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The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be S = 13×5 / 2 = 32.5 units. However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent.
A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral shape , consisting of multiple layers of pieces along each axis which can rotate independently of each ...
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
In 2015, an anonymous Japanese woman using the pen name "aerile re" published the first known method (the method of 3 circumcenters) to construct a proof in elementary geometry for a special class of adventitious quadrangles problem. [7] [8] [9] This work solves the first of the three unsolved problems listed by Rigby in his 1978 paper. [5]
The Master Pyraminx has 4 layers and 16 triangles-per-face (compared to 3 layers and 9 triangles-per-face of the original), and is based on the Skewb Diamond mechanism. This version has about 2.6817 × 10 15 combinations. [7] [8] The Master Pyraminx has 4 "tips" (same as the original Pyraminx) 4 "middle axials" (same as the original Pyraminx)
All problems that can be solved using mass point geometry can also be solved using either similar triangles, vectors, or area ratios, [2] but many students prefer to use mass points. Though modern mass point geometry was developed in the 1960s by New York high school students, [ 3 ] the concept has been found to have been used as early as 1827 ...
Each puzzle piece is a 12-polydrafter (dodecadrafter) made of twelve 30-60-90 triangles (that is, a continuous compound of twelve halves of equilateral triangles, restricted to the grid layout). Each piece has an area equal to that of 6 equilateral triangles, and the area of the entire dodecagon is exactly 209 * 6 = 1254 equilateral triangles ...
The short ladder in the complex solution in the 3, 2, 1 case appears to be tilted at 45 degrees, but actually slightly less with a tangent of 0.993. Other combinations of ladder lengths and crossover height have comparable complex solutions. With combination 105, 87, 35 the short ladder tangent is approximately 0.75.
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