Tetrahedral shoelace algorithm: calculating the volume of irregular solids

Nicholas Patrick, Indonesia 13-15

We have been calculating volume with different methods such as water displacement, convex polyhedron calculation, integration, and other methods. All of these methods have different limitations. As a mathematics student, I have been challenged to find another effective way to calculate the volume of any solid with one formula. This new method is inspired by the shoelace (aka surveyor's) formula in 2D and applying it in 3D. This research has been mathematically proven and tested with real calculations. This method can calculate the volume of any irregular solid.

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