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g

is a language that I came up with in order to record solutions to Euclidean straight edge and compass construction problems. The basic idea of this language is to combine the notion of functions with certain arithmetic symbols that make sense in geometric context.

A straight edge and a compass are the only tools allowed to carry out a given construction. These tools are theoretic - they have no markings on them and they are infinitely adjustable. An infinitely adjustable straight edge means that it can always be made long enough to connect any two points. An infinitely adjustable compass means that its legs can always be opened to span the distance between any two points.

\(\blacksquare\)

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