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Mathematics In The Modern World > History Of Mathematics > Flashcards

History Of Mathematics Flashcards

1
Q

Mathematics has its roots in _________, __________ and _________.

A

Mesopotamia, Egypt and Babylonia

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2
Q

Mathematics was developed in __________ and simultaneously in __________ and India.

A

Greece, China and India.

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3
Q

Spread to the neighboring countries in Middle East.

A

Greek mathematics together with Hindu mathematics.

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4
Q

In what language does Greek mathematics and Hindu mathematics translated?

A

Arabic and Latin

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5
Q

Which country adopted the translated mathematics?

A

Western Europe.

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6
Q

It spread throughout the world by civilizations and trade.

A

Western education

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7
Q

How does the western education spread?

A

By civilizations and trade

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8
Q

Mathematics started in 4000-3000 B. C. E ancient times in which place?

A

Sumer, Egypt and Babylon

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9
Q

300 B. C. E - 200 B. C. E

A

Greek times

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10
Q

Major progress of Greek mathematics happened in _________.

A

300-200 B. C. E

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11
Q

Mathematicians in Greek mathematics

A

Euclid
Archimede of Syracus
Hipparchus

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12
Q

775-1202 C. E

A

Hindu times

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13
Q

What happened in 775 C. E?

A

The Hindu mathematical works was translated into Arabic.

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14
Q

1489 C. E.

A

Western Europe

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15
Q

It is a region in Mesopotamia.

A

Sumer

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16
Q

What did the sumerians do?

A

They assign symbols to a group of objects to represent numbers.

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17
Q

Two works of the sumerians

A

-Assigned symbols to objects to represent numbers.
- developed the cuneiform script.

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18
Q

They were the first people to assign symbols to a group of objects to represent numbers.

A

Sumerians

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19
Q

Cuneiform script that was developed by the sumerians.

A

Earliest known writing system or pictographic numerals.

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20
Q

Mathematics takes place in Egypt in the year

A

3000 B. C. E

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21
Q

First people to developed a numerical system that was based on number 10.

A

Egyptians

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22
Q

Another work of Egyptians that they developed

A

Hieroglyphic numerals.

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23
Q

2400 B. C. E.

A

Babylonia

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24
Q

Babylonians used a ___________.

A

Sexagesimal system

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25
Q

A base 60 system.

A

Sexagesimal system

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26
Q

300-200 B. C. E.

A

Greek mathematics takes place

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27
Q

The major _______ progress in mathematics happens in 300-200 B. C. E.

A

Greek

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28
Q

Who wrote the Elements?

A

Euclid

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29
Q

A compilation of theorems, axioms in Algebra and postulates and theorems in Geometry.

A

The Elements

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30
Q

What did Euclid gain from writing the Elements?

A

The title “Father of Geometry”

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31
Q

Year when Archimedes of Syracus derived a range of formulas.

A

200 B.C.E.

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32
Q

He is a Greek mathematician, physicist, inventor and astronomer.

A

Archimedes of Syracus.

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33
Q

In what problems did Archimedes derived range of formulas?

A

Area of a circle, surface area and volume of a sphere and the area under a parabola.

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34
Q

He derived a range of formulas in area of circle, surface area and volume of a sphere and area under the parabola.

A

Archimedes of Syracus

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35
Q

Trigonometry of Hipparchus was published in _________.

A

140 B. C. E.

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36
Q

A Greek astronomer, geographer and mathematician.

A

Hipparchus

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37
Q

Hipparchus is considered to be the founder of ___________.

A

Trigonometry

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38
Q

Hindu mathematics started in __________

A

775 B. C. E.

39
Q

In what year did the Hindu mathematical works was translated into Arabic.

A

775 B. C. E.

40
Q

Hindu mathematical works was translated into __________.

A

Arabic

41
Q

In __________, Muhammad Ibn Musa Al khwarizmi introduced the Arabic algebra and Indian numerals in western Europe.

A

830 C. E.

42
Q

How did Muhammad Ibn Musa Al Khwarizmi introduce the Arabic algebra and Indian Numerals to western Europe?

A

By his writings/works

43
Q

Introduced the Arabic algebra and Indian numerals to the western Europe by his writings/works.

A

Muhammad Ibn Musa Al Khwarizmi

44
Q

What did the other Arabic scholars do?

A

Cultivated the Greek mathematics by translating the works of Apollonius, Euclid, Archimedes and Ptolemy into Arabic.

45
Q

In _________, Leonardo of Pisa became popular.

A

1202 C. E.

46
Q

Where does Leonardo came from?

A

Pisa

47
Q

Leonardo of Pisa is also known as ___________.

A

Fibonacci

48
Q

He wrote the book Liber Abaci.

A

Leonardo of Pisa

49
Q

What does Liber Abaci contain?

A

A collection of Leonardo’s arithmetical and algebraic information during his travels.

50
Q

One of the people to introduce the Hindu-Arabic system of numeration in western Europe.

A

Leonardo of Pisa

51
Q

What is the contribution of Hindu mathematics in modern mathematics?

A

The decimal position system.

52
Q

What did hindu mathematics introduced in mathematics?

A

Number zero

53
Q

What did the number zero symbolize?

A

Concept of “nothing”

54
Q

Western Europe in the year ________.

A

1489 C. E.

55
Q

A German mathematician

A

Johannes Widmann

56
Q

What appear in the book of Johannes Widmann?

A

The + and - symbols

57
Q

Where did the + and - symbol first appear?

A

In the printed book of Johannes Widmann entitled “Mercantile Arithmetic”.

58
Q

When did the Mercantile Arithmetic published?

A

In 1489 C. E.

59
Q

The + and - symbol first appear in Johannes Widmann’s book that was published in 1489 in reference to _______ and _____________.

A

Surpluses and deficits in business problems.

60
Q

In _________, he greatly extend the power of mathematics.

A

17th century

61
Q

He greatly extend the power of mathematics as a calculator science with his discovery of Logarithms.

A

John Napier

62
Q

In _______, Pierre de Fermat was given credit.

A

1629 C. E.

63
Q

He is a French lawyer and mathematician.

A

Pierre de Fermat

64
Q

Pierre de Fermat was given credit for

A

The development that led to infinitesimal calculus.

65
Q

_________ together with ________ began the mathematical study of probability.

A

Fermat, Pascal

66
Q

He laid the foundation of Probability Theory together with Fermat.

A

Blaise Pascal

67
Q

What did Blaise Pascal invented?

A

Pascaline

68
Q

What is Pascaline?

A

An early mechanical calculator

69
Q

Pascal is known for ________.

A

Pascal’s triangle

70
Q

A tool for expanding a binomial (a+b)^n

A

Pascal’s Triangle

71
Q

He is a noble mathematician of the 17th century.

A

René Descartes

72
Q

What did René Descartes invented?

A

Cartesian Coordinate system

73
Q

René Descartes load the foundation of ____________.

A

the development of calculus.

74
Q

Gottfried Leibniz first paper in the calculus was published.

A

1684 C. E.

75
Q

He discovered the infinitesimal calculus together with Sir Isaac Newton.

A

Gottfried Leibniz

76
Q

Mathematicians in 18th to 19th century.

A

> Leonhard Euler
Carl Friedrich Gauss
Joseph Louie Lagrange
John Venn
Benoit Mandelbrot
Andrew Wiles

77
Q

He is on of the important mathematician in 18th century.

A

Leonhard Euler

78
Q

Mathematical areas where Euler worked

A
  • Graph theory
    -Calculus of Variations
    -Differential Geometry
79
Q

A German mathematician

A

Carl Friedrich Gauss

80
Q

Areas where Gauss contributes

A

Number Theory, Geometry, Probability Theory, Planetary and Theory of functions.

81
Q

Year when Gauss proved the Fundamental Theory of Algebra.

A

1799

82
Q

Rise toward the end of 18th Century.

A

Joseph Louie Lagrange

83
Q

He is an Italian Mathematician

A

Joseph Louie Lagrange

84
Q

What did Lagrange began?

A

Rigorous theory of functions and of mechanics.

85
Q

Where did Lagrange played a key role?

A

In the creation of metric system of weights and measures.

86
Q

Who introduced the Venn diagram?

A

John Venn

87
Q

Introduced the Venn Diagram in ______

A

1874

88
Q

Became a useful tool for Set Theory.

A

Venn Diagram

89
Q

Introduced the Theory of Fractals.

A

Benoit Mandelbrot

90
Q

In what year did Mandelbrot introduce the theory of Fractals?

A

1975

91
Q

In 1892, Mandelbrot published the _____________.

A

Fractals Geometry of Nature.

92
Q

In 1994 he proved Fermat’s last theorem.

A

Andrew Wiles

93
Q

Mathematical challenges of 21st century was announced.

A

2000 C. E.

Mathematics In The Modern World (4 decks)

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