Non-Euclidean Geometry

Question 1

Who was the Italian priest who invented the Khayyam-Saccheri Quadrilateral?

Answer 1

Giovanni Saccheri

Question 2

Who was the German mathematician who is associated with the curved two-dimensional surface?

Answer 2

Johann Carl Friedrich Gauss

Question 3

Who independently discovered non-Euclidean geometry?

Answer 3

Nikolai Lobachevsky

Question 4

Who was the teacher of Lobachevsky?

Answer 4

Martin Bales

Question 5

Who discovered “imaginary” geometry?

Answer 5

Janos Bolyai

Question 6

What is the geometry you get by assuming all the postulates of Euclid, except the fifth one, which is replaced by its negation?

Answer 6

Hyperbolic Geometry

Question 7

Who coined the term Hyperbolic Geometry?

Answer 7

Felix Klein

Question 8

Is hyperbolic geometry applied to special relativity?

Answer 8

Yes

Question 9

TRUE OR FALSE: Rectangles exist in hyperbolic geometry.

Answer 9

FALSE

Question 10

What is the main theorem of hyperbolic geometry?

Answer 10

For every line L and every point P not on L there pass through P at least 2 distinct parallels to L. Moreover, there are infinitely many parallels to L through P.

Question 11

In hyperbolic geometry, all triangles have an angle sum of?

Answer 11

less than 180 degrees

Question 12

In hyperbolic geometry, if two triangles are similar, what are they?

Answer 12

congruent triangles

Question 13

What are some applications of hyperbolic geometry?

Answer 13

Mapping the brain, internet, and universe