Constructible number Guide, Meaning , Facts, Information and Description
A real number r is said to be constructible or Euclidean if a line segment of length r units can be constructed with compasses and an unruled straightedge, given a line segment one unit long.Sometimes the negatives of constructible numbers are also called constructible. By this definition, constructible numbers constitute a field. All rational numbers are constructible, and all constructible numbers are algebraic numbers.
The nonconstructibility of certain numbers proves the impossibility of certain problems attempted by the philosophers of ancient Greece:
| Non-constructible number | Consequently impossible construction |
|---|---|
| The cube root of a general constructible number | Duplicating the cube |
| for general constructible x | Trisecting the angle |
| Pi | Squaring the circle |
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