Podcast for 01-08-06 | The Gamut of Geekery

Re: the check.

The check is written for $.002, or two tenths of a cent.

Doing a search for Verizon Math Check on Google, I get the URL that I have linked. It seems it must be related to the check. The gentlemen at the website was told that he would be charged .002 cents (two thousandths of a cent) per kilobyte, when using his phone in Canda. Instead he was charge .002 dollars (two tenths of a cent) per kilobyte, which is 100x more than the quoted rate. Verizon doesn't seem to realize that there's any difference at all.

Anyway, back to the check. e^(pi*i)=-1, as even Google can tell you. I was in 3rd semester Calculus when I dropped out of college, and it was never explained to me how e, which like pi is a transcendental number (which means that (1) it can't be expressed as the ratio of two other numbers, and (2) it is a decimal that never ends and never repeats), when taken to the power of pi*i (i, of course, is the imaginary number, equal to the square root of -1) could possibly be equal to -1, but we did know it to be true. e^(2*pi*i) = +1, oddly enough.

The next part of check is the summation of 1/(2^n), where n goes from 1 to infinity. In other words, 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64... I couldn't remember this off the top of my head, but some quick calculations in Excel shows that this is in fact +1. So it's .002 - 1 + 1, which is the .002 cents that someone would be charged for one kilobyte of usage on their cell phone.

/Math Geek, Sorry.