Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Inactive » k12.ed.math

Topic: Pythagorean Perimeters
Replies: 1   Last Post: Sep 28, 2005 8:05 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Charles Douglas Wehner

Posts: 76
Registered: 12/8/04
Pythagorean Perimeters
Posted: Sep 28, 2005 1:01 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


It is not often that a new theorem of exquisite simplicity arrives -
least of all in the context of Pythagoras.

The world is vast, and time has aeons - so perhaps some other has made
the same discovery.

However, to me, and everyone I know this is a new discovery.

It begins with the 3 4 5 triangle.

You know - you create a square on side 3, add the square on side 4 and
get the square on side 5. This is all to do with AREAS.

However, what if you examine the PERIMETER of the square on side 3, and
compare it with the perimeter of the triangle?

What of the 5 12 13 triangle?

Create a 2:1 rectangle on side 5. That is a 10:5 rectangle. How do the
perimeters compare?

What of the 7 24 25 triangle?

Try a 3:1 rectangle - 21:7.

And so on.

These are the base triangles - the smallest.

Of course, for the square you can scale up the 3 4 5 to 6 8 10, to 9 12
15 and onward.

There are also 3:2 rectangles that convert to triangles. Indeed all
whole-number ratios relate to base triangles.

It is the kind of thing that can be taught even to children. Yet it is
new.

Go to http://wehner.org/pythag for the introduction, and follow the
link, or directly to http://wehner.org/pythag/ratios.htm for more
examples of this perimeter-classification of right triangles.

Charles Douglas Wehner


--
submissions: post to k12.ed.math or e-mail to k12math@k12groups.org
private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org
newsgroup website: http://www.thinkspot.net/k12math/
newsgroup charter: http://www.thinkspot.net/k12math/charter.html




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.