Vecten point
The two Vecten points belong to the special points of a triangle . They go back to the French mathematician Vecten (1811/1812).
First Vecten point
Three squares are drawn outwards over the sides of a triangle ABC . Each of the three centers of the square that make up the Kiepert triangle is connected to the opposite corner of the original triangle. The connecting straight lines intersect at a point which is called the first Vecten point and bears the Kimberling number X (485).
Second Vecten point
If you draw the squares inwards instead of outwards, you get the second Vecten point with Kimberling number X (486).
properties
- The two Vecten points lie on the Kiepert hyperbola .
- The Vecten points lie on a straight line with the center of the Feuerbach circle (nine-point circle).
Coordinates
Vecten points ( and ) | |
---|---|
Trilinear coordinates | |
Barycentric coordinates | |
The plus sign applies to the first Vecten point, the minus sign to the second. |
literature
- Sotirios E. Louridas, Michael Th. Rassias: Problem-Solving and Selected Topics in Euclidean Geometry: In the Spirit of the Mathematical Olympiads . Springer, 2014, ISBN 978-1-4614-7273-5 , pp. 62-63
- Claudi Alsina, Roger B. Nelsen: Pearls of Mathematics: 20 geometric figures as starting points for mathematical exploratory trips . Springer, 2015, ISBN 978-3-662-45461-9 , pp. 4-7, 93
Web links
- Kimberling's Encyclopedia of Triangle Centers (English)
- Eric W. Weisstein : Vecten Points . In: MathWorld (English).
Individual evidence
- ↑ Little is known about Vecten. It is known that from 1810 to 1816 he worked as a " professeur de mathématiques spéciales " at the Lycée de Nîmes and published 22 articles in the journal Annales published by the mathematician Joseph Gergonne . See: Claudi Alsina, Roger B. Nelsen: Pearls of Mathematics: 20 geometric figures as starting points for mathematical exploratory trips . Springer, 2015, ISBN 978-3-662-45461-9 , p. 4