3D Pythagorean Theorem — FAQ
Frequently asked questions about 3D Pythagorean Theorem (a²+b²+c²=d²).
Q1. Why is this useful if we already have 2D Pythagoras?
Many real problems are 3D — fitting furniture diagonally through a door, calculating cable lengths in 3D rooms, or determining shortest distances in 3D space all need the 3D extension.
Q2. Does this work for any rectangular box?
Yes — any rectangular cuboid (box with all right angles). The formula √(a²+b²+c²) gives the space diagonal from any corner to the opposite corner.
Q3. What is the relationship to 2D Pythagoras?
The 3D version applies Pythagoras twice: first the floor diagonal = √(a²+b²), then the space diagonal = √(floor_diagonal² + c²) = √(a²+b²+c²).
Have more questions? Try the interactive calculator at /tools/pythagorean-3d-theorem