Monday, December 6, 2010
Football scores are quite complex. Six points for touch down. One point for the extra point after a touch down. Or, you could run the ball in after a touchdown for two points. Then of course there is the three points for a field goal. Finally, the saftey for two points. 6, 3, 2, 2, 1.
So I'm thinking, what kinds of numbers can the final score be? Could it be prime? What about square or cubic? What would the score look like written in Binary?
Well, I suspected the Redskins would lose. They have a lot of players out with injuries in key places and the quarterback has been struggling. That, with the fact that the Giants have been doing very well lately.
So the final score was 7-31. Both prime numbers. How many different ways could these scores have been achieved using the posibilities given above?
Wednesday, November 24, 2010
The Indian scholar Pingala is credited with the first known use of a binary system. He used a system of dashes, a short dash and a long dash to represent 1 and 0. The Chinese used hexagrams to represent numbers. These are squares made of a stack of 6 lines that are either solid or broken in the middle to represent 1 and 0. Then finally in 1703, Leibnitz uses the 1 and 0 digits as we know them and formalized the binary system as a practical device for computation.
"How can something be nothing?" asked the ancient Greeks. But those brave Indian mathematicians about 2200-2500 years ago started using a symbol to represent this idea of nothing. Not just nothing in terms of counting, but nothing of a particular place value in a numeral! This was a huge improvement over the Babylonian's empty space between digits. By the 9th Century AD, the Indian mathematicians were making use of zero in calculations, using it like any other number.
Of course the Maya had them all beat, using a symbol for zero as a placeholder in their base 20 system. However, this system was a parallel evolution and didn't seem to influence the systems we use today.