Prove that the Hyperbolic Rectangle Does Not Exist
Using the Universal Hyperbolic Theorem we can show that the sum of the angles of a quadrilateral will be less than 360 degrees in hyperbolic geometry. The formal definition of a rectangle is a quadrilateral with four right angles therefore this figure does not exist in hyperbolic geometry.
© BrainMass Inc. brainmass.com October 10, 2019, 4:25 am ad1c9bdddfhttps://brainmass.com/math/triangles/hyperbolic-rectangle-460035
Solution Preview
This fact of the nonexistence of rectangles is sometimes sited as a lemma of the Universal Hyperbolic Theorem. I think is better illustrated by looking at angle sums of triangles and quadrilaterals. If you ...
Solution Summary
This solution is comprised of a proof that uses the formal definition of a rectangle and shows that in hyperbolic space a quadrilateral can not have four right angles.
$2.19