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Thirty Six

Karl Abate

Karl Abate

— 2 min read
A green circle with a number 36 behind a pink background.

This is my 36th entry in this blog!!!

36 is my favourite number ever, and so for me this is a milestone worth celebrating! To do so, I just wanna share some of my reasons as to why I love this number so much, as it has both a lot of personal and mathematical value.

First of all, 36 is a square number (6x6). 36 is also a triangular number, meaning that it's the sum of sequential positive integers (1+2+3+4+5+6+7+8). Excluding 1, it's the first number to be both and one of very few in general, the next one being 1,225.

Another interesting distinction 36 has is that it is both product of the first three squares (1x4x9), and the sum of the first three cubes (1+8+27). This is the only time in the sequence where they line up.

A collage of four diagrams. One showing how 36 equals 6x6, another showing how it equals 1+2+3+4+5+6+7+8, another showing how it's (1^2)*(2^2)*(3^2), and another showing how it's (1^3)+(2^3)+(3^3)

36 is also an anti-prime! (Or highly-composite number if you're boring /s) Meaning that it has more divisors than any number smaller than it. It has 9 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Additionally, 36 is itself a relatively common factor. Specifically it is (obviously) a tenth of 360, which is extremely useful as it's the amount of degrees in a circle and hues. 360 itself is also an anti-prime, having 24 divisors, which is why it's used so often for things like this.

The final mathematical thing that I want to point out is that if you have an isosceles triangle where the point is 36º, the ratio of the hypotenuse to the base is equal to the golden ratio (ϕ, approx. 1.61803…). I find this extremely interesting, as it is such a unique and important number which appears in a simple shape made from simple numbers.

A diagram showing how an isosceles triangle of angles 36-72-72 with base length 1 has its hypotenuses be φ in length.

Aside from that, though, 36 is simply a very meaningful number to me. One of my old homes was numbered 36, and because of that ever since I was a kid I get a little happy whenever I see it, which happens more often than you'd expect.

A collage of three images. Two small ones of the sign saying 36, and another of the Tutoring Center floor in Tiny Tower with 6x6=36 written on it. The large image is of a 36 menacingly standing behind the Map Men (Jay Foreman & Mark Cooper-Jones) in a car.

(360 WORDS LOLOLOL)

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