Origins and OriginalityDate: 12 Jan 1995 02:57:05 -0500 From: Cindy Suen Subject: Question : origins & originality I have always wondered how the great mathematicians derived their formulas based on nothing more than logic and tedious devotion. What are the origins of math? Of course, I understand that the answer may be somewhere in the past, never to be known. However, I what I wish to know is "How do I approach problems so that I can understand them for what they are, not just another 'pattern problem'." I noticed that some students in my class can just derive formulas they do not yet know. Is there a tactic I can use? Is there something I can do to understand formulas, not just memorize them? Please e-mail me back at csuen@walrus.mvhs.edu . Thank you. Cindy Suen Date: 14 Jan 1995 17:20:37 -0500 From: Dr. Ken Subject: Re: Question : origins & originality Hello there! Well, it seems like your question is kind of in two parts, the part about the origins of math, and the part about problem-solving tactics. If you really want to know more about the history of math, I recommend that you try your local library. I can recommend the book "A History of Pi" by Petr Beckmann, which gives a nice history of some of the broader subjects in math, framed around an inquiry into the nature of Pi. It's a neat book. Also, for what it's worth, here's a previous response that we gave someone asking about who invented math. I think the asker was somewhat younger than you are, but you might still get something out of it. WHO INVENTED MATH? Date: Sat, 26 Nov 1994 23:58:32 -0500 From: Pierre Kerr Subject: Math Question Dear Dr.Math, The Grant Alternative School, (jk to 6) Ottawa, has installed a mailbox in the library to take "Questions to a Scientist". The mailbox is a very popular item, possibly because it has sneakers, the questions slide into a 5/14" disk drive slot, and its name is IO, but I think that the students are sincerely interested in getting an answer to their carefully written questions. In the first month we received 245 questions! I am the chairman of the parent's Math, Science and Computer committee and am responsible for the creation of IO. I am also responsible for getting the questions answered. You have been chosen to answer the following question. Your response would be greatly appreciated and you will get full credit in the write-up. Thank you. Student: Andrew Lucas Grade: 3 or 4 Teacher: Jeannie Mastine Question: Who invented math? Also.. Student: Thea Mills Grade: 5 or 6 Teacher Julie Breeze Question: Where did the word Math come from? -- Pierre A. Kerr ____________________ Date: Mon, 5 Dec 1994 19:48:22 -0500 (EST) From: Dr. Sydney Subject: Re: Math Question Dear Andrew, Thanks for writing to Dr. Math! You asked a great question: Who invented math? Unlike physical objects like the lightbulb, the telephone, and the calculator that were invented by one person or a group of people, math wasn't really "invented" by anyone in particular. The theory behind math has been evolving for a very long time. People first started doing math-related things when they counted objects around them. Math didn't become a real field of study until sometime around 500 B.C.E. (that is about 2500 years ago!) I hope this helps answer your question. Feel free to write back with any more questions you might have. --Sydney, Dr. "Math Rocks" __________ Date: Mon, 5 Dec 1994 17:36:08 -0500 (EST) From: Dr. Sydney Subject: Re: Math Question Dear Thea, Hello! Thanks for writing Dr. Math! I am glad you asked where the word math comes from, because I didn't know, and I found it interesting to find out. It turns out that the word, math, has its roots in the Latin word mathematicus and the Greek word mathematikos which comes from mathema (what is learned) and manthanein (to learn). So, math comes from words that mean learning. Pretty neat, huh? Thanks for writing, and please write again. --Sydney, "dr. math" ____________________ As far as your second question goes, I think the one of the best things you can do to improve problem-solving skills is to try to relate different things to each other. For instance, think about the law of cosines: a^2 = b^2 + c^2 - 2bc Cos[A]. What happens when A is a right angle? Do you see how this formula relates to the Pythagorean Theorem? Then think about the distance formula: d = Sqrt{(x1 - x2)^2 + (y1 - y2)^2}. What happens when you square both sides? Aha! The Pythagorean Theorem again! Of course, these examples really aren't all that deep, but they do give some insight into what's happening in problems that involve them. Once you get a handle on what kinds of relationships are happening between different objects in math, you'll probably have an easier time finding these relationships yourself. So start looking! Here's one for you that will probably require some more time: what is the relationship between the Fibonacci Sequence and the Golden Ratio, and why does this relationship happen? -Ken "Dr." Math |
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