KoG, Vol. 28 No. 28, 2024.
Izvorni znanstveni članak
https://doi.org/10.31896/k.28.4
Cramer-Castillon on a Triangle's Incircle and Excircles
Dominique Laurain
; Enseeiht, Toulouse, France
Peter Moses
; Moparmatic Inc., Worcestershire, England
Dan Reznik
; Data Science Consulting, Rio De Janeiro, Brazil
*
* Dopisni autor.
Sažetak
The Cramer-Castillon problem (CCP) consists in finding one or more polygons inscribed in a circle such that their sides pass cyclically through a list of N points. We study this problem where the points are the vertices of a triangle and the circle is either the incircle or one of the excircles. We find that (i) in each case there is always a pair of solutions (total of 8 new triangles and 24 vertices); (ii) each pair shares all Brocard geometry objects, (iii) barycentric coordinates are laden with the golden ratio; and (iv) simple operations on the barycentrics of a single vertex out of the 24 yield all other 23.
Ključne riječi
Golden ratio; triangle; Brocard; symmedian
Hrčak ID:
324086
URI
Datum izdavanja:
20.12.2024.
Posjeta: 0 *