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Origins and Originality


Date: 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
    
Associated Topics:
High School History/Biography

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