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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. With the bent hypotenuse, the first figure actually occupies a combined 32 units, while the second figure occupies 33, including the "missing" square.
An excircle or escribed circle [2] of the triangle is a circle lying outside the triangle, tangent to one of its sides, and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
One of them is a circle, and one of them is the Steiner inellipse which is tangent to the triangle at the midpoints of the sides. Every acute triangle has three inscribed squares. In a right triangle two of them are merged and coincide with each other, so there are only two distinct inscribed squares. An obtuse triangle has a single inscribed ...
English: A 6-equidissection of a square. There are six triangles, all of equal area; they fill the square without overlapping. The dissection is not simplicial, because the triangles that meet along the main SW-NE diagonal overhang each other without sharing a common edge. There are also simplicial n-equidissections of a square for all even n.
black lower right triangle white square with lower right quadrant 2 ◒ ◢ ... inverse white circle square with upper left diagonal half black ...
Like most modern sets, this wooden tangram is stored in the square configuration. The tangram (Chinese: 七巧板; pinyin: qīqiǎobǎn; lit. 'seven boards of skill') is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective is to replicate a pattern (given only an outline ...
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Circle packing in a square is a packing problem in recreational mathematics where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square in order to maximize the minimal separation, d n , between points. [ 1 ]