A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed using classical geometric constructions. However, the cases for which the values of the trigonometric functions sine, cosine, tangent, etc., can be written in closed form involving square roots of real numbers are much more restricted.

# Euclidean Number

## See also

Algebraic Integer, Algebraic Number, Constructible Number, Euclid Number, Radical Integer## Explore with Wolfram|Alpha

## References

Conway, J. H. and Guy, R. K. "Three Greek Problems." In*The Book of Numbers.*New York: Springer-Verlag, pp. 192-194, 1996.Klein, F. "Algebraic Equations Solvable by Square Roots." Part I, Ch. 1 in "Famous Problems of Elementary Geometry: The Duplication of the Cube, the Trisection of the Angle, and the Quadrature of the Circle." In

*Famous Problems and Other Monographs.*New York: Chelsea, pp. 5-12, 1980.

## Referenced on Wolfram|Alpha

Euclidean Number## Cite this as:

Weisstein, Eric W. "Euclidean Number."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/EuclideanNumber.html