Chapter 8 Flashcards
What is geometry?
It is the mathematics that describes the relationships of space, volumes, and areas
What are the 5 axioms of geometry?
1) It is possible to draw a straight line from any given point to any other point
2) a straight line can go infinitely and still be straight
3) a circle can be described with any point as its centre and any distance as its radius
4) all right angles are equal
5) given a line and a point not on the line, only one line can be drawn through that point that will be parallel to the first line
What does Euclidean geometry describe?
Flat spaces
What is the great circle?
The line on a circle whose centre coincides with the centre of the sphere
On Earth, this is the equator
How many great circles can there be on a sphere?
2
How many times do thee great circles bisect?
Twice
What is the issue with parallel lines on a sphere?
There are no possible parallel lines on the surface of a sphere.
What can we change about Euclid’s original 5 postulates to define the geometry of a sphere?
Change the 5th postulate: that a parallel line is not possible on a sphere
How many parallel lines can be drawn to another line from a given point?
An infinite number of lines
What kind of dimensions do geometries come in?
Arbitrary shapes
Name the 3 types of geometries
1) spherical
2) flat
3) hyperbolic
What do all the types of geometry have in common?
- they are all homogenous
- ## they are all isotropic
Why do hyperbolic geometries have a special role to play in our universe?
they are possible geometries for a homogenous and isotropic universe
Why is the weakness of our local gravitational field problematic?
It makes it difficult to test General Relativity. We cannot automatically extrapolate the data for the stronger fields
What is the nature of space time near a large object?
It is curved
