cathetmath

A geometry workspace concept · Study 001

Make the relationship
visible.

A small space for a big mathematical idea. Move a side, watch the squares, and turn a formula into something you can see.

01 / The right triangleInteractive study · No account needed

Set the two legs

4
2 units8 units
3
2 units8 units

Use the arrow keys to change a side by one unit. All measurements update together.

Or start with a pair

FIG. 01 — THREE SQUARESPROPORTIONAL / AUTO FIT
Squares on the three sides of a right triangle Two smaller squares have areas 16 and 9. Their total equals the larger square's area of 25. a² = 16 b² = 9 c² = 25 90°
Square on aSquare on bSquare on c

A 3–4–5 triangle: all three side lengths are whole numbers.

a² + b² = c², always at 90°
02 / A WAY TO THINK

Less memorizing.
More noticing.

Cathet Math explores a simple idea for learning software: keep the diagram, the controls, and the reasoning in the same place.

This desk is one self-contained demonstration of that idea. Start with a question and let the shape help you answer it.

  1. 01Change one thing.

    Keep leg b fixed and increase leg a. Which square grows? Which measurement changes fastest?

  2. 02Find a pattern.

    Try equal legs. The two small squares match, while the largest square has twice the area of either one.

  3. 03Say it precisely.

    The areas add: a² + b² = c². The side lengths themselves do not. That distinction is the heart of the theorem.

03 / Take the idea a little further

If both legs double, does the area double too?

What does “cathet” mean?

A cathetus is either of the two sides that meet at the right angle. These are the legs, labeled a and b on this desk.

Does this work for every triangle?

This particular relationship applies to right triangles. The study keeps the angle between a and b at 90° while their lengths change.

What can I do in this concept?

Adjust the diagram, compare measurements, and reveal a worked explanation. This is a browser demonstration, with no accounts, paid plans, saved progress, or course enrollment.