File:PrimitivePythagoreanTriplesRev08.svg
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DescriptionPrimitivePythagoreanTriplesRev08.svg |
English: A depiction of all the primitive Pythagorean triples (a,b,c) with a and b < 1170 and a odd, where a is plotted on the horizontal axis, b on the vertical. The curvilinear grid is composed of curves of constant m − n and of constant m + n in Euclid's formula, . These curves can be specified parametrically as , with one of i, j held constant in {1,2,3,...} and the other varied over an interval in R. The oddness of m − n (and of m + n) required for the triple to be primitive is thus built in, with . All primitive Pythagorean triples are represented on this grid. The scaled triangles are drawn with their centroids at the corresponding (a,b). Unlabeled grid intersection points correspond to non-primitive Pythagorean triples. |
Date | |
Source | Own work. Same as PrimitivePythagoreanTriplesRev01.svg except for colors. Made using a Python program to write SVG directly. |
Author | Adam Cunningham and John Ringland |
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current | 18:23, 16 March 2012 | 1,458 × 727 (678 KB) | Darnling (talk | contribs) |
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