CTK Exchange
Front Page
Movie shortcuts
Personal info
Awards
Reciprocal links
Privacy Policy

Interactive Activities

Cut The Knot!
MSET99 Talk
Games & Puzzles
Arithmetic/Algebra
Geometry
Probability
Eye Opener
Analog Gadgets
Inventor's Paradox
Did you know?...
Proofs
Math as Language
Things Impossible
My Logo
Math Poll
Other Math sit's
Guest book
News sit's

Manifesto: what CTK is about |Store| Search CTK Buying a book is a commitment to learning Table of content Things you can find on CTK Chronology of updates Email to Cut The Knot

CTK Exchange

Subject: "Pythagorean Theorem Proof #9: any h..."     Previous Topic | Next Topic
Printer-friendly copy     Email this topic to a friend    
Conferences The CTK Exchange This and that Topic #143
Reading Topic #143
pmbrown
Charter Member
1 posts
Aug-22-01, 03:47 PM (EST)
Click to EMail pmbrown Click to send private message to pmbrown Click to add this user to your buddy list  
"Pythagorean Theorem Proof #9: any history or educational materials?"
 
   I am very enthusiastic about this proof, which could readily be used in the third or fourth grade. I expect to use it at that level. The proof is both sound and intuitive: kids would be able not only to see that it works but also to have a good sense of why. Two questions:

#1: Any history? Is it ten years old or a thousand? At minimum, I'd like to know what I can call the proof (other than "Proof #9 at https://www.cut-the-knot.org/pythagoras". Have you any leads on the discoverer, or at least the medieval abbey at which it was discovered?

#2: Are you aware of any educational supply company that produces a jigsaw-puzzle version of the proof? With such materials and a little guidance, kids could discover the theorem for themselves. Custom manufacture is of course a possibility, but it would be expensive. If there are copyright considerations, I would like to know about these as well.

Thanks in advance,

Peter Brown


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top
alexb
Charter Member
672 posts
Aug-24-01, 09:12 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
1. "RE: Pythagorean Theorem Proof #9: any history or educational materials?"
In response to message #0
 
   Can't answer your questions off the top of my head. I am pretty sure though that the proof must have been known to the ancients. There could not possibly be any copyright restrictions.

In the proof #35 there's a link to a fellow who sells a 5 pieces puzzle that goes with the proof. His product may not be very suitable for 3-4 graders as the pieces have sharp edges. However, it is remarkable that even such a simple puzzle is not altogether trivial to solve. I'd be utterly surprised if anybody discovered the Pythagorean theorem using that puzzle.

Proof #9 may be a different matter. Indeed, all you need is 4 equal right angled triangles. First arrange the triangles as to make a square hole as in the first of the diagrams in the proof and make the students trace the outer square. Then rearrange they triangles as in the second diagram.


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top
alexb
Charter Member
672 posts
Aug-24-01, 10:56 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
2. "RE: Pythagorean Theorem Proof #9: any history or educational materials?"
In response to message #1
 
   LAST EDITED ON Aug-24-01 AT 10:57 AM (EST)

I added an applet that simulates the proof at the Interactive Activities page:

https://www.cut-the-knot.com/Curriculum/Geometry/ArrangePyth.shtml|www.cut-the-knot.com/Curriculum/Geometry/ArrangePyth.shtml>

Perhaps it may serve the discovery purpose.


  Alert | IP Printer-friendly page | Edit | Reply | Reply With Quote | Top

Conferences | Forums | Topics | Previous Topic | Next Topic

You may be curious to visit the old CTK Exchange archive.

|Front page| |Contents|

Copyright © 1996-2018 Alexander Bogomolny

[an error occurred while processing this directive]
 Advertise

New Books
Second editions of J. Conway's classic On Numbers And Games and the inimitable Winning Ways for Your Mathematical Plays