Top Qs
Timeline
Chat
Perspective

Van Schooten's theorem

On lines connecting the vertices of an equilateral triangle to a point on its circumcircle From Wikipedia, the free encyclopedia

Van Schooten's theorem
Remove ads

Van Schooten's theorem, named after the Dutch mathematician Frans van Schooten, describes a property of equilateral triangles. It states:

For an equilateral triangle with a point on its circumcircle the length of longest of the three line segments connecting with the vertices of the triangle equals the sum of the lengths of the other two.
Thumb

The theorem is a consequence of Ptolemy's theorem for concyclic quadrilaterals. Let be the side length of the equilateral triangle and the longest line segment. The triangle's vertices together with form a concyclic quadrilateral and hence Ptolemy's theorem yields:

Dividing the last equation by delivers Van Schooten's theorem.

Remove ads

References

  • Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010, ISBN 9780883853481, pp. 102–103
  • Doug French: Teaching and Learning Geometry. Bloomsbury Publishing, 2004, ISBN 9780826434173 , pp. 62–64
  • Raymond Viglione: Proof Without Words: van Schooten′s Theorem. Mathematics Magazine, Vol. 89, No. 2 (April 2016), p. 132
  • Jozsef Sandor: On the Geometry of Equilateral Triangles. Forum Geometricorum, Volume 5 (2005), pp. 107–117
Remove ads
Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads