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Pi is Irrational and Therefore Has an Infinite Number of Digits

Date: 18 Jun 2026
Topic: Mathematics

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Pi is an irrational number, meaning it cannot be represented as a simple fraction and its decimal expansion goes on forever without repeating. Fundamentally, Pi represents the ratio of a circle's circumference to its diameter - or how many times the diameter fits around the outside of the circle.

Although its digits go on forever, using just 15 decimal places - 3.141592653589793 - is more than sufficient for NASA to perform highly accurate calculations for interplanetary space flight. In fact, using just 40 decimal places would allow you to calculate the circumference of the observable universe to the precision of a single atom.

This infinite nature ties into a fascinating thought experiment regarding the Simulation Hypothesis. This theory posits that our reality is a computer-generated simulation, and our experiences are the product of advanced code. Given how rapidly our own video game technology is advancing, it is entirely possible that a civilization thousands of years ahead of us could create a simulation indistinguishable from reality.

Pi actually plays a clever role in this argument due to the physical constraints of computing hardware. If our universe is a simulation running on a computer bound by physical laws, that computer would have finite memory and storage. It would be impossible for it to store an infinite, non-repeating number like Pi. Therefore, if scientists keep calculating the digits of Pi and suddenly find that the sequence abruptly ends or starts repeating perfectly, it would be a glitch in the matrix - strong evidence that our reality is simulated.

Until then, we might just be a cosmic science project sitting on the windowsill of an unimaginably intelligent alien species.

27 codebreakers  ⋅  today's code  ⋅  by James McArthur