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Automedian Triangle
In plane geometry, an automedian triangle is a triangle in which the lengths of the three medians (the line segments connecting each vertex to the midpoint of the opposite side) are proportional to the lengths of the three sides, in a different order. The three medians of an automedian triangle may be translated to form the sides of a second triangle that is similar to the first one. Characterization The side lengths of an automedian triangle satisfy the formula 2''a''2 = ''b''2 + ''c''2 or a permutation thereof, analogous to the Pythagorean theorem characterizing right triangles as the triangles satisfying the formula ''a''2 = ''b''2 + ''c''2. That is, in order for the three numbers ''a'', ''b'', and ''c'' to be the sides of an automedian triangle, the sequence of three squared side lengths ''b''2, ''a''2, and ''c''2 should form an arithmetic progression.. Construction from right triangles If ''x'', ''y'', and ''z'' are the three sides of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automedian Triangle
In plane geometry, an automedian triangle is a triangle in which the lengths of the three medians (the line segments connecting each vertex to the midpoint of the opposite side) are proportional to the lengths of the three sides, in a different order. The three medians of an automedian triangle may be translated to form the sides of a second triangle that is similar to the first one. Characterization The side lengths of an automedian triangle satisfy the formula 2''a''2 = ''b''2 + ''c''2 or a permutation thereof, analogous to the Pythagorean theorem characterizing right triangles as the triangles satisfying the formula ''a''2 = ''b''2 + ''c''2. That is, in order for the three numbers ''a'', ''b'', and ''c'' to be the sides of an automedian triangle, the sequence of three squared side lengths ''b''2, ''a''2, and ''c''2 should form an arithmetic progression.. Construction from right triangles If ''x'', ''y'', and ''z'' are the three sides of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
