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Mathematics
Pythagorean theorem — Seeing it through area
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Change a right triangle's legs to compare three squares. Rearrange four triangles to explain the Pythagorean theorem.
9 + 16 = 25 u²
Drag a handle to change a leg
The right angle stays at 90°
Try another triangle
a² + b² = c²
9 + 16 = 25 u²
- Hypotenuse
- c = 5 u
The areas of the squares on the two legs add up to the area of the square on the hypotenuse.
Lengths use u; areas use u². This is not a + b = c.
Model notes
- The triangle is always right-angled. Legs range from 1 to 8 units in steps of 0.5. This limits the controls, not the theorem.
- Areas use unrounded geometry. The hypotenuse displays ≈ when its length is rounded.
- Rearrangement compares two complete configurations. Dashed source outlines are references, not extra pieces.