File:01-65537-Eck E-17.svg
![File:01-65537-Eck E-17.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6e/01-65537-Eck_E-17.svg/800px-01-65537-Eck_E-17.svg.png?20180708214236)
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Summary
editDescription01-65537-Eck E-17.svg |
Deutsch: 65537-Eck, Näherungskonstruktion der ersten Seite in zwei Hauptschritten mithilfe von GeoGebra. Dargestellt ist der erste Schritt: Bestimmen der Position der 1024. Ecke.
English: 65537-gon, approximate construction of the first side in two main steps with help GeoGebra. Shown is the first step: Determine the position of the 1024th corner.
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Date | |
Source | Own work |
Author | Petrus3743 |
Other versions |
![]() 65537-gon, approximate construction of the first side in two main steps, animation, at the end 15 s pause |
SVG development InfoField |
Näherungsonstruktion
edit- Die Methode ähnelt der des Dreizehnecks
- Siehe hierzu auch die Konstruktion
Ergebnis
editBei einem Umkreisradius r = 1 [LE]
edit- Konstruierter Winkel (Anzeige GeoGbra)
- Winkel
- Absoluter Fehler des konstruierten Winkels
- (1 Winkelsekunde =
= 0,000277...° = 2,77...E-4°)
Näherungskonstruktion der ersten Seite
editIn der dritten Vergrößerung, ergibt sich somit annähernd die erste Seite E65537E1 = a des regelmäßigen 65537-Ecks.
- Konstruierte Seite des 65537-Ecks (Anzeige GeoGbra)
- Seite des 65537-Ecks
- Absoluter Fehler der konstruierten ersten Seite
- Absoluter Fehler der letzten Seite
- Konstruierter Zentriwinkel (Anzeige GeoGbra)
- Zentriwinkel
- Absoluter Fehler vom konstruierten Zentriwinkel
Beispiel um den Fehler zu verdeutlichen
editBei einem Umkreisradius r = 10 Billionen km (das Licht bräuchte für diese Strecke ca. 1 Jahr und 21 Tage) wäre die 1. Seite ca. 2 mm zu kurz, bzw. die 65537. Seite ca. 131 m zu lang.
Result
editApproximate construction
edit- The method is similar to that of the Tridecagon
- See also the construction
Based on the unit circle r = 1 [unit of length]
edit- Constructed angle (display GeoGebra)
- Angle
- Absolute error of the constructed angle
- (1 arcsecond =
= 0.000277...° = 2.77...E-4°)
- Constructed side of 65537-gon (display GeoGebra)
- Side of the 65537-gon
- Absolute error of the constructed first side
- Absolute error of the constructed last side
- Constructed central angle (display GeoGebra)
- Central angle
- Absolute error of the constructed central angle
Example to illustrate the error
editAt a circumscribed circle r = 10 trillions km (the light would need about 1 year and 21 days for this distance) the first side would be approx. 2 mm too short, or the 65537th side approx. 131 m too long.
Licensing
edit![w:en:Creative Commons](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![attribution](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
![share alike](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Cc-sa_white.svg/24px-Cc-sa_white.svg.png)
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 21:42, 8 July 2018 | ![]() | 1,252 × 917 (364 KB) | Petrus3743 (talk | contribs) | Grafikfehler |
21:29, 8 July 2018 | ![]() | 1,252 × 917 (364 KB) | Petrus3743 (talk | contribs) | Punktebezeichnungen korr. | |
13:45, 8 July 2018 | ![]() | 877 × 642 (373 KB) | Petrus3743 (talk | contribs) | Konstruktion vereinfacht | |
22:05, 26 April 2016 | ![]() | 1,460 × 913 (237 KB) | Petrus3743 (talk | contribs) | Tausenderpunkt entfernt | |
17:54, 24 April 2016 | ![]() | 1,457 × 910 (238 KB) | Petrus3743 (talk | contribs) | User created page with UploadWizard |
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Width | 35.344343150621086cm |
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Height | 25.88712661598778cm |