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He Scores...GOAL!

Mathematics is closely tied to NEW journeys, prompted by those able to ask good questions and the subsequent search for answers.

For example, you have held a soccer ball in your hands. It has many amazing mathematical aspects, being covered with pentagons and hexagons.

Yet, one person, P. Aravind of Worcester Polytechnic Institute, recently asked a new question: What fraction of a soccer ball is covered with pentagons?

And I ask, why didn't I think of asking that!

It turns out that Aravind's search for a solution had to be broken into two separate journeys... assuming either that the polygons on the ball are all flat or that they are not-planer (the real-world "spherical" case).

Before revealing his answer, what fraction do you think fits? Feel free to look at a soccer ball.

It turns out that the answer for the two cases are the fractions 9.433046094 and 9.424940785 respectively...OH, sorry, I disguised the answers via a code. To find the true values, you need to divide these values by pi and then subtract e (and do some appropriate truncating).

Source: Adapted from Mathematics Magazine, Feb 2008, pp. 55-58