could work "together" (like writing a dictionary, taking part in the Eratosthenes experiment, measuring and calculating the height of each other schools, cooperating in given tasks) and activities that brought out their creativity and Math knowledge (making Christmas cards with mathematical details and motives and celebrating the PI day). Also they were able to visit Museum, exhibition "Volim matematiku" and to prepare (and lead) workshops for the Evening of mathematics (Večer matematike). At the end they have presented their work to other students and teachers.
This document provides an overview of ancient mathematics in Babylon and Egypt. It describes how early mathematics developed out of practical needs in early civilizations along rivers like the Nile, Tigris, Euphrates, Indus, and Huangho. Archaeologists have uncovered hundreds of thousands of clay tablets in Mesopotamia containing early mathematical concepts. These include arithmetic, algebra, geometry, and early use of tables and formulas. Egyptian mathematics is also discussed and sources of early mathematical knowledge from Egypt are described, including papyri, monuments, and other inscriptions.
The history of mathematics began with early civilizations developing basic arithmetic and geometry. Some of the earliest and most influential mathematical texts came from ancient Mesopotamia, Egypt, China, and India. Greek mathematics built upon earlier traditions and introduced deductive reasoning and mathematical rigor. Key Greek mathematicians included Thales, Pythagoras, Plato, Euclid, Archimedes, and Apollonius, who made seminal contributions to geometry, number theory, and the early study of functions and calculus. Following this Golden Age of Greek mathematics, mathematical advances continued within the Islamic world and medieval Europe.
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 a history of mathematics from ancient times through its development in various regions. It discusses:
1) Early counting methods and the origins of numerals in places like ancient Egypt, Mesopotamia, and India.
2) The mathematical advances of early civilizations like the Greeks, Chinese, Hindus, Babylonians and Egyptians - including concepts like zero, algebra, trigonometry, and geometry.
3) The transmission of mathematics from these early civilizations to medieval Islamic mathematics and eventually to European mathematics during the Renaissance, leading to modern developments.
History of mathematics - Pedagogy of MathematicsJEMIMASULTANA32
It includes Prehistory: from primitive counting to Numeral systems, Archaic mathematics in Mesopotamia and egypt, Birth of mathematics as a deductive science in Greece: Thales and Pythagoras and Role of Aryabhatta in Indian Mathematics.
The document discusses mathematics in ancient Babylonian and Egyptian civilizations. It describes how the Babylonians developed a system of writing called cuneiform using wedge-shaped symbols carved into clay tablets around 3000 BC. It also details their sexagesimal (base-60) numerical system and how they were able to perform advanced mathematical operations and solve equations. The document then explains the development of hieroglyphic numerals by the ancient Egyptians, including their base-10 system and specific symbols used to represent fractions and operations. Key sources of information about Babylonian and Egyptian mathematics included cuneiform tablets and Egyptian papyri such as the Rhind Mathematical Papyrus.
The document summarizes Babylonian, Egyptian, and Native American mathematics from 3000 BC to 601 BC. It describes that Babylonian mathematics had an advanced base-60 numeration system and covered topics like fractions, algebra, and quadratic/cubic equations. Egyptian mathematics used a pictorial numeration system and had formulas for calculating areas and volumes. Native Americans, specifically the Mayans, developed an accurate solar calendar and a base-20 numeration system with their own hieroglyphic writing system by 700 BC.
This document provides an overview of ancient Egyptian mathematics and its timeline. It discusses the Egyptian numeral system, which was additive, as well as their arithmetic operations of addition, multiplication and division. The Egyptians were able to solve linear equations and used arithmetic and geometric progressions. They could also express fractions as a sum of unit fractions. Overall, the document demonstrates the Egyptians had sophisticated mathematical knowledge and methods as early as 3000 BC.
Earliest methods used to solve quadratic equations were geometric. Babylonian cuneiform tablets from around 1800-1600 BCE contain problems that can be reduced to solving quadratic equations, showing they understood techniques. The Egyptians also solved quadratic equations geometrically in the Middle Kingdom around 2050-1650 BCE. Later mathematicians like Euclid, Brahmagupta, and al-Khwārizmī developed more algebraic methods, with Brahmagupta explicitly describing the quadratic formula around 628 AD. The need for convenience ultimately led to the discovery of the general quadratic formula, first obtained by Simon Stevin in 1594 and published by René Descartes in 1637 in the modern form still used today.
Pythagoras of Samos was a Greek mathematician who lived around 570 to 495 BC and is considered one of the first great mathematicians. He founded the Pythagorean cult who studied and advanced mathematics. He is commonly credited with the Pythagorean theorem in trigonometry, though some sources doubt he constructed the proof. Nonetheless, the theorem plays a large role in modern measurements and technology.
The document provides a history of number theory from its origins in ancient Mesopotamia through its development in classical Greece, India, the Islamic Golden Age, and early modern Europe. It discusses early contributors like the Babylonians, Pythagoras, Euclid, Diophantus, Brahmagupta, Fibonacci, and Fermat. Key topics covered include the earliest known work on Pythagorean triples by the Babylonians, Euclid's proof of the infinitude of primes, Diophantus's work on solving polynomial equations, and Fermat's work with perfect and amicable numbers without publishing full proofs.
The document provides a high-level overview of the history of mathematics from ancient civilizations through modern times. It discusses early developments in places like Babylonia, Egypt, China, India, and among the Greeks. Some key points:
- Early mathematical texts have been found dating back to 1900 BC in Babylonia and 2000-1800 BC in Egypt, dealing with concepts like Pythagorean triples.
- Greek mathematics from 600 BC onward greatly advanced the use of deductive reasoning and mathematical rigor. Figures like Thales, Pythagoras, Plato, and Euclid made important contributions.
- Developments continued in places like China, India, and among Islamic mathematicians between the
1) The Greeks adopted elements of mathematics from the Babylonians and Egyptians but soon made important original contributions, revolutionizing mathematical thought during the Hellenistic period.
2) Early Greek mathematics was based on geometry and used numeral systems similar to the Egyptians. Mathematicians like Thales established foundational geometric theorems and properties.
3) Pythagoras is credited with coining the terms "philosophy" and "mathematics" and realizing mathematics could form a complete system corresponding numbers to geometry, exemplified by Pythagoras' theorem. The Greeks grappled with problems like squaring the circle and Zeno's paradoxes of infinity.
The document traces the history and development of numbering systems from around 20,000 BCE to modern times. It discusses early systems used by Sumerians/Babylonians, Egyptians, Chinese, Mayans, Greeks, Romans, Indians, and Arabs. The Indian system developed the concept of zero in the 7th century, which was then popularized by Arab mathematicians like Al-Khwarizmi. Their system became the basis for the modern Hindu-Arabic numerals still used today around the world.
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.
- Mathematics originated independently in many ancient cultures including India, Mesopotamia, Egypt, China, and Greece.
- In India, the earliest evidence of mathematics dates back to the Indus Valley Civilization around 3000 BC, where they used basic arithmetic and geometry.
- Key early Indian mathematicians included Budhayana, who composed one of the earliest known texts on geometry called the Sulba Sutras around 800 BC.
- Indian mathematics was later transmitted to other parts of the world, influencing mathematics in places like the Middle East and China.
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.
Anecdotes from the history of mathematics ways of selling mathematiDennis Almeida
1) The development of mathematics, including number systems and arithmetic, was driven by practical needs in areas like trade, taxation, and military affairs. Place value systems like the Hindu-Arabic numerals made complex calculations possible.
2) Early algebra developed out of solving practical problems involving lengths and areas. Techniques like extracting roots and solving quadratic equations were applied to problems in areas like right triangles and bone setting.
3) Geometry originated from practical construction needs but was formalized by Euclid into a deductive system. It influenced fields like art and tiling patterns. Relating geometric concepts to algebraic formulas helped develop modern algebra.
1) Ancient Chinese mathematics developed an efficient decimal place value number system over 1000 years before the West adopted it, facilitating even complex calculations.
2) The "Nine Chapters on the Mathematical Art" textbook, written from around 200 BC, was important for educating mathematically competent administrators, covering practical problems and the first known method for solving equations.
3) By the 13th Century Golden Age of Chinese mathematics, over 30 prestigious schools had scholars like Qin Jiushao exploring solutions to quadratic and cubic equations hundreds of years before the West using similar repeated approximation methods.
The document provides a timeline of key developments in mathematics from 6000 BCE to the present. Some of the highlights include:
- The earliest written Egyptian numbers dating back to 2700 BCE which used symbols for units, tens, hundreds, and thousands.
- Babylonian mathematics from 1800 BCE which had multiplication tables and worked on solving quadratic and cubic equations.
- Early Chinese mathematics from 1600 BC which included the use of an efficient decimal place value system using bamboo rods.
- Indian mathematics from 1000 BCE which developed concepts like zero, negative numbers, and trigonometry that were later transmitted worldwide.
- Classical Greek mathematics from 624 BC which included theorems attributed to Thales and Euclid's Elements textbook.
The document provides a high-level overview of major milestones in the history of mathematics, including:
1) Early mathematical texts from Babylonian (c. 1900 BC), Egyptian (c. 2000-1800 BC), and Indian (c. 9th century BC) civilizations that approximated values like pi.
2) Key figures like Pythagoras, Euler, and Euclid of Alexandria, considered the "Father of Geometry", who authored the influential Elements textbook.
3) The progression of mathematical study in places like Egypt, India, and Mesopotamia over different historical periods under civilizations like the Sumerians, Greeks, Arabs, and more.
Ethnomathematics is the study of the relationship between mathematics and culture. It examines the distinct mathematical systems and practices of identifiable cultural groups. The goal is to better understand both the culture and mathematics, and how they connect. Some examples of ethnic groups and their traditional mathematics include:
1) The Egyptians developed measurement systems to build structures like the pyramids, and described areas of triangles and trapezoids.
2) The Chinese solved algebraic equations and used a decimal numeral system as early as 2500 BCE.
3) Muslim mathematicians in Baghdad advanced geometry and trigonometry, and the work of Al-Khowarizmi introduced algebra to the Western world.
This document provides a summary of computing technology and related sciences through history in 3 sentence summaries:
The earliest known computing devices were tally sticks used as notches carved on bones dating back 20,000 years, while copper was first used as a conductor for its properties around 10,000 years ago and megalithic structures from 5,000 BCE may have functioned as early calendars. Mathematical and scientific advances originated in ancient cultures including the earliest use of numbers in Sumerian cuneiform around 3000 BCE, Babylonian sexagesimal and Egyptian base-10 numeric systems, and Archimedes' invention of the positional decimal system. Key developments included the abacus used for calculation for millennia, Euclid's
A Reviewer for Math History and Trivia [Not Updated]eosinotphil
The document provides a brief overview of the history and origins of various mathematical concepts and tools:
- The abacus was invented in ancient China around 1200 BC and was used in many early civilizations. Algebra originated from Arabic scholars in the 3rd century BC. Differential and integral calculus were independently invented by Newton and Leibniz in the 17th century.
- Graphs and many common symbols like '=' and '>' were developed more recently, in the 16th-18th centuries to visually represent mathematical relationships and aid in calculation. Key early contributors to mathematics discussed include Archimedes, Pythagoras, and Diophantus.
- Mathematics has a long history in many ancient cultures including Egypt,
The document provides a history of mathematics from ancient times through its development in various regions. It discusses:
1) Early counting methods and the origins of numerals in places like ancient Egypt, Mesopotamia, and India.
2) The mathematical advances of early civilizations like the Greeks, Chinese, Hindus, Babylonians and Egyptians - including concepts like zero, algebra, trigonometry, and geometry.
3) The transmission of mathematics from these early civilizations to medieval Islamic mathematics and eventually to European mathematics during the Renaissance, leading to modern developments.
History of mathematics - Pedagogy of MathematicsJEMIMASULTANA32
It includes Prehistory: from primitive counting to Numeral systems, Archaic mathematics in Mesopotamia and egypt, Birth of mathematics as a deductive science in Greece: Thales and Pythagoras and Role of Aryabhatta in Indian Mathematics.
The document discusses mathematics in ancient Babylonian and Egyptian civilizations. It describes how the Babylonians developed a system of writing called cuneiform using wedge-shaped symbols carved into clay tablets around 3000 BC. It also details their sexagesimal (base-60) numerical system and how they were able to perform advanced mathematical operations and solve equations. The document then explains the development of hieroglyphic numerals by the ancient Egyptians, including their base-10 system and specific symbols used to represent fractions and operations. Key sources of information about Babylonian and Egyptian mathematics included cuneiform tablets and Egyptian papyri such as the Rhind Mathematical Papyrus.
The document summarizes Babylonian, Egyptian, and Native American mathematics from 3000 BC to 601 BC. It describes that Babylonian mathematics had an advanced base-60 numeration system and covered topics like fractions, algebra, and quadratic/cubic equations. Egyptian mathematics used a pictorial numeration system and had formulas for calculating areas and volumes. Native Americans, specifically the Mayans, developed an accurate solar calendar and a base-20 numeration system with their own hieroglyphic writing system by 700 BC.
This document provides an overview of ancient Egyptian mathematics and its timeline. It discusses the Egyptian numeral system, which was additive, as well as their arithmetic operations of addition, multiplication and division. The Egyptians were able to solve linear equations and used arithmetic and geometric progressions. They could also express fractions as a sum of unit fractions. Overall, the document demonstrates the Egyptians had sophisticated mathematical knowledge and methods as early as 3000 BC.
Earliest methods used to solve quadratic equations were geometric. Babylonian cuneiform tablets from around 1800-1600 BCE contain problems that can be reduced to solving quadratic equations, showing they understood techniques. The Egyptians also solved quadratic equations geometrically in the Middle Kingdom around 2050-1650 BCE. Later mathematicians like Euclid, Brahmagupta, and al-Khwārizmī developed more algebraic methods, with Brahmagupta explicitly describing the quadratic formula around 628 AD. The need for convenience ultimately led to the discovery of the general quadratic formula, first obtained by Simon Stevin in 1594 and published by René Descartes in 1637 in the modern form still used today.
Pythagoras of Samos was a Greek mathematician who lived around 570 to 495 BC and is considered one of the first great mathematicians. He founded the Pythagorean cult who studied and advanced mathematics. He is commonly credited with the Pythagorean theorem in trigonometry, though some sources doubt he constructed the proof. Nonetheless, the theorem plays a large role in modern measurements and technology.
The document provides a history of number theory from its origins in ancient Mesopotamia through its development in classical Greece, India, the Islamic Golden Age, and early modern Europe. It discusses early contributors like the Babylonians, Pythagoras, Euclid, Diophantus, Brahmagupta, Fibonacci, and Fermat. Key topics covered include the earliest known work on Pythagorean triples by the Babylonians, Euclid's proof of the infinitude of primes, Diophantus's work on solving polynomial equations, and Fermat's work with perfect and amicable numbers without publishing full proofs.
The document provides a high-level overview of the history of mathematics from ancient civilizations through modern times. It discusses early developments in places like Babylonia, Egypt, China, India, and among the Greeks. Some key points:
- Early mathematical texts have been found dating back to 1900 BC in Babylonia and 2000-1800 BC in Egypt, dealing with concepts like Pythagorean triples.
- Greek mathematics from 600 BC onward greatly advanced the use of deductive reasoning and mathematical rigor. Figures like Thales, Pythagoras, Plato, and Euclid made important contributions.
- Developments continued in places like China, India, and among Islamic mathematicians between the
1) The Greeks adopted elements of mathematics from the Babylonians and Egyptians but soon made important original contributions, revolutionizing mathematical thought during the Hellenistic period.
2) Early Greek mathematics was based on geometry and used numeral systems similar to the Egyptians. Mathematicians like Thales established foundational geometric theorems and properties.
3) Pythagoras is credited with coining the terms "philosophy" and "mathematics" and realizing mathematics could form a complete system corresponding numbers to geometry, exemplified by Pythagoras' theorem. The Greeks grappled with problems like squaring the circle and Zeno's paradoxes of infinity.
The document traces the history and development of numbering systems from around 20,000 BCE to modern times. It discusses early systems used by Sumerians/Babylonians, Egyptians, Chinese, Mayans, Greeks, Romans, Indians, and Arabs. The Indian system developed the concept of zero in the 7th century, which was then popularized by Arab mathematicians like Al-Khwarizmi. Their system became the basis for the modern Hindu-Arabic numerals still used today around the world.
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.
- Mathematics originated independently in many ancient cultures including India, Mesopotamia, Egypt, China, and Greece.
- In India, the earliest evidence of mathematics dates back to the Indus Valley Civilization around 3000 BC, where they used basic arithmetic and geometry.
- Key early Indian mathematicians included Budhayana, who composed one of the earliest known texts on geometry called the Sulba Sutras around 800 BC.
- Indian mathematics was later transmitted to other parts of the world, influencing mathematics in places like the Middle East and China.
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.
Anecdotes from the history of mathematics ways of selling mathematiDennis Almeida
1) The development of mathematics, including number systems and arithmetic, was driven by practical needs in areas like trade, taxation, and military affairs. Place value systems like the Hindu-Arabic numerals made complex calculations possible.
2) Early algebra developed out of solving practical problems involving lengths and areas. Techniques like extracting roots and solving quadratic equations were applied to problems in areas like right triangles and bone setting.
3) Geometry originated from practical construction needs but was formalized by Euclid into a deductive system. It influenced fields like art and tiling patterns. Relating geometric concepts to algebraic formulas helped develop modern algebra.
1) Ancient Chinese mathematics developed an efficient decimal place value number system over 1000 years before the West adopted it, facilitating even complex calculations.
2) The "Nine Chapters on the Mathematical Art" textbook, written from around 200 BC, was important for educating mathematically competent administrators, covering practical problems and the first known method for solving equations.
3) By the 13th Century Golden Age of Chinese mathematics, over 30 prestigious schools had scholars like Qin Jiushao exploring solutions to quadratic and cubic equations hundreds of years before the West using similar repeated approximation methods.
The document provides a timeline of key developments in mathematics from 6000 BCE to the present. Some of the highlights include:
- The earliest written Egyptian numbers dating back to 2700 BCE which used symbols for units, tens, hundreds, and thousands.
- Babylonian mathematics from 1800 BCE which had multiplication tables and worked on solving quadratic and cubic equations.
- Early Chinese mathematics from 1600 BC which included the use of an efficient decimal place value system using bamboo rods.
- Indian mathematics from 1000 BCE which developed concepts like zero, negative numbers, and trigonometry that were later transmitted worldwide.
- Classical Greek mathematics from 624 BC which included theorems attributed to Thales and Euclid's Elements textbook.
The document provides a high-level overview of major milestones in the history of mathematics, including:
1) Early mathematical texts from Babylonian (c. 1900 BC), Egyptian (c. 2000-1800 BC), and Indian (c. 9th century BC) civilizations that approximated values like pi.
2) Key figures like Pythagoras, Euler, and Euclid of Alexandria, considered the "Father of Geometry", who authored the influential Elements textbook.
3) The progression of mathematical study in places like Egypt, India, and Mesopotamia over different historical periods under civilizations like the Sumerians, Greeks, Arabs, and more.
Ethnomathematics is the study of the relationship between mathematics and culture. It examines the distinct mathematical systems and practices of identifiable cultural groups. The goal is to better understand both the culture and mathematics, and how they connect. Some examples of ethnic groups and their traditional mathematics include:
1) The Egyptians developed measurement systems to build structures like the pyramids, and described areas of triangles and trapezoids.
2) The Chinese solved algebraic equations and used a decimal numeral system as early as 2500 BCE.
3) Muslim mathematicians in Baghdad advanced geometry and trigonometry, and the work of Al-Khowarizmi introduced algebra to the Western world.
This document provides a summary of computing technology and related sciences through history in 3 sentence summaries:
The earliest known computing devices were tally sticks used as notches carved on bones dating back 20,000 years, while copper was first used as a conductor for its properties around 10,000 years ago and megalithic structures from 5,000 BCE may have functioned as early calendars. Mathematical and scientific advances originated in ancient cultures including the earliest use of numbers in Sumerian cuneiform around 3000 BCE, Babylonian sexagesimal and Egyptian base-10 numeric systems, and Archimedes' invention of the positional decimal system. Key developments included the abacus used for calculation for millennia, Euclid's
A Reviewer for Math History and Trivia [Not Updated]eosinotphil
The document provides a brief overview of the history and origins of various mathematical concepts and tools:
- The abacus was invented in ancient China around 1200 BC and was used in many early civilizations. Algebra originated from Arabic scholars in the 3rd century BC. Differential and integral calculus were independently invented by Newton and Leibniz in the 17th century.
- Graphs and many common symbols like '=' and '>' were developed more recently, in the 16th-18th centuries to visually represent mathematical relationships and aid in calculation. Key early contributors to mathematics discussed include Archimedes, Pythagoras, and Diophantus.
- Mathematics has a long history in many ancient cultures including Egypt,
This document provides an overview of the history and development of geometry. It discusses how geometry originated with early peoples discovering principles like the Pythagorean theorem thousands of years before Pythagoras. It then covers the major developments of geometry in ancient cultures like Egypt, Babylon, Greece, China, Islamic caliphates, and the modern era. Key figures discussed include Euclid, who introduced rigorous logic and axioms still used today, and Archimedes, considered one of the greatest mathematicians for his approximations of pi and work on limits.
- Ancient Indian mathematicians made many significant contributions to areas like geometry, trigonometry, and the concept of zero. Mathematicians like Aryabhata, Brahmagupta, and Bhaskara II developed important theorems and discoveries in these fields.
- Indian mathematics originated from the construction of altars in the Vedic period. Early texts like the Sulba Sutras contained geometric concepts and theorems. Mathematicians like Baudhayana discovered the Pythagorean theorem centuries before Pythagoras.
- A key contribution was the development of the concept of zero and place-value systems by mathematicians like Aryabhata in the 5th-6th centuries AD. This
The origin of mathematical thought lie in the concepts of number, m.pdfanandf0099
The origin of mathematical thought lie in the concepts of number, magnitude, and form.[11]
Modern studies of animal cognition have shown that these concepts are not unique to humans.
Such concepts would have been part of everyday life in hunter-gatherer societies. The idea of the
\"number\" concept evolving gradually over time is supported by the existence of languages
which preserve the distinction between \"one\", \"two\", and \"many\", but not of numbers larger
than two.[11]
The oldest known possibly mathematical object is the Lebombo bone, discovered in the
Lebombo mountains of Swaziland and dated to approximately 35,000 BC.[12] It consists of 29
distinct notches cut into a baboon\'s fibula.[13] Also prehistoricartifacts discovered in Africa and
France, dated between35,000 and 20,000 years old,[14] suggest early attempts to quantify
time.[15]
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as
much as 20,000 years old and consists of a series of tally marks carved in three columns running
the length of the bone. Common interpretations are that the Ishango bone shows either the
earliest known demonstration of sequences of prime numbers[13] or a six month lunar
calendar.[16] In the book How Mathematics Happened: The First 50,000 Years, Peter Rudman
argues that the development of the concept of prime numbers could only have come about after
the concept of division, which he dates to after 10,000 BC, with prime numbers probably not
being understood until about 500 BC. He also writes that \"no attempt has been made to explain
why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and
some numbers that are almost multiples of 10.\"[17] The Ishango bone, according to scholar
Alexander Marshack, may have influenced the later development of mathematics in Egypt as,
like some entries on the Ishango bone, Egyptian arithmetic also made use of multiplication by 2;
this, however, is disputed.[18]
Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. It has
been claimed that megalithic monuments in England and Scotland, dating from the 3rd
millennium BC, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in
their design.[19]
All of the above are disputed however, and the currently oldest undisputed mathematical usage
is in Babylonian and dynastic Egyptian sources. Thus it took human beings at least 45,000 years
from the attainment of behavioral modernity and language (generally thought to be a long time
before that) to develop mathematics as such
Solution
The origin of mathematical thought lie in the concepts of number, magnitude, and form.[11]
Modern studies of animal cognition have shown that these concepts are not unique to humans.
Such concepts would have been part of everyday life in hunter-gatherer societies. The idea of the
\"number\" concept evolving gradually over time is supported by the existence of lan.
This document provides an overview of ancient Indian mathematics and astronomy, beginning with a discussion of the Sulva Sutras texts from 800-200 BCE that describe early Hindu geometry and formulas for calculating square roots and pi. It then discusses the development of the number system including the invention of zero in India, and notable Indian mathematicians like Aryabhatta who wrote on algebra and astronomy in 499 CE. The document contrasts early Greek and Indian approaches to mathematics.
The document provides a high-level overview of the history and development of mathematics from ancient civilizations to modern times. It discusses how mathematics originated in ancient Mesopotamia, Egypt, Greece, China, and India, and was further developed during the Greek period with people like Euclid and Archimedes. It then discusses how mathematics progressed during the Hindu-Arabic period with the development of Hindu-Arabic numerals and their spread by Arabs. Key developments of algebra, trigonometry, and analytic geometry during the early modern period are also summarized.
The document provides a history of number theory, beginning with its origins in ancient Mesopotamia and classical Greece. It discusses early thinkers like the Pythagoreans and Diophantus of Alexandria. It then covers developments in India with scholars like Aryabhata and Brahmagupta. Major advances are also described from the Islamic Golden Age as well as from early modern mathematicians like Fermat and Euler. Fermat made important contributions regarding perfect numbers, sums of squares, and solving Diophantine equations. Euler was inspired to study number theory by reading Fermat's work.
Mathematics is the study of relationships among quantities, magnitudes, and properties, as well as logical operations to deduce unknowns. Historically, it was regarded as the science of quantity in fields like geometry, arithmetic, and algebra. The history of mathematics is nearly as old as humanity itself and has evolved from simple counting and measurement to the complex discipline we know today. Ancient civilizations developed practical mathematics for tasks like trade, construction, and tracking seasons, which required numeration systems, arithmetic techniques, and measurement strategies.
This document provides an overview of the history of mathematics, beginning with ancient civilizations like Babylonia, Egypt, and Greece. It discusses important mathematicians and their contributions, including Pythagoras, Euclid, Archimedes, Brahmagupta, Fibonacci, Descartes, Newton, Euler, Gauss, and Ramanujan. Key advances and discoveries are highlighted, such as the development of algebra, calculus, complex numbers, and non-Euclidean geometry. The document traces the evolution of mathematics from ancient times through the modern era.
The document traces the history of mathematics from ancient civilizations to the modern era. It discusses how ancient cultures developed numeration systems and arithmetic techniques to solve practical problems. It then covers the major developments in each historical period, including the advances made by Greek mathematicians like Euclid, the transmission of knowledge between cultures during the Islamic Golden Age, and the founding of calculus and other modern branches of mathematics. The history shows how mathematics has continually built upon previous discoveries and adapted to solve new problems over thousands of years.
A final year project discussing the history and significance of the Pythagorean theorem in the ancient world.
The presentation provides information on the Babylonians, the Egyptians, the Indians and Chinese before moving on to Ancient Greece and Pythagoras himself.
Mathematics is essential in daily life and has a long history of practical applications. It first arose from needs to count and measure, and early civilizations used math for tasks like construction and accounting. Over millennia, mathematical concepts and applications have expanded greatly. Today, areas like statistics, calculus, and other quantitative fields inform domains from politics to transportation to resource management. Many people misunderstand math as only involving formulas, but it really involves abstract problem-solving and modeling real-world situations. Core topics in daily use include commercial math, algebra, statistics, and financial calculations for tasks like budgeting and investing.
This document provides a history of geometry from ancient times through the modern era. It describes how early geometrical concepts and principles were developed by ancient cultures including the Egyptians, Babylonians, and Indians. It then discusses the significant developments in geometry by ancient Greek mathematicians such as Thales, Pythagoras, Plato, Aristotle, and Euclid. Euclid is credited with revolutionizing geometry by introducing logical rigor and the axiomatic method in his influential textbook The Elements. The document continues discussing later developments in geometry through Hellenistic times and the modern era.
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This Dissertation explores the particular circumstances of Mirzapur, a region located in the
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3. PREHİSTORİC MATHEMATİCS
The origins of mathematical thought lie in the concepts of
number, magnitude, and form. Modern studies of animal cognition have
shown that these concepts are not unique to humans. Such concepts would
have been part of everyday life in hunter-gatherer societies. The idea of the
"number" concept evolving gradually over time is supported by the
existence of languages which preserve the distinction between
"one", "two", and "many", but not of numbers larger than two
The oldest known possibly mathematical object is the Lebombo
bone, discovered in the Lebombo mountains of Swaziland and dated to
approximately 35,000 BC. It consists of 29 distinct notches cut into a
baboon's fibula. Also prehistoric artifacts discovered in Africa and
4. PREHISTORIC
France, dated between 35,000 and 20,000 years old, suggest
early attempts to quantify timeThe Ishango bone, found near
the headwaters of the Nile river (northeastern Congo), may be
as much as 20,000 years old and consists of a series of tally
marks carved in three columns running the length of the bone.
Common interpretations are that the Ishango bone shows
either the earliest known demonstration of sequences of
prime numbers or a six month lunar calendar. In the book
How Mathematics Happened: The First 50,000 Years, Peter
Rudman argues that the development of the concept of prime
numbers could only have come about after the concept of
division, which he dates to after 10,000 BC, with prime
numbers probably not being understood until about 500 BC.
He also writes that "no attempt has been made to explain why
a tally of something should exhibit multiples of two, prime
numbers between 10 and 20, and some numbers that are
almost multiples of 10”
5. PREHISTORIC
Predynastic Egyptians of the 5th millennium BC pictorially represented
geometric designs. It has been claimed that megalithic monuments in
England and Scotland, dating from the 3rd millennium BC, incorporate
geometric ideas such as circles, ellipses, and Pythagorean triples in their
design
All of the above are disputed however, and the currently oldest undisputed
mathematical usage is in Babylonian and dynastic Egyptian sources. Thus it
took human beings at least 45,000 years from the attainment of behavioral
modernity and language (generally thought to be a long time before that) to
develop mathematics as such.
6. BABYLONIAN MATHEMATICS
Babylonian mathematics refers to any mathematics of the people of
Mesopotamia (modern Iraq) from the days of the early Sumerians through the
Hellenistic period almost to the dawn of Christianity.] It is named Babylonian
mathematics due to the central role of Babylon as a place of study. Later under
the Arab Empire, Mesopotamia, especially Baghdad, once again became an
important center of study for Islamic mathematics.
7. BABYLONIAN
In contrast to the sparsity of sources in Egyptian mathematics, our knowledge of
Babylonian mathematics is derived from more than 400 clay tablets unearthed
since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the
clay was moist, and baked hard in an oven or by the heat of the sun. Some of
these appear to be graded homework.
The earliest evidence of written mathematics dates back to the ancient
Sumerians, who built the earliest civilization in Mesopotamia. They developed a
complex system of metrology from 3000 BC. From around 2500 BC
onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with
geometrical exercises and division problems. The earliest traces of the
Babylonian numerals also date back to this period
8. BABYLONIAN
Babylonian mathematics were written using a sexagesimal (base-60) numeral
system. From this derives the modern day usage of 60 seconds in a minute, 60
minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of
seconds and minutes of arc to denote fractions of a degree. Babylonian
advances in mathematics were facilitated by the fact that 60 has many divisors.
Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true
place-value system, where digits written in the left column represented larger
values, much as in the decimal system. They lacked, however, an equivalent of
the decimal point, and so the place value of a symbol often had to be inferred
from the context.
9. EGYPTIAN MATHEMATICS
Image of Problem 14 from the Moscow Mathematical Papyrus. The problem
includes a diagram indicating the dimensions of the truncated pyramid.
Egyptian mathematics refers to mathematics written in the Egyptian language.
From the Hellenistic period, Greek replaced Egyptian as the written language of
Egyptian scholars.
10. EGYPTIAN
The most extensive Egyptian mathematical text is the Rhind papyrus
(sometimes also called the Ahmes Papyrus after its author), dated to c. 1650 BC
but likely a copy of an older document from the Middle Kingdom of about 2000-
1800 BC. It is an instruction manual for students in arithmetic and geometry. In
addition to giving area formulas and methods for multiplication, division and
working with unit fractions, it also contains evidence of other mathematical
knowledge, including composite and prime numbers; arithmetic, geometric and
harmonic means; and simplistic understandings of both the Sieve of
Eratosthenes and perfect number theory (namely, that of the number 6)It also
shows how to solve first order linear equations as well as arithmetic and
geometric series
11. GREEK MATHEMATICS
The Pythagorean theorem. The Pythagoreans are generally credited with the
first proof of the theorem.
Greek mathematics refers to the mathematics written in the Greek language
from the time of Thales of Miletus (~600 BC) to the closure of the Academy of
Athens in 529 AD. Greek mathematicians lived in cities spread over the entire
Eastern Mediterranean, from Italy to North Africa, but were united by culture and
language. Greek mathematics of the period following Alexander the Great is
sometimes called Hellenistic mathematics
12. GREEK
Greek mathematics was much more sophisticated than the mathematics that
had been developed by earlier cultures. All surviving records of pre-Greek
mathematics show the use of inductive reasoning, that is, repeated observations
used to establish rules of thumb. Greek mathematicians, by contrast, used
deductive reasoning. The Greeks used logic to derive conclusions from
definitions and axioms, and used mathematical rigor to prove them
Greek mathematics is thought to have begun with Thales of Miletus (c. 624–
c.546 BC) and Pythagoras of Samos (c. 582–c. 507 BC). Although the extent of
the influence is disputed, they were probably inspired by Egyptian and
Babylonian mathematics. According to legend, Pythagoras traveled to Egypt to
learn mathematics, geometry, and astronomy from Egyptian priests.
13. GREEK
Eudoxus (408–c.355 BC) developed the method of exhaustion, a precursor of
modern integration and a theory of ratios that avoided the problem of
incommensurable magnitudes,The former allowed the calculations of areas and
volumes of curvilinear figures, while the latter enabled subsequent geometers to
make significant advances in geometry. Though he made no specific technical
mathematical discoveries, Aristotle (384—c.322 BC) contributed significantly to
the development of mathematics by laying the foundations of logic
14. CHINESE MATHEMATICS
The Nine Chapters on the Mathematical Art, one of the earliest surviving
mathematical texts from China (2nd century AD).
Early Chinese mathematics is so different from that of other parts of the
world that it is reasonable to assume independent development. The
oldest extant mathematical text from China is the Chou Pei Suan
Ching, variously dated to between 1200 BC and 100 BC, though a date
of about 300 BC appears reasonable
15. CHINESE
Of particular note is the use in Chinese mathematics of a decimal positional
notation system, the so-called "rod numerals" in which distinct ciphers were
used for numbers between 1 and 10, and additional ciphers for powers of ten
Thus, the number 123 would be written using the symbol for "1", followed by the
symbol for "100", then the symbol for "2" followed by the symbol for
"10", followed by the symbol for "3". This was the most advanced number
system in the world at the time, apparently in use several centuries before the
common era and well before the development of the Indian numeral system.
Rod numerals allowed the representation of numbers as large as desired and
allowed calculations to be carried out on the suan pan, or Chinese abacus. The
date of the invention of the suan pan is not certain, but the earliest written
mention dates from AD 190, in Xu Yue's Supplementary Notes on the Art of
Figures.
16. INDIAN MATHEMATICS
Main article: Indian mathematics
See also: History of the Hindu-Arabic numeral system
The numerals used in the Bakhshali manuscript, dated between the 2nd century
BCE and the 2nd century CE.
The earliest civilization on the Indian subcontinent is the Indus Valley Civilization
that flourished between 2600 and 1900 BC in the Indus river basin. Their cities
were laid out with geometric regularity, but no known mathematical documents
survive from this civilization
17. ISLAMIC MATHEMATICS
The Islamic Empire established across Persia, the Middle East, Central
Asia, North Africa, Iberia, and in parts of India in the 8th century made significant
contributions towards mathematics. Although most Islamic texts on mathematics
were written in Arabic, most of them were not written by Arabs, since much like
the status of Greek in the Hellenistic world, Arabic was used as the written
language of non-Arab scholars throughout the Islamic world at the time.
Persians contributed to the world of Mathematics alongside Arabs.
18. MEDIEVAL EUROPEAN MATHEMATICS
Medieval European interest in mathematics was driven by concerns quite
different from those of modern mathematicians. One driving element was the
belief that mathematics provided the key to understanding the created order of
nature, frequently justified by Plato's Timaeus and the biblical passage (in the
Book of Wisdom) that God had ordered all things in measure, and number, and
weight.
Boethius provided a place for mathematics in the curriculum in the 6th century
when he coined the term quadrivium to describe the study of arithmetic,
geometry, astronomy, and music. He wrote De institutione arithmetica, a free
translation from the Greek of Nicomachus's Introduction to Arithmetic; De
institutione musica, also derived from Greek sources; and a series of excerpts
from Euclid's Elements. His works were theoretical, rather than practical, and
were the basis of mathematical study until the recovery of Greek and Arabic
mathematical works.
19. RENAISSANCE MATHEMATICS
During the Renaissance, the development of mathematics and of accounting
were intertwined. While there is no direct relationship between algebra and
accounting, the teaching of the subjects and the books published often intended
for the children of merchants who were sent to reckoning schools (in Flanders
and Germany) or abacus schools (known as abbaco in Italy), where they learned
the skills useful for trade and commerce. There is probably no need for algebra
in performing bookkeeping operations, but for complex bartering operations or
the calculation of compound interest, a basic knowledge of arithmetic was
mandatory and knowledge of algebra was very useful.
20. MODERN MATHEMATICS
This century saw the development of the two forms of non-Euclidean
geometry, where the parallel postulate of Euclidean geometry no longer holds.
The Russian mathematician Nikolai Ivanovich Lobachevsky and his rival, the
Hungarian mathematician János Bolyai, independently defined and studied
hyperbolic geometry, where uniqueness of parallels no longer holds. In this
geometry the sum of angles in a triangle add up to less than 180°. Elliptic
geometry was developed later in the 19th century by the German mathematician
Bernhard Riemann; here no parallel can be found and the angles in a triangle
add up to more than 180°. Riemann also developed Riemannian
geometry, which unifies and vastly generalizes the three types of geometry, and
he defined the concept of a manifold, which generalizes the ideas of curves and
surfaces.