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→Integer area and side lengths: Area formula from quarter-angle tangents |
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q_k = \frac{c_{k} - c_{k-1}}{1 + c_{k} c_{k-1}}
</math>
These rational numbers are the tangents of the individual quarter angles, using the formula for the tangent of the difference of angles. Rational side lengths for the polygon circumscribed by the unit circle are thus obtained as {{math|1=''s''<sub>''k''</sub> = 4''q''<sub>''k''</sub> / (1 + ''q''<sub>''k''</sub><sup>2</sup>)}}. The rational area is {{math|1=''A'' = ∑{{sub|''k''}} 2''q''{{sub|''k''}}(1 − ''q''{{sub|''k''}}{{sup|2}}) / (1 + ''q''{{sub|''k''}}{{sup|2}}){{sup|2}}}}. These can be made into integers by scaling the side lengths by a shared constant.
==Other properties==
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