Totally Irrational

People often fail to see mathematics behind the wonders of Creation. From the dazzling Milky Way to a soaring peak to a tumbling stream, God’s Creation points to a Creator, and we would do well to learn all we can about the laws He has put in place. We are just grasping at understanding these laws, yet we can observe some very interesting mathematical concepts that tend to pop up in the most unexpected places. This article will focus on irrational numbers, and through it all, we will see the Hand of God.

An irrational number is any number that cannot be written as a ratio. So, all the counting numbers are rational because they can be written over one. After all, any number divided by one is that number. Zero is rational because zero divided by one is zero. Fractions like one-half, three-quarters, and so on are all rational. Another way to define irrational numbers is “non-repeating, non-terminating decimals,” which makes sense if we consider that a decimal whose digits go on forever cannot be written as a fraction.

Note here that non-terminating decimals like 0.33 are not irrational because the digit(s) beneath the horizontal bar repeat themselves infinitely. An irrational number must not repeat the same digit(s) infinitely.

One widely used irrational number is known as pi, commonly rounded to 3.14.

This number is the ratio of a perfect circle’s circumference to its diameter. If you could measure the circumference and diameter of a circle to an infinite precision and divide these two numbers, you would get pi.

Since we aren’t able to calculate anywhere near the infinite digits of pi, though, how do we know that pi is irrational? A mathematician named Johann Heinrich Lambert used a trigonometry proof that is beyond the scope of this article to show the irrational nature of pi.

An interesting place to find pi is in the lengths of rivers. People have observed that the ratio of 2 times a river’s total length to its direct length from source to mouth is the same ratio for pi. An equation may clear things up:

Note that this is an approximation. If the total length of a river is 22 miles and a direct line from its spring to the ocean is 17 miles, we can plug those numbers into our equation and get 3.143. Pi is 3.142, which is very close to our answer.

People are just beginning to uncover the mysteries of ratios like pi in Creation. Why do all rivers follow this rule? Why did God make several other ratios in Creation equal 3.14? We may never find out!

Another perhaps less well-known irrational number is represented by “e.” The rounded value of e is 2.718.

This number was discovered by a mathematician named Euler, thus its name: Euler’s Number. “e” is used in Calculus for computing rates of growth and decay, but that is beyond the scope of this article.

These fascinating irrational numbers are surrounded by mystery. Why did God choose to use an infinite ratio in Creation? Why would one number form the same ratio for circles and rivers? We may never know, but there’s one thing that irrational numbers have shown me: there is so much in Creation we have yet to learn! We can learn about God through His Creation and we will never lose the awe of His infinite power!

©2026 by Anchor & Fish Ministries. All Rights Reserved.

Artwork by Joshua Venturo.

Information from:

Demme, Steve. Precalculus with Trigonometry. Lancaster, PA: Demme Learning, 2010.

Posamentier, Alfred S., and Ingmar Lehmann. [Pi]: A Biography of the World’s Most Mysterious Number. Amherst, NY: Prometheus

Books, 2004.

Rosangliana, Dr. David. History and Applications of Pi (π). 2024.