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 = 2πr) and the area, A, of a circle is proportional to the square of the radius (A = πr2), where pi (π) is defined to be approximately 3.14 .
The last four properties are characteristic of a "flat" space that has no intrinsic curvature. (See figure below.)
Other types of geometry, called non-Euclidean geometries, violate some or all of the properties of Euclidean geometry. For example, on the surface of a sphere (a positively curved space), the closest thing to a straight path is a great circle, or the path you would follow if you walked straight forward without turning right or left.
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