One can find the inverse of M if α, β and δ are known.

Since β is known in terms of α and δ, a and b can be found from another matrix operating on the unit vector defined by α. From trigonometry we also know that x and y are proportional to a.

It was known to Euclid that the lines drawn from the ends of the diameter to a point on a circle had a 90° included angle. This can be generalized but was only assumed in the second solution to the minimum links problem. The proof is as follows. If one assumes that the link from A to the connection point, X, is a vector with magnitude a and angle α with respect to the x axis and that from X to B is of magnitude b and angle β then B is the product of a matrix, M, and a vector containing a and b as components. The included angle between the segments is assumed to be δ and if α is known then so is β.

One can find the inverse of M if α, β and δ are known.

Since β is known in terms of α and δ, a and b can be found from another matrix operating on the unit vector defined by α. From trigonometry we also know that x and y are proportional to a.

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