Greek Geometry Flashcards
What was the crucial idea that came from Greek math
the idea of proof introduced in Euclid’s Elements using axiomatic statements and deductive reasoning
What is in Euclid’s Elements
it consists of 13 books covering 2D and 3D geometry, number theory, and an attempt at a theory of irrational numbers
How does elements define a point
That which has no dimension
What is the straight line postulate in elements
For any two points A and B there is one and only one straight line connecting A to B
what is the circle postulate in elements
For any point A and length r there is a circle with centre A and radius r
What is postulate 5 (parallel postulate) in elements
For any line L and point P not on L there exists a unique line L’ that passes through P and is parallel to L
How many definitions, postulates, and axioms does elements start with
23 definitions, 5 postulates, 5 axioms
what is a regular polygon
a polygon where all sides are the same length, there are infinitely many
what is a regular polyhedron
a 3D solid with faces which are polygons, in other words a 3D solid whose edges are all the same length
How many regular polyhedron are there
5
what are the 5 regular polyhedron
tetrahedron, cube, octahedron, dodecahedron, icosahedron
what is a conic section
a curve that come from the intersection of a plane with a cone
what are the four conic sections
circle, ellipse, parabola, hyperbola
