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**Hyperbolic geometry and spherical, or elliptical, geometry are two types of non-Euclidean geometry.** Spherical geometry is somewhat similar to Euclidean, or plane, geometry except that it is used to determine distances and areas on the surface of a sphere instead of the flat surfaces of Euclidean geometry. Hyperbolic geometry differs from spherical geometry by its application to surfaces with a constant negative curvature, such as the curved space first introduced in Einstein's 1915 general theory of relativity.

Euclidean geometry, which dates back to 300 B.C., had a wide variety of practical applications for the Ancient Greeks who used it to survey land, design buildings and determine distances. All of these applications dealt with flat surfaces. Spherical geometry was required for navigational purposes after it was discovered that the Earth was not flat as originally thought. In the modern world, spherical geometry is relied upon by ship captains and aircraft pilots to determine the shortest distance between two points. Because spherical geometry deals with surfaces that have a constant positive curvature, the results can often be somewhat non-intuitive.

Prior to Einstein's mathematical depiction of curved space, hyperbolic geometry had no practical application because of the lack of a real-world example of a surface with a constant negative curvature. It was discovered in 1919, however, that the light coming from a distant star could be bent if it passed close enough to an object with a huge gravitational pull. Hyperbolic geometry soon began to be used to perform calculations in the new world of space, time, light and gravity described in Einstein's general theory of relativity.

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## What are two non-collinear rays with a common endpoint?

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Full Answer >**An angle is formed by the union of two non-collinear rays that have a common endpoint.**This endpoint is the vertex of the angle, and the two rays become the sides of this angle. These two rays can form different types of angles.Filed Under: - Q:
## What is the midpoint theorem?

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Full Answer >**The midpoint theorem is a theory used in coordinate geometry that states that the midpoint of a line segment is the average of its endpoints.**Solving an equation using this method requires that both the x and y coordinates are known. This theorem can also be used in algebra and calculus.Filed Under: - Q:
## What are the geometry Regents exams?

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Full Answer >**The Regents Examination in geometry is one exam of the mathematics portion of the standardized examinations New York State uses to test high school students before graduation.**The other mathematics exams are Integrated Algebra, Algebra I and Algebra II and Trigonometry.Filed Under: - Q:
## Who is considered to be the father of geometry?

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Full Answer >**The Greek mathematician Euclid of Alexandria is considered to be the father of geometry.**His mathematical and geometric treatise "Elements" is one of the most influential works in mathematics as well as one of the most successful textbooks ever written.Filed Under: