Geometry in carpentry. Volumetric star made of wood. This method of constructing a pentagon is over 2300 years old

Somehow they ordered me three-dimensional stars made of wood. They were needed by a familiar photographer for photo sessions.

The task is not to say that it is quite simple. The plywood base itself is not particularly difficult to make - I cut it out after marking on a jigsaw.

I had to tinker with the corners of the bars for the edging of the star, especially with the sharp ones.

But first I had to remember geometry, namely the method of constructing a regular pentagon.

As it turned out, this method was described by Euclid in about 300 BC. That is, more than 2,300 years ago.

To build a regular pentagon, a compass and a ruler will be enough.

1. First, you need to build a circle in which the pentagon will be inscribed. The center point O is the green circle in the figure.
2. Next, through the center of the circle, you need to build two perpendiculars. A and B are the points of intersection of perpendiculars with a circle. Point A will be one of the vertices of the pentagon.
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3. Mark point C in the middle between O and B
4. Next, a circle is drawn with center at point C through point A. Point D is placed at its intersection with line OB.
5. Next, you need to draw a circle centered at A through point D. When this circle intersects with the original (green circle), two points E and F will be obtained - another pair of vertices of the pentagon.
6. Now we need to draw a circle centered at E through point A. The intersection with the original circle will give another point of the pentagon - point G.
7. Draw another circle centered at F through point A. We get point H - the fifth point of the pentagon.
8. To build a star, you need to connect the points A -> G -> F -> E -> H -> A

I built the stars on plywood blanks, which later served as the basis. On these blanks I measured the angles and dimensions of the bars for edging.

Sharp outer corners marked and ground the corner on a belt sander.

The inner corners of the bars for the stars, cut off on a circular with the help of an angle stop.

And then he sanded, glued, putty the joints, sanded again and got this pair of volumetric wooden stars.

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Alexander.

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