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0|0|0|||||Proof %2328 - Pythagorean Theorem|Sandy Wagner|1|14:08:14|12/19/2009|Thank you very much for the Pythagorean proofs%2C which are very useful to me.%0D%0A%0D%0AI just noticed that my brother%2C Don Wagner%2C is cited in %2328.  However the link to his work is incorrectly located under the name Elisha Loomis.%0D%0A%0D%0AI also would like to report that my remarkable 9-year old friend Toby in San Leandro California recently produced proof %2310%2C on his own%3A%0D%0A%0D%0AI was teaching him the necessary algebra manipulations so that he could develop proof %233 on his own.  However he went off on his own and invented a proof that I had never seen before.   I had trouble believing it%2C not to mention understanding his diagram %28http%3A%2F%2Fhome.comcast.net%2F%7Epapasandy%2Ftoby-pythag-diagram.jpg %29%2C which was so clear to him but hard for me to follow.  He did finally explain himself well enough so that I knew what he was trying to say%2C so I went home and proved to myself that he was absolutely right.  It%27s a rare person of any age who develops his%2Fher own proof of this theorem%2C and I%27m lucky to be working with him.%0D%0A%0D%0AI am interested in talking with others who are working with young gifted students.%0D%0A%0D%0ASandy Wagner%2C retired math teacher
1|1|0|||||RE%3A Proof %2328 - Pythagorean Theorem|alexb||14:25:18|12/19/2009|%3EThank you very much for the Pythagorean proofs%2C which are %0D%0A%3Every useful to me. %0D%0A%0D%0AThank you for letting me know.%0D%0A%0D%0A%3EI just noticed that my brother%2C Don Wagner%2C is cited in %2328. %0D%0A%3E However the link to his work is incorrectly located under %0D%0A%3Ethe name Elisha Loomis. %0D%0A%0D%0ANo%2C if you read just the next paragraph%2C Douglas Rogers%2C questioned the association of Liu Hui%27s name with this particular proof. I believe that in the ensuing correspondence Don Wagner admitted that his interpretation of Liu Hui%27s writing %28that came to us without a diagram%29 is rather tenuous. As the proof has appeared in Loomis with some comments%2C this is where I made a link to. A link to Don Wagner%27s follows at the bottom of the page.%0D%0A%0D%0A%3EI also would like to report that my remarkable 9-year old %0D%0A%3Efriend Toby in San Leandro California recently produced %0D%0A%3Eproof %2310%2C on his own%3A %0D%0A%0D%0AIt%27s quite recognizable on the drawing%2C yes.%0D%0A%3E%0D%0A%3EI was teaching him the necessary algebra manipulations so %0D%0A%3Ethat he could develop proof %233 on his own.  However he went %0D%0A%3Eoff on his own and invented a proof that I had never seen %0D%0A%3Ebefore.   I had trouble believing it%2C not to mention %0D%0A%3Eunderstanding his diagram %0D%0A%3E%28http%3A%2F%2F home.comcast.net%2F%7Epapasandy%2Ftoby-pythag-diagram.jpg %0D%0A%0D%0AThe big thing distracts from the smaller diagram which you probably had in mind.%0D%0A%0D%0A%3E%29%2C which was so clear to him but hard for me to follow.  He %0D%0A%3Edid finally explain himself well enough so that I knew what %0D%0A%3Ehe was trying to say%2C so I went home and proved to myself %0D%0A%3Ethat he was absolutely right.  It%27s a rare person of any age %0D%0A%3Ewho develops his%2Fher own proof of this theorem%2C and I%27m %0D%0A%3Elucky to be working with him. %0D%0A%0D%0AAnd what did he say%3F%0D%0A%0D%0A%3EI am interested in talking with others who are working with %0D%0A%3Eyoung gifted students. %0D%0A%0D%0ARegretfully%2C this may not be the right forum for the purpose%2C but I shall be grateful if anybody points you in the right direction.%0D%0A
2|2|1|||||RE%3A Proof %2328 - Pythagorean Theorem|papasandy||22:14:21|12/20/2009|%3E%29%2C which was so clear to him but hard for me to follow. He %0D%0A%3Edid finally explain himself well enough so that I knew what %0D%0A%3Ehe was trying to say%2C so I went home and proved to myself %0D%0A%3Ethat he was absolutely right. It%27s a rare person of any age %0D%0A%3Ewho develops his%2Fher own proof of this theorem%2C and I%27m %0D%0A%3Elucky to be working with him.%0D%0A%0D%0AAnd what did he say%3F%0D%0A%0D%0AHe said that the four ab triangles plus the middle square make a%5E2 plus b%5E2. I understood what he was saying but couldn%27t see see that it was true without making a drawing%2C and our time together that day was over.  I am sure that he didn%27t make any cutouts%2C just looked at the second diagram from proof %234 and visualized the pieces being moved around.  
3|3|2|||||RE%3A Proof %2328 - Pythagorean Theorem|alexb||22:15:56|12/20/2009|Thank you.%0D%0A%0D%0AIt%27s a great pleasure to work with talented children. They keep surprising you all the time.
4|4|3|||||RE%3A Proof %2328 - Pythagorean Theorem|papasandy||23:47:22|12/21/2009|%3EThank you. %0D%0A%3E%0D%0A%3EIt%27s a great pleasure to work with talented children. They %0D%0A%3Ekeep surprising you all the time. %0D%0A%0D%0AToby%27s mother %22confessed%22 today that he happened upon the following NLVM app while looking at his teacher%27s website%3A%0D%0Ahttp%3A%2F%2Fwww.nlvm.usu.edu%2Fen%2Fnav%2Fframes_asid_164_g_3_t_3.html%3Fopen%3Dinstructions%26from%3Dtopic_t_3.html%0D%0A%0D%0ANone of that dilutes my amazement at Toby%2C who correctly figured out the bounds of the sum of the angles in a spherical triangle while in the 2nd grade%2C and last year used the factorization of x%5E2-1 as the reason why a square is the rectangle of greatest area for a given perimeter.  All I do is try to give him interesting things to think about.%0D%0A%0D%0ABTW%2C his teacher%27s site is http%3A%2F%2Fteachermoy.com%2FAboutMr.Moy.html.  A glance at his autobiography reveals that Toby and the rest of the 4th graders are quite lucky to have Ken Moy as their teacher.%0D%0A%0D%0A-Sandy
5|5|4|||||RE%3A Proof %2328 - Pythagorean Theorem|alexb||09:39:25|12/28/2009|%3ENone of that dilutes my amazement at Toby%2C who correctly %0D%0A%3Efigured out the bounds of the sum of the angles in a %0D%0A%3Espherical triangle while in the 2nd grade%2C and last year %0D%0A%3Eused the factorization of x%5E2-1 as the reason why a square %0D%0A%3Eis the rectangle of greatest area for a given perimeter.  %0D%0A%3EAll I do is try to give him interesting things to think %0D%0A%3Eabout.%0D%0A%0D%0AThis is what I think should be happening in elementary school. Showing children things they may find interesting so that they may develop motivation for further study. Along the way they will necessarily acquire some skills required by the present curriculum. These may be easily and with little time expenditure enhanced later on%2C in the presence of motivation.%0D%0A%0D%0A%3EBTW%2C his teacher%27s site is %0D%0A%3Ehttp%3A%2F%2Fteachermoy.com%2FAboutMr.Moy.html.  A glance at his %0D%0A%3Eautobiography reveals that Toby and the rest of the 4th %0D%0A%3Egraders are quite lucky to have Ken Moy as their teacher. %0D%0A%0D%0ANot all teachers are the same of course. Your Toby is certainly lucky to have Mr. Moy as a teacher and you as a tutor.%0D%0A