Pythagoras Theorem Reverse Method Model

Quick Answer: Pythagoras Theorem (Reverse Method) is a maths lab model for the dissection proof of Pythagoras’ theorem credited to the Indian mathematician Bhaskara II, which school catalogues often call the Pythagoras theorem reverse method. Four identical right triangles and one small square fill the square on the hypotenuse, and the areas show that a² + b² = c².

Bhaskara’s Proof, Step by Step

Take a right triangle with shorter sides a and b, where b is the longer of the two, and hypotenuse c. Four copies of it can be arranged inside a square of side c, each with its hypotenuse along one side of the square, leaving a small square hole in the middle whose side equals b − a. The area of the large square therefore equals four triangles plus the small square: c² = 4 × ½ab + (b − a)².

Expanding the right-hand side gives 2ab + b² − 2ab + a², which simplifies to a² + b². The same five pieces can also be rearranged into a figure made of a square of side a and a square of side b placed side by side, so the areas match without any algebra. Bhaskara is traditionally said to have presented the figure with a single word, Behold.

The name reverse method reflects the direction of the argument: the hypotenuse square is built first and taken apart, instead of starting from the squares on the two shorter sides. Some teachers also use the phrase for the converse of the theorem, so confirm with LabEquip which demonstration this model is set up for, along with its form and size.

Care & Handling

Keep the four triangles and the centre square together, because the proof needs all five pieces.
Store the pieces flat in their tray so the edges stay straight and the fit stays exact.
Wipe with a dry cloth and keep the model away from heat.

Applications

Demonstrating Bhaskara’s proof with pieces the class can rearrange
Linking area to algebra by expanding (b − a)² and simplifying
Comparing a dissection proof with a measurement-based check
Discussing the history of the relation in Indian mathematics, from the Baudhayana Sulbasutra to Bhaskara II

Specifications

Item	Dissection model of Pythagoras’ theorem (reverse method)
Proof usually shown under this name	Bhaskara’s four-triangle arrangement: c² = 4 × ½ab + (b − a)²
Result	a² + b² = c² for every right triangle
Typical level	Middle and secondary classes
Form, material and size	Confirm at enquiry

Why Choose LabEquip

Teachers who show a unit-square check first, for example with the Pythagoras Theorem (Small Square) model, use the reverse method next, because it proves the result for any right triangle rather than one set of whole-number sides. LabEquip lists its Pythagoras models together in the Mathematics School Lab Products range, and the contact page can confirm how this one is built.

Frequently Asked Questions

Why is it called the reverse method?

The square on the hypotenuse is built first and then split into four right triangles and a small square, the reverse of starting with squares on the two shorter sides. In Indian school catalogues the name is commonly used for this proof, which is credited to Bhaskara II.

Who was Bhaskaracharya?

Bhaskara II, also called Bhaskaracharya, was a twelfth-century Indian mathematician and astronomer, author of the Lilavati and the Bijaganita. His proof of the Pythagorean relation uses four copies of a right triangle arranged around a small central square.

Does the proof work for every right triangle?

Yes. The equation c² = 4 × ½ab + (b − a)² holds whatever the lengths a and b, so a² + b² = c² follows for all right triangles. When a and b are equal, the central square disappears and the four triangles fill the large square on their own.

What is the converse of Pythagoras’ theorem?

It states that if the sides of a triangle satisfy a² + b² = c², the angle opposite c must be a right angle. Builders use it to check corners: sides of 3, 4 and 5 units always meet at a right angle.

How is this different from verifying the theorem by counting squares?

Counting unit squares checks the theorem for particular whole-number triangles such as 3, 4, 5. Bhaskara’s arrangement is a proof: it uses areas and algebra that hold for any right triangle, so it shows why the theorem is true rather than that it works in one case.

Which classes use this model?

Pythagoras’ theorem is met in the middle-school years and proved in secondary classes. The reverse method suits both stages, as a hands-on puzzle for younger students and as an area-and-algebra proof for older ones.

Last Updated: September 2026