Working Model of Pythagoras theorem (Acrylic) for School Maths Lab

Quick Answer: The Working Model of Pythagoras theorem (Acrylic) is a transparent acrylic demonstration, usually a rotating panel with square compartments on the three sides of a right triangle, partly filled with coloured liquid or granules. Turning this acrylic Pythagoras theorem model moves the fill from the two smaller squares into the square on the hypotenuse, which it fills exactly, showing a² + b² = c² as equal areas.

Why the Model Is Made of Acrylic

The model only works as a demonstration if students can see the fill move, which is why this version is made from clear acrylic. The compartments share the same depth, so the amount each holds is proportional to its face area. When the two leg squares empty into the hypotenuse square and fill it with nothing left over, the areas a² and b² have been shown to add up to c².

Rotation is the key action. Starting with the fill in the hypotenuse square, turning the model moves it into the two leg squares, and turning back returns it, so the class sees the equal capacity in both directions. That answers the natural objection that the fill only looked as if it fitted.

The demonstration is a visual argument rather than a formal proof, so pair it with an algebraic or dissection proof in the same lesson. The side lengths of the triangle, the fill used and the size of the model are not given in the title and should be confirmed.

Specifications

Applications

• Whole-class demonstration when the theorem is first introduced
• Starting a discussion on why equal-depth compartments let volume stand for area
• Contrasting a demonstration with a formal proof in higher classes
• Maths exhibitions and open days, where a moving demonstration draws attention

Care & Handling

• Clean the acrylic Pythagoras theorem model with a soft damp cloth and mild soap only; alcohol and solvent cleaners can craze acrylic.
• Rotate slowly and evenly so the fill settles fully before the next turn.
• Keep the model out of direct sun and away from heaters, and if it contains liquid, check it regularly for leaks.
• Store it cushioned against knocks, which can crack acrylic panel edges.

Why Choose LabEquip

Maths departments buy this acrylic model for teacher-led demonstrations in which every student must see the fill move. For hands-on dissection work in groups, the Pythagoras Theorem, Senior kit is the complementary resource, and the Working model of Pythagoras theorem is the other working-model listing in the Mathematics School Lab Products range. Ask for dimensions through the contact page.

Frequently Asked Questions

How does the working model prove a² + b² = c²?

All three square compartments have the same depth, so the fill each holds depends only on the area of its face. When the fill from the two smaller squares exactly fills the square on the hypotenuse, their areas must add up to the area of the hypotenuse square, which is the theorem.

Why is the model made of acrylic?

Clear acrylic lets the whole class watch the fill move between compartments. It is lighter than glass and less likely to shatter, although it scratches more easily and must be cleaned gently.

Is the working model a formal proof?

No. It is a physical demonstration that makes the theorem believable and memorable. Formal proofs use algebra or congruent and similar triangles, and students should see at least one of those alongside the model.

Does the theorem work for triangles that are not right-angled?

No. In an acute triangle the squares on the two shorter sides add to more than the square on the longest side, and in an obtuse triangle to less. The model is built on a right triangle for that reason.

How should the acrylic surface be cleaned?

Wipe it with a soft cloth dampened in mild soapy water and dry it with a microfibre cloth. Avoid alcohol, acetone and abrasive pads, which can cloud or scratch acrylic and make the fill hard to see.

What is a Pythagorean triple?

It is a set of three whole numbers that fit a² + b² = c², such as 3, 4, 5 or 5, 12, 13. Multiplying a triple by any whole number gives another one, so 6, 8, 10 also works. Triples make useful follow-up exercises after the demonstration.

Last Updated: September 2026