Dr. Colin Adams portrayed himself as a real estate broker named Mel Slugbate. Mel Slugbate was born on a greyhound bus and his wife's name is Vicious Slugbate. Mr. Slugbate is with Slugbate and Mossbutter Real Estate Brokers in Williamstown, Massachusetts. He came to talk to us about Real Estate in Hyperbolic Space: Investment Opportunities for the New Millennium. Slugbate and Mossbutter have properties in Florida, Nevada, Alaska, and many other states. The space we live in is called Euclidean space. Hyperbolic space is rounded. There are many differences between Euclidean and hyperbolic space.
In Euclidean Geometry, unlimited parallel lines resemble, but in hyperbolic space unlimited parallel lines resemble . The Upper Half Plane Model is a hyperbolic space in two dimensions. . Another example of hyperbolic space in two dimensions is The Poincare Model, . The angles in a triangle in Euclidean space all add up to 180ÃÂ°.
In hyperbolic space all of the angles in a triangle do not add up to 180ÃÂ°, but they are between 0ÃÂ° and 180ÃÂ°. A triangle in hyperbolic space is simply a triangle in Euclidean space with the vertices stretched. .
If you have an octagon in hyperbolic space then all of the angles are equal to 90ÃÂ°. To find the distance in hyperbolic space you refer towith the formula . Also, the area of a Euclidean disk is A = pr 2 . Whereas in hyperbolic space, there is more space, and the area of a disk is A = pe r H. For example, Waco is a disk with a radius of 10 miles. If you increase the city limits by 1 mile all the way around, then you will have a 21% increase of population in Euclidean space, and a 172% increase in hyperbolic space. In the...