Griffiths' theorem

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Griffiths' theorem: every red circle is a pedal circle of a blue point on the line through the circumcenter O, and G is the Griffiths point Pedal circle griffith point2 schar.svg
Griffiths' theorem: every red circle is a pedal circle of a blue point on the line through the circumcenter O, and G is the Griffiths point

Griffiths' theorem, named after John Griffiths (1837-1916), is a theorem in elementary geometry. It states that all the pedal circles for a points located on a line through the center of the triangle's circumcircle share a common (fixed) point. Such a point defined for a triangle and a line through its circumcenter is called a Griffiths point. [1]

Contents

Griffiths published the theorem in the Educational Times in 1857. Its later rediscoveries include works by M. Weil in Nouvelles Annales de Mathématiques, 1880, and by W. S. McCay in Transactions of the Royal Irish Academy, 1889. [2] [3] Additionally, in 1906, Georges Fontené  [ fr ] refound the theorem. [4] So the theorem is also called the Fontené's (Second) theorem. [5]

See also

References

  1. ↑ Weisstein, Eric W., "Griffiths' Theorem", MathWorld
  2. ↑ Johnson, Roger A. (1929), Advanced Euclidean Geometry, Houghton Mifflin, p. 245; reprint, Dover Books, 1960.
  3. ↑ Tabov, Jordan (1995), "Four Collinear Griffiths Points", Mathematics Magazine, 68 (1): 61–64, JSTOR   2691382, MR   1573071
  4. ↑ G. Fontene (1906). Sur le cercle pédal (PDF). Nouvelles annales de mathématiques. pp. 508–509.
  5. ↑ Weisstein, Eric W. "Fontené Theorems". MathWorld .
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