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?

Leave your answer in the comments!


  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)

  6. ...they just don't teach 355/113 like they should. I remember you showing it to me when I was 8. I include it prominently in one of my shows on mathematics in the plant world as an illustration of rational approximation of irrational numbers (a central idea in the plant world, believe it or not!)