A Kepler triangle is a right triangle formed by three squares with areas in geometric progression according to the golden ratio.
A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is where is the golden ratio, and the progression can be written: , or approximately . Squares on the edges of this triangle have areas in another geometric progression, . Alternative definitions of the same triangle characterize it in terms of the three Pythagorean means of two numbers, or via the inradius of isosceles triangles.
This triangle is named after Johannes Kepler, but can be found in earlier sources. Although some sources claim that ancient Egyptian pyramids had proportions based on a Kepler triangle, most scholars believe that the golden ratio was not known to Egyptian mathematics and architecture.
A Keplertriangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is φ {\displaystyle {\sqrt {\varphi...
University of Tübingen in a letter to Kepler, his former student. The same year, Kepler wrote to Maestlin of the Keplertriangle, which combines the golden ratio...
A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...
Alternatively, the same triangles can be derived from the square triangular numbers. The Keplertriangle is a right triangle whose sides are in geometric...
chosen such that r = √φ it generates a right triangle that is always similar to the Keplertriangle. The triangle inequality can be extended by mathematical...
Chapter 11, "Keplertriangle theory", pp. 80–91, for material specific to the Keplertriangle, and p. 166 for the conclusion that the Keplertriangle theory...
astronomy History of physics Kepler orbit KeplertriangleKepler–Bouwkamp constant Penrose tiling Radiation pressure "Kepler's decision to base his causal...
Pythagorean theorem Hsuan thu Inverse Pythagorean theorem Keplertriangle Linear algebra List of triangle topics Lp space Nonhypotenuse number Parallelogram...
Golden rhombus – Rhombus with diagonals in the golden ratio Keplertriangle – Right triangle related to the golden ratio Silver ratio – Ratio of numbers...
Johnson circles Keplertriangle Kobon triangle problem Kosnita's theorem Leg (geometry) Lemoine's problem Lester's theorem List of triangle inequalities...
geometry) Isosceles triangleKeplertriangle Reuleaux triangle Right triangle Sierpinski triangle (fractal geometry) Special right triangles Spiral of Theodorus...
golden ratio. If this was the design method, it would imply the use of Kepler'striangle (face angle 51°49'), but according to many historians of science,...
Base:hypotenuse(b:a) ratios for the Pyramid of Khufu could be: 1:φ (Keplertriangle), 3:5 (3-4-5 Triangle), or 1:4/π Supposed ratios: Notre-Dame of Laon Golden rectangles...
approximating the "quadrature of the circle" can be achieved using a Keplertriangle. Doubling the cube is the construction, using only a straightedge and...
45) and (10, 40). Arithmetic–geometric mean Average Golden ratio Keplertriangle If AC = a and BC = b. OC = AM of a and b, and radius r = QO = OG. Using...
root-φ rectangle is divided by a diagonal, the result is two congruent Keplertriangles. Jay Hambidge, as part of his theory of dynamic symmetry, includes...
1446\dots } . Consequently, the square on the middle-sized edge of a Keplertriangle is similar in perimeter to its circumcircle. Some believe one or the...
right triangle in which two of the medians are perpendicular to each other. median triangle Integer triangleKeplertriangle, a right triangle in which...
antiprism was first depicted by Johannes Kepler, as an example of the general construction of antiprisms. Kepler, Johannes (1619), "Book II, Definition...
temperament, one advantage being that 36-TET includes traditional 12-TET. Keplertriangle Zipf's distribution Bohlen, Heinz (last updated 2012). "An 833 Cents...
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