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 notplaner (the realworld "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. 5558
