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| https://xkcd.com/410/ |
Monday, May 30, 2016
Monday, May 23, 2016
Pi In Prime Time
If you're a fan of the Big Bang Theory (a "prime time" comedy!), it will probably come as no surprise that the show has lots of geeky math references. One that you might not have caught is that Amy Farrow Fowler's apartment number is 314.
Monday, May 16, 2016
Leibniz Formula for Pi
With pi being irrational, we're all familiar with various approximations for it:
- 22/7
- 3.14
- 355/113
- 3.1416
I've always been fascinated with how to calculate pi, and was amazed when I first learned of the Leibniz formula for calculating it:
pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...
I was shocked that such a simple formula could calculate it, and worked diligently trying to use it to calculate pi myself, only to discover that it zeroes in on pi *very* slowly:
I've only recently discovered that the Leibniz formula can be written as an Euler product (the math of which I'm sure my wife could expand upon):
pi/4 = 3/4 * 5/4 * 7/8 * 11/12 * 13/12 * 17/16 ...
In this product, each numerator is an odd prime number, and each denominator is the nearest multiple of four to the numerator. Here, in one simple equation, was something relating two of my favorite math subjects, pi and prime numbers. You can see it converges a little more haphazardly than the previous equation (and just as slowly):
Friday, May 6, 2016
On-Line Encyclopedia of Integer Sequences (OEIS)
The On-Line Encyclopedia of Integer Sequences (OEIS) is a great resource for finding details on your favorite integer sequences. Each entry contains historical information about the sequence, mathematical motivations, key people in finding or defining the sequence, literature links, and more.A few of my favorites:
Another sequence that's really esoteric, but one that I have played around on with the kids:
- A250001 Number of arrangements of n circles in the affine plane.
I'll probably make a separate post about this one later.
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