△ Triangle Physics ExplorerGeometry · experiment · evidence
3–4–5 triangle

The physics behind the point

Compare behavior across triangle shapes

Seven diagrams and a near-equilateral expansion connect shape to position.

A small guide to the explorer

Drag the three large vertex handles, or focus a handle and move it with the arrow keys. Select centers to overlay their locations. The two other views explain the physical definitions and compare their shape fingerprints.

A triangle center must commute with rigid motions, scaling and vertex relabeling. An attractive center moves in a nonnegative projected direction when one vertex is displaced: δv · δc ≥ 0.