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Subject: "Proof Of Pythagorean Theorem By Translation"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #691
Reading Topic #691
Bui Quang Tuan
Member since Jun-23-07
Aug-19-08, 08:17 AM (EST)
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"Proof Of Pythagorean Theorem By Translation"
 
   Dear All My Friends,
Suppose ABC is right triangle and AB is hypotenuse, BC<=AC. I suggest here one proof of Pythagorean theorem by translation and with two squares constructed on legs: one outward, one inward with ABC.
Rotate ABC around A by 90 to get AB1C1
Translate AB1C1 by AB to get BB2C2 (ABB2B1 is a square)
D = intersection of BC2 and B1B2
E = intersection of BC2 and B1C1 (ACEC1 is a square)
Translate B2C2D by B2B to get BC3D1
E1 = intersection of C3D1 and AC (BCE1C3 is a square)
From this two right triangles EB1D, E1AD1 are congruent and E1AD1 = tranlation of EB1D by B1A.
Two squares ACEC1 and BCE1C3 can bound square ABB2B1 by three translations 1, 2, 3 as in attach file. Two parts ACDB1 and BCE1D1 are in place.
It completes Pythagorean theorem.
May be it is new one?
Thank you and best regards,
Bui Quang Tuan

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alexb
Charter Member
2262 posts
Aug-19-08, 11:11 AM (EST)
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1. "RE: Proof Of Pythagorean Theorem By Translation"
In response to message #0
 
   > May be it is new one?

This is the geometric proof #127 from Loomis' book. #174 moves square BCE'C3 to the position EC2B2X. This gives you an idea of the length Loomis went to to make the number of proofs beyond 300.

I think we both may find a better occupation than seeking additional proofs of the Pythagorean theorem. For me, the important thing is a novel outlook - a new view point - rather than the sheer novelty of the method. There are about 250 proofs in Loomis' book that I have no plans of including in my pages.


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Bui Quang Tuan
Member since Jun-23-07
Aug-19-08, 11:48 AM (EST)
Click to EMail Bui%20Quang%20Tuan Click to send private message to Bui%20Quang%20Tuan Click to view user profileClick to add this user to your buddy list  
2. "RE: Proof Of Pythagorean Theorem By Translation"
In response to message #1
 
   >I think we both may find a better occupation than seeking
>additional proofs of the Pythagorean theorem. For me, the
>important thing is a novel outlook - a new view point -
>rather than the sheer novelty of the method. There are about
>250 proofs in Loomis' book that I have no plans of including
>in my pages.

Dear Alex,
Thank you very much for your kind advice! I understand what you say. If you don't give me this message, may be I try to find all another 250 proofs??? :-)
Thank you again and best regards,
Bui Quang Tuan


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