36 is the natural number following 35 and preceding 37. But that, of course, is obvious. Unless you're a mathematician, in which case you need proof.

It is the square of 6 as well as a triangular number. As a square number, it can be arranged in the form of a, well, square. As a triangular number it can be arranged as an equilateral triangle.

Amazingly, it is also a 13-gonal number. That means it can be arranged it can be arranged in a polygon of 13 sides.

It is a highly composite number. It means that it is a positive integer which has more divisors than any positive integer below it.

It is a Harshad number. A Harshad number is an integer that is divisible by the sum of its digits in a given number base. In base 10, 36 is divisible by 9, which is the sum of its digits (3+6). Harshad is Sanskrit for "great joy."

It is the sum of a twin prime (17 + 19), and the sum of the cubes of the first three integers.

It is the smallest number with exactly 9 divisors.

It is the smallest number n with exactly 8 solutions to the equation φ(x) = n. This is Euler's phi function. This is the number of positive integers less or equal than n and coprime to n.

It is the largest numeric base that most computer systems support because it exhausts the numerals, 0 - 9, and the letters, A - Z.

It is the atomic number of krypton.

"36" is also the title of the song by System of a Down. The lyrics aren't particularly any good, but I do like a couple of stanzas:

Television in disgrace

Life you get old, it's the race,

Can you break out,

Can you break out,

Will you live at your own pace?

It is the number of living righteous people without whom, according Jewish tradition, the world would end.

Finally, it is how old I am today.

happy birthday! i turn 36 in may.

ReplyDeletemaligayang kaarawan! =)

ReplyDeletesana you'll be happiest in these coming years.

may your 36th be as formidable and your experiences be as wonderfully diverse and deep as the math it represents. =)

Geez... what'll happen when you turn 37? :)

ReplyDeleteHappy Birthday, Dominique!

hahaha a pretty interesting entry about your age. the math confused me.

ReplyDeleteanyway happy birthday.

Kewl way to tell us your age...anywayz, hapi bday... :D

ReplyDeletecheers,

MarkV

and a happy birthday to you! make it count :)

ReplyDeleteAwww, thanks all. I just thought 36 was a cool number (and a cool age to be in). Like MLQ, drop me a note when you hit it.

ReplyDeletehappy birthday, man! hmm so you have the same bday as sam :)

ReplyDeletecheers,

joey

happy birthday! i have 11 years to go before I drop you that note for my 36th. :-)

ReplyDeletehope you had a great birthday!

Happy Birthday! :D

ReplyDelete