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Explain Stuff With Maths (This challenge is now closed)

As we don't like the idea of anyone taking it easy over Christmas, this week's challenge is to explain things using maths, like this example, or to submit other mathematics-inspired imagery.
(, Wed 23 Dec 2009, 19:15)
What a bargin...

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First post so be kind, feel free to add more Tesco rip-offs!
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(, Tue 5 Jan 2010, 10:09, More)
Using maths to explain...maths

This picture, courtesy of Wikipedia, proves that 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3.
Let’s say the whole area in this picture has an area of 1. Now, concentrate on the black squares. The one in the bottom left hand corner is 1/4 of the total area. The next black square is a quarter of the top right hand corner, a quarter the size of the biggest black square, so 1/16 of the total area. The next one is a quarter again, 1/64, and so on. So, we know that all of the black squares together are equal to 1/4 + 1/16 + 1/64 + 1/256 + ...
Now, look at the grey squares. In total they are the same as the black squares. Similarly, the white squares are in the same arrangement as the black squares. We have three identical sequences of squares, and when added together they give the total area of 1. Consequently, we can conclude each sequence of squares has area 1/3. So, 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3.
I know this isn't funny, but it is big and it is clever, and I like this sort of thing.
(, Sun 3 Jan 2010, 2:44, More)
This Explains Nothing!

Other than how my brain works/doesnt work...
Also, Pains me to say that I wasnt sure if I'd labelled the opposite and adjacent right...
(, Sat 26 Dec 2009, 18:52, More)

As we don't like the idea of anyone taking it easy over Christmas, this week's challenge is to explain things using maths, like this example, or to submit other mathematics-inspired imagery.
(, Wed 23 Dec 2009, 19:15)

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First post so be kind, feel free to add more Tesco rip-offs!
-----------------------
(, Tue 5 Jan 2010, 10:09, More)

This picture, courtesy of Wikipedia, proves that 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3.
Let’s say the whole area in this picture has an area of 1. Now, concentrate on the black squares. The one in the bottom left hand corner is 1/4 of the total area. The next black square is a quarter of the top right hand corner, a quarter the size of the biggest black square, so 1/16 of the total area. The next one is a quarter again, 1/64, and so on. So, we know that all of the black squares together are equal to 1/4 + 1/16 + 1/64 + 1/256 + ...
Now, look at the grey squares. In total they are the same as the black squares. Similarly, the white squares are in the same arrangement as the black squares. We have three identical sequences of squares, and when added together they give the total area of 1. Consequently, we can conclude each sequence of squares has area 1/3. So, 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3.
I know this isn't funny, but it is big and it is clever, and I like this sort of thing.
(, Sun 3 Jan 2010, 2:44, More)

Other than how my brain works/doesnt work...
Also, Pains me to say that I wasnt sure if I'd labelled the opposite and adjacent right...
(, Sat 26 Dec 2009, 18:52, More)

