# Powers!

Mike Schilling

Mike has been a software engineer far longer than he would like to admit. He has strong opinions on baseball, software, science fiction, comedy, contract bridge, and European history, any of which he's willing to share with almost no prompting whatsoever.

### 12 Responses

1. Aaron W says:

Euler’s formula!! Not something I’d expect to find here necessarilyReport

• Murali in reply to Aaron W says:

nobody expects the Spanish inquisition Euler’s formulaReport

• Mike Schilling in reply to Aaron W says:

2. Rod says:

Thanks, Mike!

While it’s not exactly a Homer doh headslap moment, the end result with the trig functions isn’t terribly surprising to me. Quite the opposite in retrospect, given that we’re playing on the complex plane.

I could only give it a quick read tonight given family interruptions but I’ll work through it in more detail tomorrow.

And again, I really appreciate you humoring my curiosity.Report

3. Brandon Berg says:

It’s important to remember that the goal isn’t to mess with people

I call bullshit.Report

If that’s too much to try to see in your mind’s eye (and the best I ever do is to frustratingly get almost there)…

I’m imagining f(z, t) = e^(z + it) as a parametric describing a circularly polarized photon traveling through an exponentially expanding universe.

I think…Report

Oops… Actually, the wavelength isn’t increasing with time. It’s the amplitude that’s increasing exponentially. Somethin’s blowing up, that’s for sure!Report

5. Kolohe says:

Your phasors are stunning, Mr. Schilling.Report

Just a reminder, for those who gave up on Math in high school, all the exclamation marks in this:

cos(x) = 1 – x2/2! + x4/4! – x6/6! + …
sin(x) = x – x3/3! + x5/5! – x7/7! + …

is the factorial, not Mike getting really excited about Math. The factorial works like this:

4! = 1*2*3*4 = 24
6! = 1*2*3*4*5*6 = 720Report

7. Wyrmnax says:

I do not know what is worse.

That i have taken the time to read it all, or that i actually liked the article.

Damned engeenering years!Report

8. Ken S says:

These series are incredibly powerful. (Pun semi-intended.) In his classic book, Real and Complex Analysis, using nothing but their power series, Walter Rudin derives every imaginable property of the exponential, sine and cosine functions (both the real and complex versions) in three pages of text.Report

• Mike Schilling in reply to Ken S says:

The impressive thing was when he used the power series expansion to prove that cosine, compared to sine, has two extra letters.Report