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Heesch's problem is the problem of determining the set of numbers that can be Heesch numbers. Both are named for geometer Heinrich Heesch , [ 1 ] who found a tile with Heesch number 1 (the union of a square, equilateral triangle, and 30-60-90 right triangle) [ 2 ] and proposed the more general problem.
Then ABD is a 30°–60°–90° triangle with hypotenuse of length 2, and base BD of length 1. The fact that the remaining leg AD has length √ 3 follows immediately from the Pythagorean theorem. The 30°–60°–90° triangle is the only right triangle whose angles are in an arithmetic progression.
When faced with the choice between a red ball and a black ball, the probability of 30 / 90 is compared to the lower part of the 0 / 90 – 60 / 90 range (the probability of getting a black ball). The average person expects there to be fewer black balls than yellow balls because, in most real-world situations, it would be ...
A right triangle is a triangle containing one right angle of 90°. Two particular forms of right triangle have attracted the attention of rep-tile researchers, the 45°-90°-45° triangle and the 30°-60°-90° triangle.
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
30–60–90 triangle. In recreational mathematics, a polydrafter is a polyform with a 30°–60°–90° right triangle as the base form. This triangle is also called a drafting triangle, hence the name. [1] This triangle is also half of an equilateral triangle, and a polydrafter's cells must consist of halves of triangles in the triangular ...
A 30°–60°–90° triangle has sides of length 1, 2, and . When two such triangles are placed in the positions shown in the illustration, the smallest rectangle that can enclose them has width 1 + 3 {\displaystyle 1+{\sqrt {3}}} and height 3 {\displaystyle {\sqrt {3}}} .
Chapter five considers Monsky's theorem on the impossibility of partitioning a square into an odd number of equal-area triangles, and its proof using the 2-adic valuation, and chapter six applies Galois theory to more general problems of tiling polygons by congruent triangles, such as the impossibility of tiling a square with 30-60-90 right ...