File:01-257-Eck E-15.svg

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Summary

257-gon, approximate construction of the first side

Based on the unit circle r = 1 [unit of length]

Constructed side of 257-gon in GeoGebra (Display 15 significant decimal places, rounded) $\overline{E_{257}E_1} = a = 2.44475829850863E-2 \; [LE]$
Side of the 257-gon, 15 significant decimals, also rounded $a_{target} = 2\cdot\sin\left(\frac{180^\circ}{257} \right) = 2.44475829850863E-2\; [LE]$
Absolute error of the constructed side in GeoGebra $F_a = a - a_{target} = 0\;[unit\;of\;length]$
Constructed central angle in GeoGebra (Display 14 significant decimal places, rounded) $\mu = 1.40077821011673^\circ$
Central angle of the 257-gon in GeoGebra, 14 significant decimals, also rounded $\mu_{target} = \frac{360^\circ}{257} = 1.40077821011673^\circ$
Absolute error of the constructed central angle $F_\mu = \mu - \mu_{target} = 0^\circ$

At a radius r = 1 billion km (the light would need about 55 min for this distance) the absolute error of the first side a would be < 1 mm.

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	Date/Time	Dimensions	User	Comment
current	23:38, 18 February 2019	0 × 0 (393 KB)	Thales (talk \| contribs)	257-gon, approximate construction of the first side ===Result=== '''Based on the unit circle r = 1 [unit of length]''' * Constructed side of 257-gon in [https://en.wikipedia.org/wiki/GeoGebra GeoGebra] (Display 15 significant decimal places, rounded)...

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