Purchase Solution

Prove that the Hyperbolic Rectangle Does Not Exist

Not what you're looking for?

Ask Custom Question

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.

Purchase this Solution

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.

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 ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.