### Happy Pi Day!

Yes, tomorrow is 3.14, making it pi day.

Although mathematicians probably stole the idea from chemists, who have been celebrating mole day on 10/23 for quite some time, I'll use this opportunity to post my favorite pi-related factoid:

e^{i*pi} = -1

This result combines two transcendental numbers and an imaginary number to produce the negative (crucial for subtraction) of the most basic number of them all. But it is more than a curiosity, because this property of the exponential function is crucial for a variety of results in mathematical physics (particularly scattering theory) and electrical engineering.

Some of the high-end scientific calculators (Casio fx115 ms, TI-83) will evaluate this expression if you put it in "complex" or "a+ib" mode. While you are doing that, notice that ln(-1) is equal to pi*i = pi*sqrt(-1). It is almost like two wrongs make a right, since neither ln(-1) nor sqrt(-1) are legitimate calculations when you are restricted to the Real numbers.

When 2015 rolls around, Pi Day will be 3.14.15. Watch for it.

## No comments:

Post a Comment