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