*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## Universe, Geometry Of

For centuries, mathematicians and physicists believed that the universe was accurately described by the axioms of Euclidean geometry, which now form a standard part of high school mathematics. Some of the distinctive properties of Euclidean geometry follow:

- Straight lines go on forever.
- Parallel lines are unique. That is, given a line and a point not on that line, there is one and only one parallel line that passes through the given point.
- Parallel lines are equidistant. That is, two points moving along parallel lines at the same speed will maintain a constant distance from each other.
- The angles of a triangle add to 180°.
- The circumference of a circle is proportional to its radius,
*r*, (*C*= 2π*r*) and the area,*A*, of a circle is proportional to the square of the radius (*A*= π*r*^{2}), where pi (π) is...

This section contains 2,044 words(approx. 7 pages at 300 words per page) |