File:01-257-Eck E-15 Animation.gif
Summary
| Description |
Deutsch: 257-Eck mit Näherungskonstruktion der ersten Seite als Animation, mit einer Pause 15 s
English: 257-gon with approximate construction of the first side as an animation, with a pause 15 s |
| Date | |
| Source | Own work |
| Author | Petrus3743 |
Ergebnis
Bezogen auf den Einheitskreis r = 1 [LE]
- Konstruierte Seite des 257-Ecks in GeoGebra (Anzeige 15 sigifikante Nachkommastellen, gerundet)
- Seite des 257-Ecks, 15 sigifikante Nachkommastellen, ebenfalls gerundet
- Absoluter Fehler der konstruierten Seite
- Konstruierter Zentriwinkel in GeoGebra (Anzeige 14 sigifikante Nachkommastellen, gerundet)
- Zentriwinkel des 257-Ecks, 14 sigifikante Nachkommastellen, ebenfalls gerundet
- Absoluter Fehler des konstruierten Zentriwinkels
![{\displaystyle {\overline {E_{257}E_{1}}}=a=2{,}44475829850863E-2\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f7d426a8541464d840d9aac71682663473617e7)
![{\displaystyle a_{SOLL}=2\cdot \sin \left({\frac {180^{\circ }}{257}}\right)=2{,}44475829850863E-2\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6afb31fc572f77bd11dd2826eb56026a63f97db)
![{\displaystyle F_{a}=a-a_{SOLL}=0\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f5ab6b83a8b5c3f53c0bd5c167cb98e78fadf2a)
Beispiel um den Fehler zu verdeutlichen
Bei einem Radius r = 1 Mrd. km (das Licht bräuchte für diese Strecke ca. 55 min) wäre der absolute Fehler der konstruierten Seitenlänge a < 1 mm.
Result
Based on the unit circle r = 1 [unit of length]
- Constructed side of 257-gon in GeoGebra (Display 15 significant decimal places, rounded)
- Side of the 257-gon, 15 significant decimals, also rounded
- Absolute error of the constructed side in GeoGebra
- Constructed central angle in GeoGebra (Display 14 significant decimal places, rounded)
- Central angle of the 257-gon in GeoGebra, 14 significant decimals, also rounded
- Absolute error of the constructed central angle
![{\displaystyle {\overline {E_{257}E_{1}}}=a=2.44475829850863E-2\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eae94be538cb79f5dcdf64883f4dc90dfa1468bc)
![{\displaystyle a_{target}=2\cdot \sin \left({\frac {180^{\circ }}{257}}\right)=2.44475829850863E-2\;[LE]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a95d9bacb84e283b15db3df729b341a0004693a9)
![{\displaystyle F_{a}=a-a_{target}=0\;[unit\;of\;length]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1e55282a2bd4b52f9b91f0db8294bb65c1ec389)
Example to illustrate the error
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.
Licensing
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