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Special Number

written Tuesday, 12/30/2008

I woke up this morning with a smile on my face.

Ahhh, what a special day.

After all, my age can be now expressed both as the sum of the cubes of two positive integers as well as the difference of the squares of two positive integers. Finally!

“What about 9 and 28?” you say.

Well true, those numbers also fit that description. Rest assured that I celebrated those momentous occasions with due fanfare. However, my age today is the smallest such number that can be expressed as the difference of two positive squares in two different ways.

A special day indeed!

As a little kid I assumed that by this age, the binary (base-2) equivalent of 100011, I would probably have gotten married, produced a handful of kids if me and the theoretical little lady felt like it, found myself happily settled into a profitable and fulfilling career, and published a few groundbreaking mathematical theorems in my spare time to make the world a more miserable place for schoolchildren everywhere.

Ahhh, silly childhood dreams!

Nevermind the put-aside plans and the perennial pondering that perhaps my personal and professional pursuits are persistently paving a path to a prodigious post-youth panic. On this special day I shall simply bask in the glory of knowing that my new age is the number that is precisely 50 times bigger than the tangent of its degree angle measure (within an impressive .03% accuracy). How many people can boast that today?
Mmmm, tofu.

When I hit the last decade milestone I was quite distraught over a general lack of life direction. On this day I boldly cross a halfway point, finding myself closer to the next decade milestone than the last. I still wonder how much time and opportunity I’ve squandered and might continue to waste on my current course. On any other day such contemplations might bother me. Not today though.

Some people thought I might long for the moment three years ago when my age converted into a perfect power of two, or that I might anxiously look ahead to next year when my age will become a perfect square (as well as a perfect square number of years away from the century mark). Au contraire, I say, for those distinctions occur multiple times during an average lifespan. On this uniquely marvelous day, at last I can now reverse the digits of my age and then re-write the result as a hexadecimal (base-16) number, and thereby arrive at a number which is identical to my original age expressed as a decimal. That only happens once in a person’s life! (Unless you reach 173, which is the only three-digit decimal to exhibit this property.) Frikkin’ cool!!!

It’s mid afternoon and I’m still in my jammies trying to think up more impressive facts about my age. I’ve just slathered about ten gobs of peanut butter onto my tongue with a butter knife, and I ain’t finished. Yep. Thinking back, a few good things have occurred in the past year. Life’s really not too bad.
Photos of the girls, totally unrelated to anything written above.