# Viviani curve

From Encyclopedia of Mathematics

The curve of intersection of the surfaces of a sphere of radius $R$ and a certain circular cylinder of radius $R/2$ through the centre of the sphere. The part of the solid sphere located inside the cylinder is known as the Viviani solid. So named after V. Viviani (17th century).

#### Comments

Viviani's window is the set of points in $E^3$ given by $$ \{ (x,y,z)\ :\ x^2+y^2+z^2 \le 1\,,\ x^2+y^2 \le x \} \ . $$

#### References

[a1] | M. Berger, "Geometry" , II , Springer (1987) pp. 84 |

**How to Cite This Entry:**

Viviani curve.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Viviani_curve&oldid=41906

This article was adapted from an original article by E.V. Shikin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article