Morley triangle
The Morley triangle , named after Frank Morley , is an equilateral triangle that can be constructed within any triangle.
Morley's definition and theorem
The interior angles of any triangle are divided into three equal angles (which is generally not possible with a compass and ruler ). For each side of the triangle, consider the intersection of those two dividing lines that start from the end points of this side and are adjacent to this side. The Morley triangle is the triangle whose corners are the three points of intersection obtained in this way.
The set of Morley is: Regardless of the shape of the original triangle, the Morley triangle is always equilateral.
See also
Excellent points in the triangle
literature
- HSM Coxeter , SL Greitzer: Timeless geometry. Klett, Stuttgart 1983.
- Horst Hischer: Fundamental terms of mathematics: Origin and development: structure - function - number . Springer 2012, ISBN 9783834886323 , pp. 2-4
- Lorenz Halbeisen, Norbert Hungerbühler, Juan Läuchli: With harmonious proportions to conic sections: pearls of classical geometry . Springer 2016, ISBN 9783662530344 , pp. 182-185
- Martin Erickson: Mathematical Appetizers: Fascinating Pictures. Gripping formulas. Charming sentences. Springer, 2015, ISBN 9783662454596 , pp. 60–63 (with Conway's elegant proof)
Web links
- Morley's Miracle - sentence, illustration and background information as well as 26 different proofs on cut-the-knot.org
- Florian Modler: Forgotten sentences on the triangle. Part 8: The Butterfly and Morley's Theorem . Matroids math planet
- Eric W. Weisstein : Morley's Theorem . In: MathWorld (English).
- Eric W. Weisstein : First Morley Triangle . In: MathWorld (English).
- Rudolf Fritsch : A simple proof of Morley's theorem. (PDF; 70 kB, archived version)
Individual evidence
- ↑ Max Koecher , Aloys Krieg : level geometry . 3. Edition. Springer-Verlag, Berlin 2007, ISBN 978-3-540-49327-3 , p. 131