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 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.
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.
The document provides a brief history of mathematics from ancient to modern periods. It covers the development of numeration systems and arithmetic, geometry, algebra, trigonometry, calculus, and analytic geometry. Key developments include ancient civilizations developing practical math for trade and construction, Greeks establishing logic-based math and Euclidean geometry, Hindus and Arabs advancing the decimal numeral system and algebra, and Europeans in the early modern period making advances in trigonometry, logarithms, analytic geometry, and calculus.
The document provides a brief history of mathematics from ancient civilizations to modern times. It summarizes that ancient mathematics developed in Mesopotamia, Egypt, Babylonia, Greece, China, and India to meet practical needs like trade, construction, and tracking seasons. Key developments included numeration systems, arithmetic techniques, measurement strategies, and early geometry. It then discusses important contributions from Greek mathematicians like Euclid, Archimedes, and Apollonius that advanced the field, establishing logic-based systems and analyzing geometric concepts like conic sections. The document traces how these ancient Greek mathematics spread and influenced other civilizations over time.
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.
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.
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.
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 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.
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.
The document provides a brief history of mathematics from ancient to modern periods. It covers the development of numeration systems and arithmetic, geometry, algebra, trigonometry, calculus, and analytic geometry. Key developments include ancient civilizations developing practical math for trade and construction, Greeks establishing logic-based math and Euclidean geometry, Hindus and Arabs advancing the decimal numeral system and algebra, and Europeans in the early modern period making advances in trigonometry, logarithms, analytic geometry, and calculus.
The document provides a brief history of mathematics from ancient civilizations to modern times. It summarizes that ancient mathematics developed in Mesopotamia, Egypt, Babylonia, Greece, China, and India to meet practical needs like trade, construction, and tracking seasons. Key developments included numeration systems, arithmetic techniques, measurement strategies, and early geometry. It then discusses important contributions from Greek mathematicians like Euclid, Archimedes, and Apollonius that advanced the field, establishing logic-based systems and analyzing geometric concepts like conic sections. The document traces how these ancient Greek mathematics spread and influenced other civilizations over time.
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.
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.
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.
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.
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.
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.
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.
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, discoveries, and texts from each historical period and culture.
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.
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.
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.
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.
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.
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.
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
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 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.
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.
Islamic mathematics flourished between the 7th-16th centuries under Islamic empires spanning the Middle East and North Africa. Key developments included establishing algebra as its own discipline through the works of al-Khwarizmi, who wrote the first book systematically dealing with algebraic equations up to the second degree. Omar Khayyam expanded on this by providing both geometric and algebraic solutions to cubic equations. Later mathematicians like al-Karaji, al-Tusi, and al-Qalasadi further advanced algebraic notation and concepts like the binomial theorem and trigonometry. Their works had significant influence on mathematics in other cultures.
The History of Mathematics and Application of Matrices.pptxSamjhauta Thapa
This document discusses the history of mathematics and applications of matrices to business and economics. It begins by covering the development of numeration systems and arithmetic techniques in ancient civilizations. It then discusses the evolution of mathematics through various periods, including developments in geometry, algebra, calculus, and modern abstract concepts. The document concludes by providing examples of how matrices can represent economic and business situations, and how operations like addition, subtraction, and multiplication on matrices can model real-world scenarios. Specific applications to economics are discussed, including using matrices to calculate GDP and model input-output relationships between industries using the Leontief model.
International Journal of Computational Engineering Research(IJCER) ijceronline
This document provides a historical overview of the development of the Fundamental Theorem of Algebra. It discusses early contributions from mathematicians like Diophantus, Cardan, Euler, and Gauss. It describes how earlier proofs were flawed because they assumed the existence of roots before proving them. The first rigorous proof is credited to Gauss in 1799, who showed that assuming the existence of roots first is circular reasoning. Later proofs include one by Argand in 1814 using the concept of minimization of continuous functions.
Islamic & arabic contributions to mathematicsTony Guerra
The document provides an overview of the contributions of Islamic/Arabian civilization to mathematics and science during their Golden Age from approximately the 8th to 13th centuries. Some key contributions included developing the concept of zero, the decimal numeral system, and advances in algebra, trigonometry, and geometry that were built upon Greek and Indian mathematics. Many important Islamic scholars are mentioned who made advances in fields like optics, astronomy, medicine, and engineering.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
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.
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.
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.
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, discoveries, and texts from each historical period and culture.
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.
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.
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.
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.
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.
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.
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
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 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.
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.
Islamic mathematics flourished between the 7th-16th centuries under Islamic empires spanning the Middle East and North Africa. Key developments included establishing algebra as its own discipline through the works of al-Khwarizmi, who wrote the first book systematically dealing with algebraic equations up to the second degree. Omar Khayyam expanded on this by providing both geometric and algebraic solutions to cubic equations. Later mathematicians like al-Karaji, al-Tusi, and al-Qalasadi further advanced algebraic notation and concepts like the binomial theorem and trigonometry. Their works had significant influence on mathematics in other cultures.
The History of Mathematics and Application of Matrices.pptxSamjhauta Thapa
This document discusses the history of mathematics and applications of matrices to business and economics. It begins by covering the development of numeration systems and arithmetic techniques in ancient civilizations. It then discusses the evolution of mathematics through various periods, including developments in geometry, algebra, calculus, and modern abstract concepts. The document concludes by providing examples of how matrices can represent economic and business situations, and how operations like addition, subtraction, and multiplication on matrices can model real-world scenarios. Specific applications to economics are discussed, including using matrices to calculate GDP and model input-output relationships between industries using the Leontief model.
International Journal of Computational Engineering Research(IJCER) ijceronline
This document provides a historical overview of the development of the Fundamental Theorem of Algebra. It discusses early contributions from mathematicians like Diophantus, Cardan, Euler, and Gauss. It describes how earlier proofs were flawed because they assumed the existence of roots before proving them. The first rigorous proof is credited to Gauss in 1799, who showed that assuming the existence of roots first is circular reasoning. Later proofs include one by Argand in 1814 using the concept of minimization of continuous functions.
Islamic & arabic contributions to mathematicsTony Guerra
The document provides an overview of the contributions of Islamic/Arabian civilization to mathematics and science during their Golden Age from approximately the 8th to 13th centuries. Some key contributions included developing the concept of zero, the decimal numeral system, and advances in algebra, trigonometry, and geometry that were built upon Greek and Indian mathematics. Many important Islamic scholars are mentioned who made advances in fields like optics, astronomy, medicine, and engineering.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
3. The Mathematics that we know in the modern world has its roots in ancient
Mesopotamia, Egypt and Babylonia. Then it was developed in Greece, and
simultaneously in China and in India. This ancient Greek mathematics, along
with some influence of Hindu mathematics spread to the neighboring countries
in the Middle East. It was translated into Arabic and Latin and was adopted by
Western Europe. Western education was spread throughout the world by
colonization and trade. Today’s Mathematics has been enriched by the
contributions of different civilizations and individual mathematicians who
unselfishly passed on their discoveries and knowledge to us. It is therefore
fitting for us to look back and appreciate how Mathematics have developed
and who made these developments possible.
Overview/Introduction:
4. A. Number Systems and Arithmetic
• Development of numeration systems.
• Creation of arithmetic techniques, lookup tables, the abacus and other
calculation tools.
B. Practical Measurement, Geometry and Astronomy
• Measurement units devised to quantify distance, area, volume, and
time.
• Geometric reasoning used to measure distances indirectly.
• Calendars invented to predict seasons, astronomical events.
• Geometrical forms and patterns appear in art and architecture.
Ancient Period (3000 B.C. to 260 A.D.)
5. Practical Mathematics
As ancient civilizations developed, the
need for practical mathematics
increased. They required numeration
systems and arithmetic techniques for
trade, measurement strategies for
construction, and astronomical
calculations to track the seasons and
cosmic cycles.
6. Babylonian Numerals
The Babylonian Tablet Plimpton 322
This mathematical tablet was recovered from an unknown place in the Iraqi
desert. It was written originally sometime around 1800 BC. The tablet
presents a list of Pythagorean triples written in Babylonian numerals. This
numeration system uses only two symbols and a base of sixty.
7. Chinese Mathematics
Diagram from Chiu Chang
Suan Shu, an ancient Chinese
mathematical text from the
Han Dynasty (206 B.C. to A.D.
220).
This book consists of nine
chapters of mathematical
problems. Three involve
surveying and engineering
formulas, three are devoted to
problems of taxation and
bureaucratic administration,
and the remaining three to
specific computational
techniques. Demonstration of the Gou-Gu
(Pythagorean) Theorem
9. A. Greek Logic and Philosophy
• Greek philosophers promote logical, rational explanations of
natural phenomena.
• Schools of logic, science and mathematics are established.
• Mathematics is viewed as more than a tool to solve practical
problems; it is seen as a means to understand divine laws.
• Mathematicians achieve fame, are valued for their work.
B. Euclidean Geometry
• The first mathematical system based on postulates, theorems and
proofs appears in Euclid's Elements.
Greek Period (600 B.C. to 450 A.D.)
10. Area of Greek Influence
Archimedes of
Syracuse
Euclid and Ptolemy of
Alexandria
Pythagoras of
Crotona
Apollonius of
Perga
Eratosthenes of
Cyrene
11. Mathematics and Greek Philosophy
Greek philosophers viewed the universe in mathematical terms.
Plato described five elements that form the world and related
them to the five regular polyhedra.
12. Euclid’s Elements
Greek, c. 800 Arabic, c. 1250 Latin, c. 1120
French, c. 1564 English, c. 1570 Chinese, c. 1607
Translations of Euclid’s Elements of Gemetry:
The Pythagorean Theorem
15. Archimedes Screw
Archimedes’ screw is a mechanical device used to lift water and such light
materials as grain or sand. To pump water from a river, for example, the
lower end is placed in the river and water rises up the spiral threads of the
screw as it is revolved.
16. Ptolemaic System
Ptolemy described an Earth-
centered solar system in his book
The Almagest.
The system fit well with the
Medieval world view, as shown
by this illustration of Dante.
17. Hindu-Arabian Period (200 B.C. to 1250 A.D. )
A. Development and Spread of Hindu-Arabic Numbers
• A numeration system using base 10, positional notation, the zero symbol and
powerful arithmetic techniques is developed by the Hindus, approx. 150 B.C. to
800 A.D..
• The Hindu numeration system is adopted by the Arabs and spread throughout
their sphere of influence (approx. 700 A.D. to 1250 A.D.).
B. Preservation of Greek Mathematics
• Arab scholars copied and studied Greek mathematical works, principally in
Baghdad.
C. Development of Algebra and Trigonometry
• Arab mathematicians find methods of solution for quadratic, cubic and higher
degree polynomial equations. The English word “algebra” is derived from the
title of an Arabic book describing these methods.
• Hindu trigonometry, especially sine tables, is improved and advanced by Arab
mathematicians
19. Baghdad and the House of Wisdom
About the middle of the ninth
century Bait Al-Hikma, the "House
of Wisdom" was founded in
Baghdad which combined the
functions of a library, academy, and
translation bureau.
Baghdad attracted scholars from
the Islamic world and became a
great center of learning.
Painting of ancient Baghdad
20. The Great Mosque of Cordoba
The Great Mosque, Cordoba
During the Middle Ages
Cordoba was the greatest
center of learning in Europe,
second only to Baghdad in the
Islamic world.
22. Arabic Translation of Ptolemy’s Almagest
Pages from a
13th century
Arabic edition
of Ptolemy’s
Almagest.
23. Islamic Astronomy and Science
Many of the sciences developed from
needs to fulfill the rituals and duties of
Muslim worship. Performing formal
prayers requires that a Muslim faces
Mecca. To find Mecca from any part of the
globe, Muslims invented the compass and
developed the sciences of geography and
geometry.
Prayer and fasting require knowing the
times of each duty. Because these times
are marked by astronomical phenomena,
the science of astronomy underwent a
major development.
Painting of astronomers at work in
the observatory of Istanbul
24. Al-Khwarizmi
Abu Abdullah Muhammad bin Musa al-
Khwarizmi, c. 800 A.D. was a Persian
mathematician, scientist, and author. He
worked in Baghdad and wrote all his
works in Arabic.
He developed the concept of an
algorithm in mathematics. The words
"algorithm" and "algorism" derive
ultimately from his name. His systematic
and logical approach to solving linear and
quadratic equations gave shape to the
discipline of algebra, a word that is
derived from the name of his book on the
subject, Hisab al-jabr wa al-muqabala
(“al-jabr” became “algebra”).
26. A. Discovery of Greek and Hindu-Arab mathematics
• Greek mathematics texts are translated from Arabic into
Latin; Greek ideas about logic, geometrical reasoning,
and a rational view of the world are re-discovered.
• Arab works on algebra and trigonometry are also
translated into Latin and disseminated throughout
Europe.
B. Spread of the Hindu-Arabic numeration system
• Hindu-Arabic numerals slowly spread over Europe
• Pen and paper arithmetic algorithms based on Hindu-
Arabic numerals replace the use the abacus.
Period of Transmission (1000 AD – 1500 AD)
27. Leonardo of Pisa
From Leonardo of Pisa’s famous book Liber Abaci (1202 A.D.):
"These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1.
With these nine figures, and with this sign 0 which in Arabic is
called zephirum, any number can be written, as will be
demonstrated."
28. “Jealousy” Multiplication
Page from an anonymous Italian treatise
on arithmetic, 1478.
16th century Arab copy of an early
work using Indian numerals to show
multiplication. Top example is 3 x 64,
bottom is 543 x 342.
29. This woodblock engraving of a
competition between arithmetic
techniques is from from
Margarita Philosphica by
Gregorius Reich, (Freiburg, 1503).
Lady Arithmetic, standing in the
center, gives her judgment by
smiling on the arithmetician
working with Arabic numerals
and the zero.
The Abacists and Algorists Compete
30. Rediscovery of Greek Geometry
Luca Pacioli (1445 - 1514), a
Franciscan friar and
mathematician, stands at a
table filled with geometrical
tools (slate, chalk, compass,
dodecahedron model, etc.),
illustrating a theorem from
Euclid, while examining a
beautiful glass
rhombicuboctahedron half-
filled with water.
31. Pacioli and Leonardo Da Vinci
Luca Pacioli's 1509 book The Divine Proportion was illustrated by
Leonardo Da Vinci.
Shown here is a drawing of an icosidodecahedron and an "elevated"
form of it. For the elevated forms, each face is augmented with a
pyramid composed of equilateral triangles.
32. Early Modern Period (1450 A.D. – 1800 A.D.)
A. Trigonometry and Logarithms
• Publication of precise trigonometry tables, improvement of surveying methods using
trigonometry, and mathematical analysis of trigonometric relationships. (approx. 1530 –
1600)
• Logarithms introduced by Napier in 1614 as a calculation aid. This advances science in a
manner similar to the introduction of the computer
B. Symbolic Algebra and Analytic Geometry
• Development of symbolic algebra, principally by the French mathematicians Viete and
Descartes
• The cartesian coordinate system and analytic geometry developed by Rene Descartes
and Pierre Fermat (1630 – 1640)
C. Creation of the Calculus
• Calculus co-invented by Isaac Newton and Gottfried Leibniz. Major ideas of the calculus
expanded and refined by others, especially the Bernoulli family and Leonhard Euler.
(approx. 1660 – 1750).
• A powerful tool to solve scientific and engineering problems, it opened the door to a
scientific and mathematical revolution.
33. In his influential treatise In Artem
Analyticam Isagoge (Introduction
to the Analytic Art, published
in1591) Viète demonstrated the
value of symbols. He suggested
using letters as symbols for
quantities, both known and
unknown.
François Viète
1540-1603
Viète and Symbolic Algebra
34. The Conic Sections and Analytic Geometry
General Quadratic Relation
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Parabola
-x2 + y = 0
Ellipse
4x2 + y2 - 9 = 0
Hyperbola
x2 – y2 – 4 = 0
35. Some Famous Curves
Fermat’s Spiral
r2 = a2
Archimede’s Spiral
r = a
Trisectrix of Maclaurin
y2(a + x) = x2(3a - x)
Lemniscate of Bernoulli
(x2 + y2)2 = a2(x2 - y2)
Limacon of Pascal
r = b + 2acos()
36. Curves and Calculus: Common Problems
Find the area between curves.
Find the volume and
surface area of a
solid formed by
rotating a curve.
Find the length of a curve.
Find measures of a curve’s shape.
37. Napier’s Logarithms
In his Mirifici Logarithmorum Canonis
descriptio (1614) the Scottish
nobleman John Napier introduced
the concept of logarithms as an aid
to calculation.
John Napier
1550-1617
38. Henry Briggs and the Development of Logarithms
Napier’s concept of a logarithm is not
the one used today. Soon after
Napier’s book was published the
English mathematician Henry Briggs
collaborated with him to develop the
modern base 10 logarithm. Tables of
this logarithm and instructions for
their use were given in Briggs’ book
Arithmetica Logarithmica (1624). A
page from this work is shown on the
left.
Logarithms revolutionized scientific
calculations and effectively “doubled
the life of the astronomer”. (LaPlace)
39. Kepler and the Platonic Solids
Johannes Kepler
1571-1630
Kepler’s first attempt to
describe planetary orbits used a
model of nested regular
polyhedra (Platonic solids).
40. Newton’s Calculus
Newton developed the main
ideas of his calculus in private
as a young man. This research
was closely connected to his
studies in physics. Many years
later he published his results to
establish priority for himself as
inventor the calculus.
Newton’s Analysis Per Quantitatum
Series, Fluxiones, Ac Differentias,
1711, describes his calculus.
41. Leibniz’s Calculus
Leibniz and Newton independently
developed the calculus during the
same time period. Although
Newton’s version of the calculus led
him to his great discoveries, Leibniz’s
concepts and his style of notation
form the basis of modern calculus.
Gottfied Leibniz
1646 - 1716
A diagram from Leibniz's famous
1684 article in the journal Acta
eruditorum.
42. Leonhard Euler
Leonhard Euler was of the generation that
followed Newton and Leibniz. He made
contributions to almost every field of
mathematics and was the most prolific
mathematics writer of all time.
His trilogy, Introductio in analysin infinitorum,
Institutiones calculi differentialis, and Institutiones
calculi integralis made the function a central part
of calculus. Through these works, Euler had a
deep influence on the teaching of
mathematics. It has been said that all calculus
textbooks since 1748 are essentially copies of
Euler or copies of copies of Euler.
Euler’s writing standardized modern mathematics
notation with symbols such as:
f(x), e, , i and .
Leonhard Euler
1707 - 1783
43. Modern Period (1800 A.D. – Present)
A. Non-Euclidean Geometry
• Gauss, Lobachevsky, Riemann and others develop alternatives to Euclidean geometry in the 19th century.
• The new geometries inspire modern theories of higher dimensional spaces, gravitation, space curvature and nuclear
physics.
B. Set Theory
• Cantor studies infinite sets and defines transfinite numbers
• Set theory used as a theoretical foundation for all of mathematics
C. Statistics and Probability
• Theories of probability and statistics are developed to solve numerous practical applications, such as weather
prediction, polls, medical studies etc.; they are also used as a basis for nuclear physics
D. Computers
• Development of electronic computer hardware and software solves many previously unsolvable problems; opens
new fields of mathematical research
E. Mathematics as a World-Wide Language
• The Hindu-Arabic numeration system and a common set of mathematical symbols are used and understood
throughout the world.
• Mathematics expands into many branches and is created and shared world-wide at an ever-expanding pace; it is
now too large to be mastered by a single mathematician
44. Non-Euclidean Geometry
In the 19th century Gauss, Lobachevsky, Riemann and other
mathematicians explored the possibility of alternative geometries
by modifying the 5th postulate of Euclid’s Elements.
This opened the door to greater abstraction in geometrical
thinking and expanded the ways in which scientists use
mathematics to model physical space.
Bernhard Riemann
1826 - 1866
Nikolai Lobachevsky
1792 - 1856
Carl Gauss
1777 - 1855
45. Pioneers of Statistics
In the early 20th century a
group of English
mathematicians and
scientists developed
statistical techniques that
formed the basis of
contemporary statistics.
William Gosset
1876 - 1937
Francis Galton
1822 - 1911
Karl Pearson
1857 - 1936
Ronald Fisher
1890- 1962
46. Gossett’s Student t Curve
Diagram from the ground breaking 1908 article “Probable
Error of the Mean” by Student (William S. Gossett).
47. ENIAC: First Electronic Computer
In 1946 John W.
Mauchly and J.
Presper Eckert Jr.
built ENIAC at the
University of
Pennsylvania.
It weighed 30
tons, contained
18,000 vacuum
tubes and could
do 100,000
calculations per
second.
48. Von Neumann and the Theory of Computing
John von Neumann with Robert Oppenheimer
in front of the computer built for the Institute
of Advanced Studies in Princeton, early 1950s.
Von Neumann
Architecture