Group 2 Flashcards
When did the Hellenistic period began
3rd century BC
- Alexander’s conquest of the Eastern Mediterranean
What became the language of scholarship throughout the Hellenistic world
Greek
What became the great center of learning under the beneficent rule of Ptolemies
Alexandria in Egypt
Alexandria in Egypt became the great center of learning under the beneficent rule of who
Ptolemies
Who are the among the best known and most influential mathematicians who studied and taught at Alexandria
- Euclid
- Archimedes
- Eratosthenes
- Heron
- Menelaus
- Diophantus
- (choi chi yeol CHAREZ HAHAHAHAHA)
- Father of Geometry
- wrote successful mathematical textbook of the “Stoicheion” or “Elements”
Euclid
What did Euclid write
“Stoicheoin” or “Elements”
represents the culmination of the mathematical revolution
Euclid’s “Elements”
study of geometrical shapes (plane and solid) and figures based on different axioms and theorems
Euclidean geometry
Euclid’s Five (5) General Axioms
- Things which are equal to the same thing are equal to each other.
- If equals are added to equals, the wholes (sums) are equal.
- If equals are substracted from equals, the remainders are equal.
- Things that coincide with one another are equal to one another.
- The whole is greater than the part.
first known example of a proof by contradiction
Euclid’s proof of Pythagoras’ Theorem
Euclid’s basis of his proof is often known as
Euclid’s Theorem
- 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
Archimedes
When did Archimedes study at Alexandria
3rd century BCE
What is Archimedes known for
- military innovations
- formulation of a hydrostatic principle (Archimedes’ principle)
- Archimedes screw
Who produced formulas to calculate the areas of regular shapes, using a revolutionary method of capturing new shapes by using shapes he already understood
Archimedes
Archimedes produced formulas to calculate what
areas of regular shapes
- 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
Method of Exhaustion
- 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
Quadrature Parabola
What did Archimedes discover regarding the relationship between the sphere and circumscribing cylinder of the same height and diameter
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
an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object
Archimedes’ Principle
- 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
Eratosthenes
What did Eratosthenes devise
first system of latitude and longitude
What did Eratosthenes calculate
circumference of the earth to a remarkable degree of accuracy
algorithm for identifying prime numbers and his greatest legacy as a mathematician
Sieve of Eratosthenes
- Famously known as the ‘Hero of Alexandria’. - first mathematician to confront at least the idea of √-1
Heron
Heron is famously known as
Hero of Alexandria
What idea did Heron confront
√-1 (imaginary number)
Heron is best known in mathematical circles for
Heronian triangles
finding the area of a triangle from its side lengths
Heron’s formula
iteratively computing a square root
Heron’s method
first to recognize geodesics on a curved surface as the natural analogues of straight lines on a flat plane
Menelaus
What did Menelaus recognize
geodesics on a curved surface
- dealt with geometry of the sphere and its application in astronomical measurements and calculations
- introduced the concept of spherical triangle
Sphaerica
Menelaus’ book
Sphaerica
figure formed of three great circle arcs
trilateral
- sometimes called the “Father of Algebra”
- wrote an influential series of books called Arithmetica
Diophantus
collection of algebraic problems which greatly influenced the subsequent development of number theory
Arithmetica
- 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
Diophantine equations
During the Roman Empire and Republic, there were no ___ involved
mathematicians
What originated in Rome
Roman Numerals
Seven (7) basic symbols of Roman Numerals
I, V, X, L, C, D, and M
When were the Roman Numerals first used
900 - 800 BC
referred to one unit or finger
I
represented five finger, specifically the V-shaped made by the thumb and forefinger
V
equaled two hands
X
What did the Romans prefer
utilitarian mathematics
How did the Romans use mathematics
- quantify personal and government accounts
- keep military records
- aid in the construction of aqueducts and buildings
What spurred the development of counting boards in the Roman Empire
aid with multiplication and division
Flaws of Roman Numeral system
- absence of a way to numerically express fractions
- absence of concept of zero (0)
What replaced the Roman Numeral system
Hindu-Arabic system
How long was the Roman Numeral system used
1,800 years
constituted the most sophisticated mathematical system ever developed in the Americas
Mayan mathematics
Purpose of the Mayan’s Mathematical System
for astronomical and calendar calculations
What number system did the Mayans use
Vigesimal Number System
Vigesimal number system is based on base __
20 (some extent, base 5)
The vigesimal number system probably originally developed from what
counting on fingers and toes
three (3) symbols of the Vigesimal number system
- 0 = shell shape
- 1 = dot
- 5 = bar
(6-13 are represented by various arrangements of bars and dots)
What is the value of 0 for Mayans
plenitude instead of no value
What does the zero symbolize for Mayans
ending of a cycle and the beginning of another
First mathematician identified as such on a glyph in Mayans mathematics
female figure
