I'm terrible at geometry; I simply didn't bring that part of my brain from the hospital. So I need help.
I'm building a platform of boards around an octagonal tower. Each side of the tower will have its own "flap," and the eight flaps will form a continuous bridge. Each flap extends one meter from the façade. If the base of each flap (i.e., the length against the façade) is one meter, how long will the other side be (i.e., one meter out)? I hope someone with geometry/mathematics knowledge can answer without too much work.
And then I read in another thread that the angle of the flaps is 135 degrees around the octagon, I'd also appreciate confirmation on that.
The octagon's "exterior angles" (red) are indeed 135 degrees. Half of that is 67.5 degrees. If we start with a width of 1 m and go 1 m outward, two yellow triangles are formed with a height of 1 m and angles of 90, 67.5, and 22.5 degrees. The base of such a triangle (blue line) is then tan(22.5), which is approximately 0.414 m. The total distance along the edge of an octagon sector then becomes 1.828 m.
The octagon's exterior angles are indeed 135 degrees. Half of that is 67.5 degrees. If we start with a width of 1 m and go 1 m outward, two yellow triangles are formed with a height of 1 m and angles of 90, 67.5, and 22.5 degrees. The base of one of these (blue line) becomes tan(22.5), which is approximately 0.414 m. The total distance along the outer edge of an octagon sector becomes 1.828 m.
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Brilliant! I would never have figured out going through two smaller triangles. In other words, the total length of both your blue and green markings is 1.828 m. Surprisingly to me, the length is almost doubled with just one meter depth, interesting. Well then, time to get out the saw. Thanks!
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