## Wednesday, January 12, 2011

### Birthday puzzle

It's my birthday today. Hurray! On the table this morning are some presents wrapped in mathematical wrapping paper. I haven't opened them yet, but I did enjoy identifying the formulas.

Here's a quiz for you: One of the formulas has an error. That is, one of the formulas is supposed to be a well-known formula, but it's written incorrectly so it's some other formula. Can you find it?

1. there's no way that e=lim.... not in a million years. Plus I think you're missing an "i" in there somewhere. It's always the imaginary numbers that get left out.

Gratulerer med dagen!

2. I believe it's meant to show the mandelbrot set: Z_(n + 1) = (Z_n)^2 + c rather than an equation which leads to Z_n = 1/2 +/- sqrt((-3/4)) - d)?

Sorry for the dodgy notation. Blogspot didn't want to let me use sub- and superscript tags...

3. err... d = c, obviously, despite what the linguists may think...

4. That limit does indeed produce e (try for n = 1, 2, 3, 4, etc and watch what happens).

5 points for Xilly! Well done! (and good notation with the underscore to indicate subscript). Who are you?

5. They really like Newton's gravitation equation, but in my day it was
G x m1 x m2 / r squared not d squared.
(Where "r" is the distance between the mass centers of m1 and m2) I guess that's not an error but a difference in nomenclature.
The wrapping paper was eminently suitable for you because it has Pi shown several times! (Although, personally, I still like old Zu Chongzhi's approximation which is close enough for my engineer's brain)