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Some Similarities Between the Balls Used in Sports
Look at a basketball, football or soccer ball and do the
following calculation: Count the number of pieces of material
used to make the ball (or the number of regions between the lines
on the ball). Subtract from this the number of seams on the ball
(or the number of edges of separating the regions). Then add the
number of points where two or more seams come together. The
simplest is a football where there are 4 regions, 4 seams and two
points where the seams come together. So for a football you get 4-4+2=2.
Getting Started
- What number to you get for the other types of balls (basketball and soccer ball)?
- Take a balloon and mark it into regions with a marker. How does the
number of regions - number of edges + number of corners change as
you divide the balloon into
more and more regions? Can you explain the pattern?
Going Deeper
Try the same proceedure with a sheet of paper (mark it into regions and
compute the number of regions - number of edges + number of corners).
Try it with a bagel or doughnut.
Communicated by G. Hall.
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