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  2. Special right triangle - Wikipedia

    en.wikipedia.org/wiki/Special_right_triangle

    For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio.

  3. Penrose triangle - Wikipedia

    en.wikipedia.org/wiki/Penrose_triangle

    Penrose triangle. The Penrose triangle, also known as the Penrose tribar, the impossible tribar, [1] or the impossible triangle, [2] is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing.

  4. Kepler triangle - Wikipedia

    en.wikipedia.org/wiki/Kepler_triangle

    [3] [5] A little earlier than Kepler, Pedro Nunes wrote about it in 1567, and it is "likely to have been widespread in late medieval and Renaissance manuscript traditions". [3] It has also been independently rediscovered several times, later than Kepler. [1] A right triangle formed by an edge midpoint, base center point, and apex of a square ...

  5. Exercise (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Exercise_(mathematics)

    A similar sentiment was expressed by Marvin Bittinger when he prepared the second edition [3] of his textbook: In response to comments from users, the authors have added exercises that require something of the student other than an understanding of the immediate objectives of the lesson at hand, yet are not necessarily highly challenging.

  6. Pick's theorem - Wikipedia

    en.wikipedia.org/wiki/Pick's_theorem

    Because each special triangle has area , a polygon of area will be subdivided into special triangles. [ 5 ] The subdivision of the polygon into triangles forms a planar graph , and Euler's formula V − E + F = 2 {\displaystyle V-E+F=2} gives an equation that applies to the number of vertices, edges, and faces of any planar graph.

  7. Missing square puzzle - Wikipedia

    en.wikipedia.org/wiki/Missing_square_puzzle

    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.

  8. File:Special right triangles for trig.svg - Wikipedia

    en.wikipedia.org/wiki/File:Special_right...

    English: Special right triangles in a unit circle are helpful for remembering trig functions of multiples of 30 and 45 degrees. This figure illustrates cos(30) = sin ...

  9. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    [1] 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. [3]