Constructible number

A real number r is said to be constructible if a line segment of length r units can be constructed with a compass and unruled straightedge, given a line segment one unit long. Constructible numbers comprise a field.

The nonconstructibility of certain numbers proves the impossibility of certain problems attempted by the philosophers of ancient Greece. For example, the cube root of a constructible number is generally not constructible (hence the impossibility of "duplicating the cube"), the sine of (1/3)arcsin(x) is in general not constructible for arbitrary constructible x (hence the impossibility of "trisecting the angle"), nor is the constant pi (hence the impossibility of "squaring the circle").

... Enter your search terms Submit search form   Web www.wikilookup.info   This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.