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AP Calculus KAMSC > History of Math > Flashcards

History of Math Flashcards

1
Q

What did the Babylonians do?

A

Fractions, quadratics, Pythagorean theorem, and calendars.

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2
Q

What did the early Europeans and Americans do?

A

Stonehenge and standing stones.

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3
Q

What did the Egyptians do?

A

Fractions, multiplication, Pythagorean theorem, and Pyramids.

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4
Q

What did the Chinese do?

A

Decimals, negative numbers, base 2 and 10, and geometry.

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5
Q

When did the Babylonians come around?

A

3000 BC

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6
Q

When did the Egyptians come around?

A

2000 BC

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7
Q

When did the early Europeans and Americans come around?

A

2500 BC

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8
Q

When did the Chinese come around?

A

1100 BC

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9
Q

What document did we find from the Egyptians that explained their mathematical thinking?

A

The Rhind Papyrus. Much use of the Pythagorean theorem.

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10
Q

How was math used before Greece?

A

All math was for practical use and could be applied.

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11
Q

Which civilization was Pythagoras a part of?

A

The Greeks.

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12
Q

What did Pythagoras initially call the Pythagorean theorem?

A

The musical tuning theorem.

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13
Q

How did Greeks do math?

A

Greeks used brainpower and did not do any experiments.

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14
Q

What did Pythagoras think about the Universe?

A

He thought the Earth was the center of the universe and that every orbit had a perfect circle.

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15
Q

Who were the Pythagorens?

A

A cult that worshipped Pythagoras. They only used and studied ratios and beans were banned.

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16
Q

How did Pythagoras die?

A

He was murdered in a bean field.

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17
Q

What did Pythagoras accomplish?

A

The fundamentals of mathematics.

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18
Q

What civilization was Zeno part of?

A

The Greeks.

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19
Q

What limit story did Zeno use?

A

Tortoise and the Hare.

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20
Q

What did Zeno accomplish?

A

Limits and Paradoxes of Infinite series.

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20
Q

What was a core math belief that Euclid believed?

A

All math is geometric.

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20
Q

What civilization was Euclid a part of?

A

The Greeks

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21
Q

What book did Euclid write?

A

The Elements.

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22
Q

What did Euclid accomplish?

A

Geometry and prime numbers.

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23
Q

What civilization was Archimedes part of?

A

The Greeks

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24
Q

What famous moment is Archimedes known for?

A

Jumping from the bathtub, yelling Eureka, and running naked down the streets. He figured out water displacement.

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25
Q

What two things did Archimedes write in his books?

A

The formula for circles and spheres and the estimate of pi.

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26
Q

What did Archimedes accomplish?

A

3-D Geometry, Pi, and Infinite series.

27
Q

How did Archimedes die?

A

He was stabbed by a Roman soldier who was supposed to keep him alive.

28
Q

What did Archimedes death signify?

A

Archimedes death signified the end of the Greek math era.

29
Q

What civilization was al-Khwarizmi a part of?

A

al-Khwarizmi was part of the Persian empire.

30
Q

What was the main thing al-Khwarizmi did?

A

He discovered the basics of algebra.

31
Q

What did Abu Kamil accomplish?

A

Negative numbers.

32
Q

What did Khojandi accomplish?

A

Spherical trigonometry. Defined the law of sines and found connections between sine and cosine with circular motion.

33
Q

What did al-Karaji accomplish?

A

Mathematical induction.

34
Q

What civilization was Khayyam a part of?

A

The Persian Empire.

35
Q

What is Khayyam mostly known for?

A

Poetry and Philosophy.

36
Q

What did Khayyam question?

A

Khayyam questioned astrology and suggested that it was made-up nonsense, which it is.

37
Q

What is the famous book Khayyam wrote?

A

Khayyam wrote the Rubaiyat.

38
Q

What did Khayyam accomplish mathematically?

A

Geometric algebra, the parallel postulate, the binomial theorem, and cubic functions.

39
Q

How did the math renaissance come to be?

A

Cities began to rely on external structure, and more wealth flowed through the population allowing for math to be studied as survival was not the most important thing.

40
Q

What was Fermet’s previous job before mathematician?

A

Lawyer.

41
Q

What was Fermet the founding father of?

A

The modern Modular/Time System.

42
Q

What did Fermet nearly develop?

A

Calculus but he had no notation.

43
Q

What is a ‘fun’ fact about Fermet?

A

He made the Last Theorem, which wasn’t proved until 1994 by Andrew Wiles.

44
Q

What is the Last Theorem?

A

A^n+B^n can never equal C^n where n>2

45
Q

What did Fermet accomplish?

A

Minimums, Maximums, and Number Theory.

46
Q

What did Descartes accomplish?

A

Descartes accomplished connecting algebra and geometry.

47
Q

What book did Descartes write?

A

La Geometrie.

48
Q

What did John Wallis write?

A

The first book of notation.

49
Q

What did John Wallis accomplish?

A

Arithmetic Functions.

50
Q

What era did Isaac Newton show up in?

A

The Renaissance.

51
Q

What famous book did Newton write?

A

Newton’s Principia

52
Q

Whose work did Newton use for his book Principia?

A

Descarte’s work.

53
Q

What anomaly happened at Newton’s birth?

A

Newton was born premature and was thought to die.

54
Q

What is Newton’s title?

A

Most prolific scientist and mathemetician.

55
Q

Where did Newton go to college?

A

Cambridge.

56
Q

What shut down Cambridge and the rest of England?

A

The Black Plague.

57
Q

What is Newton’s biggest accomplishment?

A

Developing Calculus.

58
Q

How long did it take Newton to develop Calculus?

A

6 weeks.

59
Q

What did Leibniz do?

A

Finished Calculus.

60
Q

What notations did Leibniz create?

A

dx and S

61
Q

What did Leibniz study?

A

The area under curves using verticle lines to find the area.

62
Q

What did Eulur accomplish?

A

Infinitesimal calculus.

63
Q

What did LaPlace accomplish?

A

Analytical Geometry.

64
Q

What did Gauss accomplish?

A

Fundamental theorem of algebra.

65
Q

What did Hamilton accomplish?

A

Vectors and differential geometry.

66
Q

What did Riemann accomplish?

A

Integration Theory.

AP Calculus KAMSC (1 decks)

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