Saturday, February 11, 2012
My assignment was:
The logo of the 6 time Super Bowl Champion Pittsburgh Steelers has a mathematical legacy that goes back to Sir Isaac Newton and Sir Christopher Wren. Research this logo and explain its mathematical significance. Do you guys have any idea?|||As a Steelers fan this question got my attention and I was interested in seeing what I could come up with. I found some information about it. There's a lot of information & I couldn't post it all. Here's a little bit to get you started.
The Steelmark consists of three four-pointed starlike figures within a circle. The stars in the design approximate a type of geometric figure called an astroid, a particular type of hypocycloid with four cusps.
In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle
For the hypocycloid, an example of which is shown above, the circle of radius b rolls on the inside of the circle of radius a. The point P is on the circumference of the circle of radius b. For the example a = 5 and b = 3.
These curves were studied by D眉rer (1525), Desargues (1640), Huygens (1679), Leibniz, Newton (1686), de L'H么pital (1690), Jacob Bernoulli (1690), la Hire (1694), Johann Bernoulli (1695), Daniel Bernoulli (1725), Euler (1745, 1781).
The cycloid was first studied by Nicholas of Cusa and later by Mersenne. It was named by Galileo in 1599. In 1634 G.P. de Roberval showed that the area under a cycloid is three times the area of its generating circle. In 1658 Christopher Wren showed that the length of a cycloid is four times the diameter of its generating circle. The cycloid has been called "The Helen of Geometers" as it caused frequent quarrels among 17th century mathematicians.|||The Chicago Bears' Dan Fortmann in 1936 was 20|||go do your own damn research kid.|||Football is a sport for muscle heads. You know they can't do math.
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