In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral

Quadrilateral

In Euclidean plane geometry, a quadrilateral is a polygon with four sides and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on...

. Starting with a given quadrilateral (a polygon having four sides), construct a square

Square (geometry)

In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

 on each side. Van Aubel's theorem holds that the two line segments connecting the centers of opposite squares are of equal lengths and are at right angle

Right angle

In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles...

s to one another. The theorem is named after H. H. van Aubel, who published it in 1878.

External links

• Van Aubel's Theorem: an interactive JavaSketch of the figure.
• Van Aubel's Theorem for Quadrilaterals and Van Aubel's Theorem for Triangles by Jay Warendorff, The Wolfram Demonstrations Project.
• Van Aubel's Theorem and some generalizations at Dynamic Geometry Sketches