A lot of people ask me where “M3L6H” came from. The answer is simple. MLH is my initials, and 36 is my favorite number.

Why 36? Other people ask, well, here’s 10 reasons why (Note some of these might not be *completely* legitimate, but come on, who cares about the rules anyway? jk):

First off, everybody must know what I’m talking about. I assume you know what a square number is, the product of two numbers of the same value, but fewer people seem to know what I call a triangular number. A triangular number, in my terminology, is a number in this sequence: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55… If you didn’t already catch on, well, basically, it starts from zero, then you add 1 to get the next term, then you add 2 to get the next term, then you add 3, then 4, and so on. 36 is the eighth number in this sequence.

Well, here it goes:

1. 36 is the lowest square and triangular number, excluding 0 and 1.

2. It is the eighth triangular number (Not really a reason, but very important)

3. The factorial of eight can be divided by thirty-six. Not surprising since the factorial of 8 has x2, x6, and x3 in it, but still points to the relationship between 36 and 8 which I am about to show.

4. This one’s a bit random but still interesting in its turn: The square of thirty-six is 1296. You will notice that if you divide this number into two parts, 12 and 96, you will then notice that ninety-six can be divided by twelve leaving eight (AGAIN) twelve being the largest factor of thirty-six other than thirty-six itself.

5. Another random one, but still fun: The cube of 36 is 46656. Split it into three numbers and you have 46, 6, and 56 all of these end in six, the square root of 36, so it makes sense to split the number there (I guess, I wrote this so long ago it’s challenging trying to remember some of the reasons I thought of). Now 36+10=46 36+20=56 and 36-30=6. Notice I didn’t use random numbers but instead used 10, 20, and 30. Now is it coincidence that 46, 56, and 6 happened to be the three numbers we split the cube of 36 into?

6. It has the most factors compared to any other number in the range 31-39 (I’m feeling like an advertiser now).

7. 36×1=36 whose digits add up to nine. 36×2=72 whose digits also add up to nine. 36×3=108 36×4=144 (the square of 12, one of 36’s factors) 36×5=180 36×6=216 36×7=252 36×8=288 (the pattern terminates at EIGHT for a while where 288’s digits add up to eighteen) 36×9=324 36×10=360 Now is this really coincidence? I’m beginning to doubt it.

8. Another interesting note: The pattern above terminates at thirty-six times ten where ten is the fourth triangular number. If you subtract four from ten, you have six which is the square root of thirty-six. Also cool is that there are 360 degrees in total.

9. Back to the square of thirty-six-the number 1296. Recall how we discussed the two parts of this number: 12 and 96. Remember how we discussed that twelve multiplied by eight is ninety-six. (Recall the fact that thirty-six is the eighth triangular number.) Well, in the previous pattern, remember how I put that note in the parenthesis, 144 is the square of twelve? Well now, I can show you a curious relationship between the two patterns. One thousand, two hundred and ninety-six (the square of thirty-six), divided by one hundred and forty-four gives us an answer of, you guessed it, nine (This is special because it is what the digits of thirty-six (and its multiples) added up to 36, plus it is a factor of 36.

10. Thirty-six to the power of five is 60466176. The digits of this number add up to, can you guess, thirty-six. Again!

So…I’m an AP Calc classmate who found you through my friend Victoria’s blog and I have to say, this post was absolutely fantastic. =D

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hahaha. I’m glad you enjoyed it. XD

~Michael Hollingworth

Disce Ferenda Pati – Learn to endure what must be borne

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