Theodorus of Cyrene is known for his work with irrational numbers, specifically in relation to the construction of square roots. He demonstrated that the square roots of non-square numbers are irrational, which means they cannot be expressed as a simple fraction.

There is no "wheel" associated with Theodorus, nor specific calculations attributed to him. However, the Spiral of Theodorus, a visual representation of his work, is often used to demonstrate these concepts.

Here's how the Spiral of Theodorus works:

1. Start with a right triangle: Draw a right triangle with legs of length 1. The hypotenuse will have length √2.

2. Construct the next triangle: Use the hypotenuse of the previous triangle as one leg of a new right triangle, with the other leg also having length 1. The hypotenuse of this new triangle will have length √3.

3. Repeat: Continue this process, using the hypotenuse of each triangle as one leg of the next. Each new hypotenuse will have a length equal to the square root of the next natural number.

The significance of the Spiral of Theodorus:

* It visually demonstrates that the square roots of non-square numbers become increasingly irrational, as their decimal representations become infinitely long and non-repeating.

* It shows how each new hypotenuse builds upon the previous ones, illustrating a relationship between square roots.

While Theodorus did not create the specific calculations for the Spiral, he is credited with the underlying mathematical concepts:

* He proved that the square roots of non-square numbers are irrational.

* He explored the relationship between square roots and the geometrical construction of right triangles.

The Spiral of Theodorus is a visual representation of his work and a powerful tool for understanding the nature of irrational numbers.