Calculation of the edge cut margin to obtain an octagonal face

This online calculator calculates the indentation of the beginning of the cut along the edge of a square in cross-section bar to obtain a regular octagon at the base (the end is a regular octagon).

A one-line calculator, the purpose of which cannot be explained without a picture. So, the problem is as follows: there is a square cross section bar. It should be so sawed off at the edges that the end face becomes an octahedron (a regular octagon). Sawing is done at a known angle of 45 degrees. Now look at the picture:

Cut
Cut

You can see that the angle marked in green is 45 degrees. The width of the whole side is known - this is the width of the bar. The cut also goes at 45 degrees. We saw off, thus, a correct pyramid, with the octagon at its base, and the angle between the edge and the side of the base is also equal to 45.

That is, our indentation from the edge is:

b={s} \cdot cos 45^o

Where s is the side of the octagon.

The side of the octagon relates to the width of the bar as:

s = \frac{a}{1+\sqrt2}

Thus, the final formula is:

b=\frac{a}{1+\sqrt2}{cos 45^o}

PLANETCALC, Calculation of the edge cut margin to obtain an octagonal face

Calculation of the edge cut margin to obtain an octagonal face

Digits after the decimal point: 1
Cut edge indentation
 

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PLANETCALC, Calculation of the edge cut margin to obtain an octagonal face

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