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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
Hieroglyphic numbers is a base __ system
10
26
Hieroglyphic numbers: 10 is shown by
drawing of a hobble for cattle
27
Hieroglyphic numbers: 100 is represented by
coil of rope
28
Hieroglyphic numbers: 1,000 is represented by
drawing of lotus plant
29
Hieroglyphic numbers: 10,000 is represented by
a finger
30
Hieroglyphic numbers: 100,000 is represented by
tadpole or frog
31
Hieroglyphic numbers: 1,000,000 is represented by
a god with arms raised above his head
32
- oldest mathematical text in ancient Egypt so far - dates from the Egyptian middle kingdom around 2,000 - 1,800 BCE
Moscow Papyrus
33
Moscow Papyrus dates from the Egyptian middle kingdom around _____
2,000 - 1,800 BCE
34
- 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
Rhind Papyrus
35
Rhind Papyrus measurement
- 6 meters long - 1/3 meter wide
36
When was the Rhind Papyrus written
around 1650 BCE
37
Who wrote the Rhind Papyrus
scribe Ahmes
38
Rhind Papyrus is a kind of instruction manual for what
arithmetic and geometry
39
Rhind Papyrus gives an explicit demonstration of what
multiplication and division carried out at the time
40
- dates from around 1300 BCE - shows that Egyptians could order algebraic (quadratic equations) - where the Pythagorean Theorem was written on
Berlin Papyrus
41
Berlin Papyrus dates from around what
1300 BCE
42
What does the Berlin Papyrus show
Egyptians could order algebraic (quadratic) equations
43
What was written on Berlin Papyrus
Pythagorean Theorem
44
- base 10 system similar to the earlier Egyptian - with symbols for 1, 5, 10, 50, 500, and 1000
Greek Numeral System
45
Timeline of the Greek Numeral System
450 BCE - 7th Century
46
Greek Numeral System is a base __ system
10
47
Greek Numeral System has symbols for what
1, 5, 10, 50, 500, and 1000
48
The ancient Greek numeral system is known as
Attic or Herodianic numerals
49
- one of the Seven Sages of Ancient Greece - considered to have been the first to lay down guidelines for the abstract development of geometry
Thales
50
What did Thales establish
- Thales' Theorem - Thales' Intercept Theorem
51
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
Thales' Theorem
52
about the ratios of the line segments that are created if two intersecting lines are intercepted by a pair of parallels
Thales' Intercept Theorem
53
What are the Three Classical Problems
1. Squaring (quadrature) of the circle 2. Doubling (duplicating) of the cube 3. Trisection of an angle
54
wrote "The Elements"
Euclid
55
- compilation of theorems, axioms in Algebra and postulates and theorems in Geometry - written by Euclid
The Elements
56
The Elements was used from ___
300 BCE - 200 AD
57
idea of proof, and the deductive method of using logical steps to prove or disprove theorems
- Pythagoras - Plato - Aristotle
58
- 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
Pythagoras
59
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”)
Pythagorean Theorem
60
Pythagorean Theorem equation
a^2 + b^2 = c^2
61
What did Pythagoras impose
"god is number" or "all is number"
62
- 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”
Plato
63
When did Plato establish his academy in Athens
387 BCE
64
Where did Plato establish his academy
Athens
65
What does Plato's academy entrance say
"Let no-one ignorant of geometry enter here."
66
Who is Plato's inspiration for his academy
Pythagoras
67
Plato's academy taught mathematics as a branch of what
Philosophy
68
Plato is also known as the "__ _ __"
maker of mathematicians
69
Platonic Solids
1. Tetrahedron 2. Octahedron 3. Icosahedron 4. Cube 5. Dodecahedron
70
Who discovered the octahedron and icosahedron
Theaetetus (contemporary of Plato)

Mathematics in the Modern World (13 decks)

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