Show:
Euclid
Euclid's Five Postulates
Spherical Geometry
Hyperbolic Geometry
Plane Euclidean
100
What was Euclid referred to as?
"The Father of Geometry"
100
Name the postulate: You can draw a straight line between any two points.
Postulate 1
100

What is the sum of angles in a triangle in spherical geometry?

More than 180 degrees

100
What is the sum of angles in a triangle in Hyperbolic geometry?
The sum of the angles in a triangle is less than 180 degrees.
100
True or False: Euclidean geometry's sum of angles in a triangle is exactly 180 degrees?
True.
200
What else did Euclid work on?
Wrote works on perspcective, spherical geometry, number theory, rigor, and conic sections.
200
Name the postulate: You can draw any circle at any given point as the center and any given radius.
Postulate 3
200
Are there any parallel lines that be constructed?
No
200
Does Hyperbolic geometry use a disk surface?
Yes
200

How many postulates does Euclid have?

Five

300
What is another name for "Euclid's Fifth Postulate"?
The "parallel postulate".
300
Name the postulate: Through a given point not on a line, one parallel line can be constructed.
Postulate 5
300
What are lines in spherical geometry?
Great circles
300
What is Hyperbolic geometry?
A simple closed curve in topology.
300

Does Euclidean geometry have to do with Euclid's Elements?

Yes

400
What was one of Euclid's accomplishments?
To present Elements by making it easy to use and easy to reference.
400
What is the second postulate?
When you can extend any segment indefinitely.
400
What is spherical geometry?
The geometry of figures on the surface of a sphere.
400
What's a characteristic property of Hyperbolic geometry?
The angles of a triangle add to less than a straight line.
400
What is the opposite of Euclidean geometry?
Non-Euclidean
500
What serves as the main textbook for teaching math, especially geometry?
Euclid's Elements
500
What is the fourth postulate?
When all right angles are congruent.
500
Is spherical geometry considered Euclidean?
No
500
What does Hyperbolic geometry mean?
Parallel postulate.
500
True or false: For over two thousand years, the adjective "Euclidean" wasn't necessary because there was no other type of geometry.
True.