At school you were probably taught that there was a right angle triangle with sides exactly 3, 4, 5 units long, and it was remarkable that the sides were exactly whole numbers. That triangle is in the first diagram.

What I was not told, and probably you weren’t either, is that there is a further remarkable property of this triangle, and you will see this in the second diagram. If one adds a circle so it just touches the three sides, it has a radius of another whole number: exactly 1.

But there is also something in the diagram which is not a whole number and is a long way from being a whole number. What is the area of the circle? Πr2, if you remember your elementary maths, and since the radius is 1 the area of the circle is the never-ending number Pi! Yes, you can see pi visible! You are seeing something never-ending.

Some other right-angled triangles exist, whose sides are exact numbers, and their similar inscribed circles are multiples of pi.

Never-ending infinity exists, but the details are hidden in the everyday whole numbers we know.

All whole number right angle triangles give a multiple of pi.

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