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Why Did Pythagoras Believe that Three was a Sacred Number?

Depiction of Pythagoras from School of Athens, by Raphael, 1511
Depiction of Pythagoras From School of Athens, by Raphael, 1511. Credit: Public domain

Pythagoras was one of the greatest philosophers and intellectuals of Greek history. He made many profound contributions to knowledge in various areas. One interesting fact about Pythagoras’ beliefs is that he considered the number three to be a very special number. What was his reasoning behind this?

Pythagoras’ fascination with numbers

Pythagoras was not simply interested in the number three. He was fascinated by numbers in general. He viewed them as the key to understanding the universe as a whole. His investigation into the nature of numbers has even had a lasting impact on terminology still in use today.

For example, Pythagoras had a practice of viewing numbers geometrically rather than simply writing them out with symbols. He would use dots to arrange numbers into patterns, such as squares and triangles. The number six, for instance, is a triangular number because the number six laid out with dots literally forms a triangle. In other words, there is a base of three dots, a middle section of two dots, and a single dot forming the peak.

Square numbers are those which literally form square shapes when laid out with dots. The number nine is a good example, as it is formed of three rows of three dots, comprising a perfect square. We still use the terms ‘square numbers‘ and ‘triangular numbers’ even to this day. This shows the impact of Pythagoras’ ideas.

Why was the number three special to Pythagoras?

Of all the numbers, Pythagoras considered the number three to be particularly special. There are a few reasons for this. For one thing, Pythagoras noted that three is the only number which is the sum of all the numbers below it. In other words, when you add one and two together (the numbers below three), you get three, whereas the same is not the case for any other number.

For example, if you were to add together all the numbers below the number four, the total would be six rather than four. Therefore, Pythagoras noted that this makes three a unique number.

There is also another reason it is unique. When you take the previous numbers (one and two) and add them together with the number three, you get six. Likewise, when you multiple all those numbers together (one, two, and three), you also get six. This harmony does not exist with any other number.

The number three and the universe

In addition to the properties of the number three on a mathematical level, Pythagoras also considered it to be special for several other reasons. Notably, it seems to reflect our world well on a conceptual level. In our human experience, we are familiar with the concept of a beginning, a middle, and an end. These three parts sum up the entirety of any given thing. Similarly, humans experience birth, life, and death.

Pythagoras also considered the number three to be special for an ethical reason. According to Pythagoras, a person’s virtue is composed of three distinct parts. First, there was understanding, followed by power, and finally chance.

One philosopher who followed the teachings of Pythagoras was Ion of Chios. He wrote: “All things are three, and there is nothing more or less than this three.”

Clearly, the number three was extremely important for Pythagoras and his followers. As we have seen, there are some fascinating mathematical and conceptual reasons for this.

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