Some FormulaeScans from the papers of Lawrence EdwardsExamples of the formulae in use (Images © G. Calderwood; the mathematical content is public domain.) |
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Plot points A, B, C and D on a line
If the positions of points X and Y have been correctly calculated and plotted, Points A and D should fall, by pure construction, on their plotted positions. Given four points A, B, C & D on the line, and their spacings, we want the invariants, X & Y We need the cross ratio, R, of the four points A, B, C & D to find the multiplier, m. |
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A Natural Example We use John's arrows and ruler to obtain three sets of three intervals (My markings) Results We see that only the third set, s3, gives real invariants: the X invariant lies 16.86 mm (by John's ruler) left of the fourth arrow from the left. Using the position of this invariant for the check-by-construction, we see that the positions of the nodes corresponding to s3 are accurately traced, but that other node-positions are not. This suggests that we may have a measure that varies smoothly in "amplitude" along the length of the bamboo.
With thanks to John Blackwood. |