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
