There is a legend that Pythagoras wanted to see if he could teach someone geometry. after finding a somewhat reluctant student, Pythagoras agreed to pay him a penny for each theorem he learned. because the student was very poor he worked diligently. After a time, however, the student realized that he had become more interested in geometry thatn in the money he was accumulating. in fact, he became so intrigued with his studies that he begged Pythagoras to go faster, offering now to pay him back a penny for each new theorem. Eventually Pythagoras got all of his money back.
What is there about geometry that student could have found so fascinating? Perhaps it was the logical way in which Pythagoras was able to present it. geometry was the first system of ideas developed by man in which a few simple statements were assumed and then used to derive more complex ones. Sucha a system is called deductive.
One of the goals of studying geometry is to develop the ability to think critically. An understanding of the methods of deductive reasoning is fundamental in the development of critical thinking, and therefore we should devote some attention to this subject:
drawing conclusions/ conditional statements/ equivalent statements/ valid and invalid deductions/ undefined terms and definitions/ direct and indirect proofs/ arguments with several premises
Lewis Carroll, the author of Alice's Adventures in Wonderland, and Through the Looking Glass, was a mathematics teacher who write stories as a hobby. His books contain many amusing examples of both good and deliberately poor logic and, as a result, have long been favorites among mathematicians.
Consider the following conversation held at the Mad Hatter's tea party:
"Then you should say what you mean", the March Hare went on,
"I do", Alice hastily replied; "at least - at least I mean what I say - that's the same thing, you know."
"Not the same thing a bit!" said the Hatter. "Why, you might just as well say that 'I see what I eat' is the same thing as 'I eat what I see'!"
"You might just as well say," added the March Hare, "that 'I like what I get' is the same as 'I get what I like'!"
"You might just as well say," added the Dormouse, who seemed to be talking in his sleep, "that 'I breathe when I sleep' is the same thing as 'I sleep when I breathe'!"
"it is the same thing with you," said the Hutter, and here the conversation dropped, adn the party sat silent for a minute.
posted by Mikela @ 6:15 AM
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