Uncomputable numbers

Real numbers we can never know the value of

We all remember learning that the decimals of pi are infinite in number, 3.14159265359… Some of us even recall learning that you can approximate upper and lower bounds on the value of pi to as high of a degree as you want by measuring the sides of polygons. As the number of sides of the polygons approach infinity and the length of their sides approach zero, your approximation gets closer.

Archimedes (c. 287- 212) invented this early ‘polygonal algorithm’, which dominated for over 1000 years as the most efficient way of computing pi to any desired precision. The very primitive and geometric algorithmic function serves the purpose of estimating a real number, pi, whose value must be computed, as it is not expressible as a rational number (fraction/ratio). Continue reading


Read the full essay in Cantor’s Paradise on Medium