Module 1. History of Mathematics Flashcards
The Mathematics that we know in the modern world has its roots in ancient __, __, and __
- Mesopotamia
- Egypt
- Babylonia
Mathematics was then developed in __, and simultaneously in __ and in __
- Greece
- China
- India
This ancient Greek mathematics, along with some influence of __ mathematics spread to the neighboring countries in the __ __
- Hindu (mathematics)
- Middle East
Mathematics was translated into __ and __, and was adopted by __ __
- Arabic and Latin
- Western Europe
- first people to assign symbols to group of objects to represent numbers
- developed the earliest known writing system
Sumerians
Sumerians are from
Sumer, a region of Mesopotamia
What writing system did the Sumerians develop
cuneiform script (pictographic writing system)
When: Sumerians
4,000 - 3,000 B.C.E.
first people to develop a numerical system that was based on the number 10
Egyptians
What developed in Egypt
Hieroglyphic Numerals
When: Egyptians
3,000 B.C.E.
used the Sexagesimal System
Babylonians
What did the Babylonians use
Sexagesimal Numeral System
When: Babylonians
2,400 B.C.E.
When was the major Greek progress in mathematics
300 BC - 200 AD
What did Euclid write during 300 BC - 200 AD era
Elements
compilation of theorems, axioms in Algebra and postulates and theorems in Geometry
Elements
With the Elements, Euclid gained the title of
Father of Geometry
When: major Greek progress
300 B.C.E.
- a Greek mathematician, physicist, inventor and astronomer
- derived a range of formulas in Geometry
Archimedes of Syracuse
What are the formulas that Archimedes derived
- area of circle
- surface area and volume of sphere
- area under a parabola
When: Archimedes of Syracuse
200 B.C.E.
Greek astronomer, geographer, and mathematician considered as founder of trigonometry
Hipparchus of Nicaea
When: Trigonometry of Hipparchus
140 B.C.E.
When: Hindu mathematical works translated to Arabic
775 C.E.
How did the Arabic Algebra and Indian numerals come to Western Europe
through Muhammad ibn Musa Al-Khwarizmi’s writings
Other Arabic scholars also cultivated Greek mathematics translating the writing of __, __, __, __, etc. into Arabic
- Apollonius
- Archimedes
- Euclid
- Ptolemy
When: Arabic Algebra and Indian numerals came to Western Europe
830 C.E.
- also called Fibonacci
- wrote Liber Abaci
Leonardo of Pisa
Leonardo of Pisa is also called
Fibonacci
What did Leonardo of Pisa write
Liber Abaci
a book filled with arithmetical and algebraic information which he had collected during his travels
Liber Abaci
Liber Abaci was one of the means by which the ___________ was introduced to Western Europe
Hindu-Arabic System of Numeration
What is the best known contribution of Hindu mathematics to modern mathematics?
decimal position system
What did the Hindi mathematics also introduce
number zero
When: Leonardo of Pisa
1202 C.E.
- German mathematician
- the + and - first appeared in print in his book
Johannes Widmann
What is the book where the + and - symbols first appeared
Mercantile Arithmetic
When and where was the Mercantile Arithmetic book published
Leipzig in 1489
Mercantile Arithmetic referred to
surpluses and deficits in business problems
When: Johannes Widmann
1489 C.E.
discovered logarithms
John Napier
What did John Napier discover
logarithms
When: John Napier
17th century
- given credit for early developments that led to infinitesimal calculus
- French lawyer and mathematician
Pierre de Fermat
Pierre de Fermat was given credit for early developments that led to what
infinitesimal calculus
__ and __ began the mathematical study of probability
- Fermat
- Pascal
What did Fermat and Pascal begin
mathematical study of probability
laid the foundations of the Probability Theory together with Fermat
Blaise Pascal
early mechanical calculator
Pascaline
tool for expanding a binomial
Pascal’s Triangle
binomial
(a + b)^n
- invented the Cartesian coordinate system
- developed analytic geometry
- laid foundation for the development of calculus
- another notable mathematician of the 17th century
Rene Descartes
Rene Descartes invented the __ __ __
Cartesian coordinate system
Rene Descartes developed __ __
analytic geometry
Rene Descartes laid the foundation for the development of __
calculus
When: Pierre de Fermat, Blaise Pascal, Rene Descartes
1629 C.E.
- discovered infinitesimal calculus along with Sir Isaac Newton
- each one made the discovery alone, not while working together
Gottfried Leibniz
When: Leibniz’ first paper on the calculus published
1684 C.E.
- most important mathematician of the 18th century
- worked in a wide range of mathematical areas
- started the Graph Theory, the Calculus of Variations, and Differential Geometry
Leonhard Euler
Leonhard Euler started the __ __, the __ __ __, and __ __
- Graph Theory
- Calculus of Variations
- Differential Geometry
- German mathematician
- regarded as one of the greatest mathematicians of all time
- contributed to number theory, geometry, probability theory, planetary, and the theory of functions
- proved the Fundamental Theorem of Algebra
Carl Friedrich Gauss
Carl Friedrich Gauss contributed to __ __, __, __ __, __, and the __ _ __
- number theory
- geometry
- probability theory
- planetary
- theory of functions
When did Carl Friedrich Gauss prove the Fundamental Theorem of Algebra
1799
What did Carl Friedrich Gauss prove in 1799
Fundamental Theorem of Algebra
- began a rigorous theory of functions and of mechanics toward the end of 18th century
- played a key role in the creation of the Metric system of weights and measures
Joseph Louie Lagrange
What did Joseph Louie Lagrange began toward the end of the 18th century
rigorous theory of functions and of mechanics
Joseph Louie Lagrange played a key role in the creation of the __ __ of weights and measures
Metric system
introduced the Venn Diagram in 1874 which became a useful tool in Set Theory
John Venn
What did John Venn introduce in 1874
Venn Diagram
When did John Venn introduce the Venn Diagram
1874
The Venn diagram became a useful tool in __ __
Set Theory
When: Leonhard Euler, Carl Friedrich Gauss, Joseph Louie Lagrange, John Venn
18th - 19th Century
- introduced the theory of fractals
- published The Fractal Geometry of Nature in 1982
Benoit Mandelbrot
What did Benoit Mandelbrot introduce
theory of fractals
When did Benoit Mandelbrot publish The Fractal Geometry of Nature
1982
What did Benoit Mandelbrot publish in 1982
The Fractal Geometry of Nature
When: Benoit Mandelbrot
1975 C.E.
proved Fermat’s Last Theorem
Andrew Wiles
What did Andrew Wiles prove
Fermat’s Last Theorem
When: Andrew Wiles
1994 C.E.
What was announced in 2000 C.E.
Mathematical challenges of the 21st Century
When: Mathematical challenges of the 21st Century announced
2000 C.E.
