File:Construction of an almost regular hexagon and dodecagon..svg

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Description Square of the circle (approximation) -- almost regular hexagon constructed by placing vertices on integer points of a 17x17 grid. Based on the fact that arctan(4/7)=29.74488°, a close approximation to 30°. Some of the vertices of the slightly irregular hexagon are 8 units away from the origin, while others are sqrt(4²+7²) or 8.06226...
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Source made by me (Inkscape)
Author user:Mjchael
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SVG development
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The SVG code is valid.
 
This trigonometry was created with CorelDRAW.
 
The file size of this SVG trigonometry may be irrationally large because its text has been converted to paths inhibiting translations.
llink=Category:Qs icons SVGThis SVG trigonometry shows a very simple image. Drawing uncomplicated graphics with a text editor seems more adequate than using a vector graphics program, and will often result in a dramatic reduction of file size.
Deutsch: Der Name der Grafik besagt, dass es möglich ist, nur durch das Abzählen von quadratischen Rechenkästchen 12 Punkte so auf einer Kreisbahn zu positionieren, dass sich daraus ein annähernd regelmäßiges Zwölfeck ergibt.
Annäherung an 30° durch einen Tangens von 7/4.
Abweichung vom Ideal < 0,8%.

Für viele praktische Zwecke erreicht man eine ausreichende Annäherung an ein reguläres Sechseck, wenn man dieses aus annähernd gleichseitigen Dreiecken konstruiert. Ein annähernd gleichseitiges Dreieck erhält man, wenn die Grundseite des Dreiecks zur Höhe in einem Verhältnis von 8:7 steht. Die Berechnung in der Grafik zeigt, dass die beiden Schenkel des so konstruierten Dreiecks annähernd die Länge der Grundseite besitzen. Diese Annäherung findet dort Anwendung, wo ein Fehler von knapp 1 % toleriert werden kann. So können zum Beispiel Karten oder Spielfelder in leicht zu zeichnende und leicht zu berechnende Sektoren eingeteilt werden. Die Konstruktion gelingt auch problemlos Kindern im Grundschulalter, da nicht mehr benötigt wird, als das Abzählen von Rechenkästchen. Aufwendige Konstruktionen mit Zirkel und Geodreieck entfallen.

Praktischer Nutzen: einfache Graphiken und Design, Kartographie, Sechseckkonstruktionen am Computer bei Zeichenprogrammen ohne Winkelfunktion (ausschließlich mit Punkten).

Für größere Konstruktionen könnte auch ein Verhältnis von 7:12 interessant sein: 72 + 122 = 193 = 13,89...2 ~ 196 = 142 (Abweichung < 0,8%)

Vektorkoordinaten

Die Punkte Pi (x|y) sind im folgenden nach den Ziffern einer Uhr nummeriert, das Zentrum ist (0|0):

  • Koordinaten eines liegenden Sechsecks

P1 (4|7), P3 (8|0), P5 (4|−7), P7 (−4|−7), P9 (−8|0), P11 (−4|7)

  • Koordinaten eines auf der Spitze stehenden Sechsecks
P2 (7|4), P4 (7|−4), P6 (0|−8), P8 (−7|−4), P10 (−7|4), P12 (0|8)


English: The name of the graphic says that it is possible to position only by counting computation of square boxes 12 points on a circular path so that it results in an almost regular dodecagon.
approximation at 30° with a tangent of 7/4
Deviation from the ideal < 0.8%

For many practical purposes, you can reach a sufficient approximation to a regular hexagon when you designed this for nearly equilateral triangles. A nearly equilateral triangle is obtained when the base of the triangle to the amount present is in a ratio of 8:7. The calculation in the graph shows that the two legs of the triangle thus constructed have nearly the length of the base side. This approach is used in applications where an error by almost 1% can be tolerated . Thus, for example, cards or playing fields and easy to drawings can be divided easily be calculated sectors. The design also easily manage children of primary school age, there is not more needed, as the counting of computational box. Elaborate constructions with compass and set square is no longer necessary.


Practical advantage: simple design and graphics, cartography, construction of hexagons on the computer by drawing programs without angular function (only with points). For larger structures could also be interesting to have a ratio of 7:12

72 + 122 = 193 = 13,89...2 ~ 196 = 142.

Deviation from the ideal < 0.8%

vector coordinates

The points Pi (x|y) depend on the numbers of a clock, the center is (0|0):

  • Coordinates of a hexagon is
P1 (4|7), P3 (8|0), P5 (4|−7), P7 (−4|−7), P9 (−8|0), P11 (−4|7)
  • Coordinates of a hexagon below the top
P2 (7|4), P4 (7|−4), P6 (0|−8), P8 (−7|−4), P10 (−7|4), P12 (0|8)
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current11:31, 11 December 2011Thumbnail for version as of 11:31, 11 December 2011400 × 400 (59 KB)Mjchael (talk | contribs){{Information |Description= Square of the circle (approximation) |Source = made by me (Inkscape) |Date = 2007-08 |Author=user:Mjchael |Permission = {{self|cc-by-sa-2.5}} }} ;Deutsch Der Name der Grafik besagt, dass es möglich ist, nur durch das Abz

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