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Mathematics in the Modern World > Group 2 > Flashcards

Group 2 Flashcards

1
Q

When did the Hellenistic period began

A

3rd century BC
- Alexander’s conquest of the Eastern Mediterranean

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2
Q

What became the language of scholarship throughout the Hellenistic world

A

Greek

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3
Q

What became the great center of learning under the beneficent rule of Ptolemies

A

Alexandria in Egypt

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4
Q

Alexandria in Egypt became the great center of learning under the beneficent rule of who

A

Ptolemies

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5
Q

Who are the among the best known and most influential mathematicians who studied and taught at Alexandria

A
  • Euclid
  • Archimedes
  • Eratosthenes
  • Heron
  • Menelaus
  • Diophantus
  • (choi chi yeol CHAREZ HAHAHAHAHA)
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6
Q
  • Father of Geometry
  • wrote successful mathematical textbook of the “Stoicheion” or “Elements”
A

Euclid

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7
Q

What did Euclid write

A

“Stoicheoin” or “Elements”

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8
Q

represents the culmination of the mathematical revolution

A

Euclid’s “Elements”

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9
Q

study of geometrical shapes (plane and solid) and figures based on different axioms and theorems

A

Euclidean geometry

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10
Q

Euclid’s Five (5) General Axioms

A
  1. Things which are equal to the same thing are equal to each other.
  2. If equals are added to equals, the wholes (sums) are equal.
  3. If equals are substracted from equals, the remainders are equal.
  4. Things that coincide with one another are equal to one another.
  5. The whole is greater than the part.
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11
Q

first known example of a proof by contradiction

A

Euclid’s proof of Pythagoras’ Theorem

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12
Q

Euclid’s basis of his proof is often known as

A

Euclid’s Theorem

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13
Q
  • known for his military innovations and formulation of a hydrostatic principle and a device for raising water
  • Greek mathematician who studied at Alexandria in 3rd century
  • Father of Geometry
A

Archimedes

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14
Q

When did Archimedes study at Alexandria

A

3rd century BCE

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15
Q

What is Archimedes known for

A
  • military innovations
  • formulation of a hydrostatic principle (Archimedes’ principle)
  • Archimedes screw
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16
Q

Who produced formulas to calculate the areas of regular shapes, using a revolutionary method of capturing new shapes by using shapes he already understood

A

Archimedes

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17
Q

Archimedes produced formulas to calculate what

A

areas of regular shapes

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18
Q
  • mathematical technique invented by Eudoxus
  • finds the area of a shape by inscribing polygons inside of it, with an increasing number of sides. ‍ Eventually, the areas of the successive polygons merge to equal the area of the original shape
A

Method of Exhaustion

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19
Q
  • Archimedes’ proof and most sophisticated use of the method of exhaustion
  • remained unsurpassed until the development of integral calculus in the 17th Century- that the area of a parabolic segment is 4⁄3 that of a certain inscribed triangle
A

Quadrature Parabola

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20
Q

What did Archimedes discover regarding the relationship between the sphere and circumscribing cylinder of the same height and diameter

A

sphere has a volume equal to 2/3 that of the cylinder, and a surface area also equal to 2/3 that of the cylinder

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21
Q

an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object

A

Archimedes’ Principle

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22
Q
  • devised the first system of latitude and longitude
  • calculated the circumference of the earth to a remarkable degree of accuracy
  • near contemporary of Archimedes in the 3rd century BCE
A

Eratosthenes

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23
Q

What did Eratosthenes devise

A

first system of latitude and longitude

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24
Q

What did Eratosthenes calculate

A

circumference of the earth to a remarkable degree of accuracy

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25
Q

algorithm for identifying prime numbers and his greatest legacy as a mathematician

A

Sieve of Eratosthenes

26
Q
  • Famously known as the ‘Hero of Alexandria’. - first mathematician to confront at least the idea of √-1
A

Heron

27
Q

Heron is famously known as

A

Hero of Alexandria

28
Q

What idea did Heron confront

A

√-1 (imaginary number)

29
Q

Heron is best known in mathematical circles for

A

Heronian triangles

30
Q

finding the area of a triangle from its side lengths

A

Heron’s formula

31
Q

iteratively computing a square root

A

Heron’s method

32
Q

first to recognize geodesics on a curved surface as the natural analogues of straight lines on a flat plane

A

Menelaus

33
Q

What did Menelaus recognize

A

geodesics on a curved surface

34
Q
  • dealt with geometry of the sphere and its application in astronomical measurements and calculations
  • introduced the concept of spherical triangle
A

Sphaerica

35
Q

Menelaus’ book

A

Sphaerica

36
Q

figure formed of three great circle arcs

A

trilateral

37
Q
  • sometimes called the “Father of Algebra”
  • wrote an influential series of books called Arithmetica
A

Diophantus

38
Q

collection of algebraic problems which greatly influenced the subsequent development of number theory

A

Arithmetica

39
Q
  • Can be defined as polynomial equations with integer coefficients to which only integer solutions are sought
  • purpose is to solve for all the unknowns in the problem
A

Diophantine equations

40
Q

During the Roman Empire and Republic, there were no ___ involved

A

mathematicians

41
Q

What originated in Rome

A

Roman Numerals

42
Q

Seven (7) basic symbols of Roman Numerals

A

I, V, X, L, C, D, and M

43
Q

When were the Roman Numerals first used

A

900 - 800 BC

44
Q

referred to one unit or finger

A

I

45
Q

represented five finger, specifically the V-shaped made by the thumb and forefinger

A

V

46
Q

equaled two hands

A

X

47
Q

What did the Romans prefer

A

utilitarian mathematics

48
Q

How did the Romans use mathematics

A
  • quantify personal and government accounts
  • keep military records
  • aid in the construction of aqueducts and buildings
49
Q

What spurred the development of counting boards in the Roman Empire

A

aid with multiplication and division

50
Q

Flaws of Roman Numeral system

A
  • absence of a way to numerically express fractions
  • absence of concept of zero (0)
51
Q

What replaced the Roman Numeral system

A

Hindu-Arabic system

52
Q

How long was the Roman Numeral system used

A

1,800 years

53
Q

constituted the most sophisticated mathematical system ever developed in the Americas

A

Mayan mathematics

54
Q

Purpose of the Mayan’s Mathematical System

A

for astronomical and calendar calculations

55
Q

What number system did the Mayans use

A

Vigesimal Number System

56
Q

Vigesimal number system is based on base __

A

20 (some extent, base 5)

57
Q

The vigesimal number system probably originally developed from what

A

counting on fingers and toes

58
Q

three (3) symbols of the Vigesimal number system

A
  1. 0 = shell shape
  2. 1 = dot
  3. 5 = bar

(6-13 are represented by various arrangements of bars and dots)

59
Q

What is the value of 0 for Mayans

A

plenitude instead of no value

60
Q

What does the zero symbolize for Mayans

A

ending of a cycle and the beginning of another

61
Q

First mathematician identified as such on a glyph in Mayans mathematics

A

female figure

Mathematics in the Modern World (13 decks)

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