The Fourth Harmonic Point of a Triangle
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The fourth harmonic point of a triangle is an invariant point under a certain geometric transformation. Given a triangle with and fixed, extend the segment to another fixed point . Draw a line through to intersect the line at and the line at . Let be the intersection of the lines and . Let the line intersect at . Then , called the fourth harmonic point, is invariant either by moving or changing the slope of the line .
[more]
Contributed by: Shenghui Yang (June 2012)
Open content licensed under CC BY-NC-SA
Snapshots
Details
References
[1] J. Gray, Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century, London: Springer-Verlag, 2007.
[2] L. Cremona, Elements of Projective Geometry, 3rd ed. (C. Leudesdorf, trans.), New York: Dover, 1960.
[3] R. A. Johnson, Modern Geometry, New York: Houghton–Mifflin, 1929.
Permanent Citation