This piece demonstrates one method of constructing an approximate regular heptagon using ruler and compass (it is mathematically impossible to construct a perfect heptagon using only ruler and compass. Interestingly though, it is possible through the technique of neusis which introduces a moveable set length, and through paper-folding). This particular construction combines the circle, triangle, and square in order to arrive at the measurement for one side of a regular heptagon. This measurement is found where the equilateral triangle (formed using the length of one side of the square) cuts the original circle. This measurement can then be transferred around the circle to define the full heptagon.
With approximate polygon constructions, the compass radius often needs to be adjusted a millimetre or so in order to establish equal divisions. They are, however, still useful from a practical perspective, as well as being philosophically potent. - Gillian Turnham
© Gillian Turnham 2023