File:01 Neuneck-60°.svg
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Summary
[edit]Description01 Neuneck-60°.svg |
Deutsch: Neuneck (Nonagon) bei gegebenem Umkreis mit Winkeldreiteilung, Näherungskonstruktion
English: Nonagon for a given circumference with an angle trisection, an approximation construction |
Date | |
Source | Own work |
Author | Petrus3743 |
SVG development InfoField |
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Konstruktion
[edit](Siehe hierzu auch die Animation)
- Kreis mit beliebigem Radius um Mittelpunkt
- Winkelschenkel und Winkelschenkel schließen den Winkel im Scheitel ein.
- Kreis um mit Radius ; die Verlängerung des Winkelschenkels schneidet Kreis in
- Durchmesser des Kreises mit
- Bestimme Punkt auf Kreis so, dass
- Strecke in halbieren, die anschließende, nicht eingezeichnete, Mittelsenkrechte von schneidet in ergibt
- Linie durch und ; deren Enden liegen nahe am Kreis
- Parallele zu ab erreicht Kreis in
- Bestimme Punkt mithilfe eines nicht eingezeichneten Kreisbogens (Radius um , auf Linie durch und so, dass
- Linie ab durch erreicht Kreis in anschließend Linie ab bis
- Hinweis: Die Punkte und liegen nicht auf der Strecke
- Parallele zu ab erreicht Kreis in
- Bestimme Punkt mithilfe eines nicht eingezeichneten Kreisbogens (Radius ) um , auf Linie durch und so, dass die werdende Strecke
- Linie ab durch erreicht Kreis in
- Bestimme Punkt so, dass Winkel
- Bestimme Punkt durch Verdoppelung des Kreisbogens und verbinde mit
- Der konstruierte Winkel ist nahezu gleich zwei Drittel des Winkels , d. h. nahezu
Ergebnis, bezogen auf den Einheitskreis r = 1 [LE]
[edit]In GeoGebra werden max. 15 Nachkommastellen angezeigt.
- Bei einem Radius r = 1 Mrd. km (das Licht bräuchte für diese Strecke ca. 56 min) wäre der Fehler der konstruierten Seitenlänge a des Neunecks < 1 mm.
Construction
[edit](See also the animation)
- Circle with any radius around centre
- Angle leg and angle leg enclose angle at vertex .
- Circle around with radius ; the extension of the angle leg intersects circle in .
- Diameter of circle with
- Determine point on circle such that
- Bisect the line segment in , the subsequent, not drawn, median perpendicular of intersects in gives
- Line through and ; their ends are close to circle .
- Parallel to from reaches circle in
- Determine point using an undrawn arc of a circle (radius around , on the line through and such that
- Line from through reaches circle in then line from to
- Note: The points and are not on the line
- Parallel to from reaches circle in
- Determine point using an undrawn arc of a circle (radius ) around , on the line through and such that the becoming distance is
- Line from through reaches circle in
- Determine point such that angle
- Determine point by doubling arc of a circle and connect with
- The constructed angle is nearly equal to two thirds of the angle , i.e. nearly
Result, related to the unit circle r = 1 [LE]
[edit]In GeoGebra, max. 15 decimal places are displayed.
- For a radius r = 1 billion km (the light would need approx. 56 min for this distance) the error of the constructed side length a of the neuneck would be < 1 mm.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:24, 21 September 2022 | 905 × 596 (68 KB) | Petrus3743 (talk | contribs) | Kurzhinweis korr. | |
17:14, 21 September 2022 | 905 × 596 (68 KB) | Petrus3743 (talk | contribs) | Kurzhinweis korrigiert | ||
16:26, 21 September 2022 | 905 × 596 (69 KB) | Petrus3743 (talk | contribs) | Kurzbeschreibung angepasst | ||
21:24, 20 September 2022 | 905 × 596 (85 KB) | Petrus3743 (talk | contribs) | Farbe angeglichen | ||
17:38, 20 September 2022 | 905 × 596 (85 KB) | Petrus3743 (talk | contribs) | Uploaded own work with UploadWizard |
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Height | 595.71 |