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Mathematics in the Modern World > Group 1 > Flashcards

Group 1 Flashcards

1
Q
  • region in Mesopotamia
  • modern-day Iraq
  • called the “Cradle of Civilization”
A

Sumer

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2
Q

Sumer is called the “__ _ __”

A

Cradle of Civilization

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3
Q

Sumer is modern-day __

A

Iraq

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4
Q
  • earliest known writing system
  • created by the Sumerians
A

cuneiform script

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5
Q

cuneiform script was a __ writing system

A

pictographic

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6
Q

When did Sumer’s society stabilize and advance in agriculture

A

6th millenium BCE

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7
Q

Sumerian mathematics was first mostly a response to what

A

governmental requirements for measurement of land plots, taxing of individuals, etc.

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8
Q

When is the first recorded use of abacus

A

2700 - 2300 BC in Mesopotamia

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9
Q

Where is the first recorded use of abacus

A

Mesopotamia

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10
Q

numeral system with 60 as its base

A

Sexagesimal Numeral System

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11
Q

Sumerians were the first civilization to use a __ __ numeral system

A

place value (numeral system)

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12
Q

Sumerians’ place value numeral system was developed and passed on to the

A

ancient Babylonians

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13
Q

Who created a circle character for zero

A

Babylonians

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14
Q

Zero was another groundbreaking mathematical idea that the __, __, and __ did not have

A
  • Egyptians
  • Greeks
  • Romans
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15
Q

oldest known evidence of humans using applied geometry

A

Babylonian clay tablet

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16
Q

When is the oldest known evidence of humans using applied geometry made

A

1900 - 1600 BCE

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17
Q

Babylonian clay tablet, notable as containing an example of Babylonian mathematics.

A

Plimpton 322 Clay Tablet

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18
Q

When did the early Egyptians settle along the fertile Nile valley to record the lunar phases and seasons

A

6000 BCE

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19
Q

The Egyptians settled along the fertile Nile valley to record the lunar phases and seasons for what purposes

A

religion and agricultural purposes

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20
Q

What did the Pharaoh’s surveyors use as a basis to measure land and buildings

A

body parts

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21
Q

body part used to measure width

A

palm

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22
Q

body part used to measure cubit

A

elbow to fingertips

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23
Q
  • little pictures that represent words or numbers
  • used around 3000 BCE
A

Hieroglyphic Numbers

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24
Q

When were hieroglyphic numbers used

A

around 3000 BCE

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25
Q

Hieroglyphic numbers is a base __ system

A

10

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26
Q

Hieroglyphic numbers:
10 is shown by

A

drawing of a hobble for cattle

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27
Q

Hieroglyphic numbers:
100 is represented by

A

coil of rope

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28
Q

Hieroglyphic numbers:
1,000 is represented by

A

drawing of lotus plant

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29
Q

Hieroglyphic numbers:
10,000 is represented by

A

a finger

30
Q

Hieroglyphic numbers:
100,000 is represented by

A

tadpole or frog

31
Q

Hieroglyphic numbers:
1,000,000 is represented by

A

a god with arms raised above his head

32
Q
  • oldest mathematical text in ancient Egypt so far
  • dates from the Egyptian middle kingdom around 2,000 - 1,800 BCE
A

Moscow Papyrus

33
Q

Moscow Papyrus dates from the Egyptian middle kingdom around _____

A

2,000 - 1,800 BCE

34
Q
  • kind of instruction manual in arithmetic and geometry
  • gives explicit demonstration of how multiplication and division was carried out at the time
  • scroll about 6 meters long and 1/3 meter wide
  • written around 1650 BCE by scribes Ahmes
A

Rhind Papyrus

35
Q

Rhind Papyrus measurement

A
  • 6 meters long
  • 1/3 meter wide
36
Q

When was the Rhind Papyrus written

A

around 1650 BCE

37
Q

Who wrote the Rhind Papyrus

A

scribe Ahmes

38
Q

Rhind Papyrus is a kind of instruction manual for what

A

arithmetic and geometry

39
Q

Rhind Papyrus gives an explicit demonstration of what

A

multiplication and division carried out at the time

40
Q
  • dates from around 1300 BCE
  • shows that Egyptians could order algebraic (quadratic equations)
  • where the Pythagorean Theorem was written on
A

Berlin Papyrus

41
Q

Berlin Papyrus dates from around what

A

1300 BCE

42
Q

What does the Berlin Papyrus show

A

Egyptians could order algebraic (quadratic) equations

43
Q

What was written on Berlin Papyrus

A

Pythagorean Theorem

44
Q
  • base 10 system similar to the earlier Egyptian
  • with symbols for 1, 5, 10, 50, 500, and 1000
A

Greek Numeral System

45
Q

Timeline of the Greek Numeral System

A

450 BCE - 7th Century

46
Q

Greek Numeral System is a base __ system

A

10

47
Q

Greek Numeral System has symbols for what

A

1, 5, 10, 50, 500, and 1000

48
Q

The ancient Greek numeral system is known as

A

Attic or Herodianic numerals

49
Q
  • one of the Seven Sages of Ancient Greece
  • considered to have been the first to lay down guidelines for the abstract development of geometry
A

Thales

50
Q

What did Thales establish

A
  • Thales’ Theorem
  • Thales’ Intercept Theorem
51
Q

if a triangle is drawn within a circle with the long side as a diameter of the circle, then the opposite angle will always be a right angle

A

Thales’ Theorem

52
Q

about the ratios of the line segments that are created if two intersecting lines are intercepted by a pair of parallels

A

Thales’ Intercept Theorem

53
Q

What are the Three Classical Problems

A
  1. Squaring (quadrature) of the circle
  2. Doubling (duplicating) of the cube
  3. Trisection of an angle
54
Q

wrote “The Elements”

A

Euclid

55
Q
  • compilation of theorems, axioms in Algebra and postulates and theorems in Geometry
  • written by Euclid
A

The Elements

56
Q

The Elements was used from ___

A

300 BCE - 200 AD

57
Q

idea of proof, and the deductive method of using logical steps to prove or disprove theorems

A
  • Pythagoras
  • Plato
  • Aristotle
58
Q
  • imposed “god is a number” or “all is number” in his scholars
  • complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth
A

Pythagoras

59
Q

for any right-angled triangle, the square of the length of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the square of the other two sides (or “legs”)

A

Pythagorean Theorem

60
Q

Pythagorean Theorem equation

A

a^2 + b^2 = c^2

61
Q

What did Pythagoras impose

A

“god is number” or “all is number”

62
Q
  • One of ancient Greece’s most important patrons of mathematics.
  • founded an Academy in Athens in 387 BCE making Pythagoras as his inspiration. His academy entrance says: “Let no-one ignorant of geometry enter here”.
  • His Academy taught Mathematics as a branch of Philosophy.
  • also known as the “maker of mathematicians”
A

Plato

63
Q

When did Plato establish his academy in Athens

A

387 BCE

64
Q

Where did Plato establish his academy

A

Athens

65
Q

What does Plato’s academy entrance say

A

“Let no-one ignorant of geometry enter here.”

66
Q

Who is Plato’s inspiration for his academy

A

Pythagoras

67
Q

Plato’s academy taught mathematics as a branch of what

A

Philosophy

68
Q

Plato is also known as the “__ _ __”

A

maker of mathematicians

69
Q

Platonic Solids

A
  1. Tetrahedron
  2. Octahedron
  3. Icosahedron
  4. Cube
  5. Dodecahedron
70
Q

Who discovered the octahedron and icosahedron

A

Theaetetus (contemporary of Plato)

Mathematics in the Modern World (13 decks)

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