Tetrahedral Analog of the Pythagorean Theorem
18 days ago
- #python
- #mathematics
- #geometry
- A tetrahedron has four triangular faces, with three meeting at a right angle.
- De Gua's theorem states: A0² = A1² + A2² + A3² for the areas of the faces.
- Python code demonstrates De Gua's theorem numerically, confirming the theorem holds.
- The theorem generalizes to higher dimensions, such as a 4-simplex in a hypercube.
- For a 4-simplex, V0² = V1² + V2² + V3² + V4², extending De Gua's theorem.
- Python code for the 4-simplex shows the theorem holds, with minor floating-point errors.
- Floating-point arithmetic limitations cause precision loss when subtracting nearly equal numbers.