The smallest side of the square that contains 2*n regular polygon where n is odd

Revision en2, by nhantran0, 2020-05-18 14:19:45

Half square on the left, full square on the right

Recall: $$$n$$$ is odd. Let $$$u=\lfloor{\frac{n}{2}}\rfloor$$$, $$$v=n-u$$$, $$$v-u=1$$$.

In the figures, $$$u$$$ is the number of polygon sides between $$$\sphericalangle{RWP}$$$, $$$v$$$ is the number of polygon sides between $$$\sphericalangle{PWM}$$$.

TODO: 1. Prove $$$\measuredangle{RMN}\leq\measuredangle{RMU}$$$

Tags #geometry

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en9 English nhantran0 2020-05-21 17:45:16 190 Tiny change: 'c{2\pi}{n}.\lfloor\fr' -> 'c{2\pi}{n}\lfloor\fr'
en8 English nhantran0 2020-05-20 14:21:03 73
en7 English nhantran0 2020-05-19 02:27:21 97 Tiny change: Remove redundant 'Let $d$ be'
en6 English nhantran0 2020-05-19 02:20:09 340 Added GeoGebra information
en5 English nhantran0 2020-05-18 21:33:41 14 Tiny change: 'mference. Recall that in failed c' -> 'mference. In failed c'
en4 English nhantran0 2020-05-18 21:25:35 1960 Tiny change: '\n$\theta=360^{\circ}/{m}$\n\n$r.\' -> '\n$\theta=\frac{360^{\circ}}{2n}$\n\n$r.\' (published)
en3 English nhantran0 2020-05-18 19:29:58 3095 Tiny change: 'frac{s}{2}$$\implies$$r=\frac{1}' -> 'frac{s}{2}{\implies}r=\frac{1}'
en2 English nhantran0 2020-05-18 14:19:45 409 Tiny change: ' proof for ' -> ' proof for:\n1. '
en1 English nhantran0 2020-05-18 09:06:27 170 Initial revision (saved to drafts)