File:01 Neuneck-60°.svg
![File:01 Neuneck-60°.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/2/23/01_Neuneck-60%C2%B0.svg/800px-01_Neuneck-60%C2%B0.svg.png?20220921172459)
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Summary
editDescription01 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 |
Licensing
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- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
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- 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.
Konstruktion
edit(Siehe hierzu auch die Animation)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/01_Neuneck-60%C2%B0_Animation.gif/405px-01_Neuneck-60%C2%B0_Animation.gif)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/23/01_Neuneck-60%C2%B0.svg/550px-01_Neuneck-60%C2%B0.svg.png)
- 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
- Hinweis: Die Punkte
- 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]
editIn 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)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/01_Neuneck-60%C2%B0_Animation.gif/405px-01_Neuneck-60%C2%B0_Animation.gif)
![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/23/01_Neuneck-60%C2%B0.svg/550px-01_Neuneck-60%C2%B0.svg.png)
- 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
- Note: The points
- 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]
editIn 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 | |
---|---|---|---|---|---|
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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