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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).
Unfolding a 3D sphere to 2D shapes
If you want to made a DIY sphere, you need to unfold the sphere to 2D shapes, or, more strictly speaking, approximate the sphere using petals, or "orange peels" (also called the lunes) on the plane. The calculator calculates basic parameters of such 2D peel and displays coordinates of points for drawing one peel on a plane.
Volume of the hemisphere cut at an angle
Volume of hemisphere asymmetrically cut by a flat plane under a given angle.
Cutting a circle
Two ways to cut a circle into equal parts : sector cuts and parallel cuts.
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