180 Really Big Numbers

Let's take a break from my anecdotes from the North, and celebrate the wonders of the number 180. An 180, as it's typically used in everyday speech means "a complete reversal", from the mathematical properties of the number.

180 is a special number in many ways:

  • Since its the angle of any point on a straight line, which gave it the name, "the straight angle".

  • Anything rotated by 180 degrees on any axis is completely inverted, and hence the meaning "complete reversal".

  • It's equivalent to pi radiants, where the ratio of the radius of that arc to the length of the arc is the famous irrational number, 3.14159...

  • The sum of the internal angles of a triangle, the most basic polygon in Euclidian geometry.

  • It is divisible by the first 6 natural numbers, and all but two of the first 10 natural numbers, making it the smallest number that has this property.

  • It's the sum of both six and eight consecutive primes, (19 + 23 + 29 + 31 +37 + 41) and (11 + 13 + 17 +19 + 23 + 29 + 31 +37).

  • The number of degrees Farenheit between the boiling point and melting point of water.

But let's not concentrate on merely one number. Since the topic of some really large numbers have been cropping up around me recently, let's explore some of the lesser known names of large numbers. The name of large numbers after a million basically change every 3 zeros, or the 10^3 factor of the previous number name. For example:

10^6 is a million, 10^9 is a billion, and 10^12 is a trillion, notice the ascending prefixes, i.e. mil- (one), bi- (two), and tri- (three), the desingnation is such that, for 10^n, the prefix= (n/3) - 1.

After that, there's quadrillion (10^15), quintillion (10^18), sextillion (10^21), septillion (10^24), octillion (10^27), nonillion (10^30), decillion (10^33), undecillion (10^36) ... novemdecillion (10^60), vigintillion (10^63), unvigintillion (10^66), ... novemvigintillion (10^90), trigintillion (10^93), untrigintillion (10^96)...

The largest designated number name is the googolplex. A googolplex was originally defined as a "1 followed by as many zeros you can write until you get tired". After that, the definition was formalised to mean a "1 with a googol zeros after it", but there's no number of any objects in this known universe that matches this number. But, what's a googol? A googol is defined as 10^100, and that became the well-known name of an internet search engine. By the way, it was a 9-year old who made the names up. Go figures!

Other strange names that have been used to describe large numbers, with no particular real number definitions are umpteen, gazillion, zillion, bajillion, and googlion (or something like that, pronounced go-gee-li-on, by Ben Stiller). One notable thing I must point out is that the googlion is, as defined by Ben Stiller, the a 1 followed by a googlion zeros. Other than the fact that it's very unhelpful, there can be no number that fulfills this condition (i.e n = 10^n) other than infinity. So, there it is, the impossible number... but very large, to say the least. (no pun intented)

PS: ...and speaking of really large numbers, the petrol price just went up again to RM 2.70, from RM 1.92, i.e a 78 cents increase or about a 40% hike. Now, those are some more practical but less interesting and welcoming large numbers.