(Quick formula/graph lesson: Everyone remembers the formula for a parabola (y=x

^{2}), right? When plotted on graph paper, it resembles a smooth letter "v" extending upwards forever.)

So, why is the above formula (or inequality, to be exact) so amazing. Well, if you plot it on a very, very, very tall piece of graph paper, and look way-y-y up, you'll see this:

An image of the formula is found in the graph of the formula! (Wow!!) I'm a math geek so this kind of thing excites me.

Had these types of problems ("Roughly sketch the graph of this self-referential formula.") appeared in high school math class, I'm sure a lot of us would have done better.

I wonder if this could be applied to cryptography, ie. create a function which graphs a secret message somewhere in the x-y plane.

Formula images thanks to:

Weisstein, Eric W. "Tupper's Self-Referential Formula." From

*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html

## 2 comments:

way interesting, mathman!

I agree anonymous. Very very interesting!

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