demonstration of pythagoras' theorem in three moves
TRANSCRIPT
Demonstration of Pythagoras' Theorem in Three MovesAuthor(s): Roger BakerSource: Mathematics in School, Vol. 26, No. 2 (Mar., 1997), p. 27Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30211822 .
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DEMONSTRATION OF PYTHAGORAS" THEOREM IN THREE MOVES
by Roger Baker
Resources A square wooden 'picture frame' - the 'picture' being plain coloured cardboard. Four congruent wooden right-angled triangles (one with one side painted white) - the sum of the two shorter sides being equal to the side of the 'picture'.
As the triangles are slid about within the frame, the area of visible cardboard remains constant. Hence all that is required is to describe the areas of cardboard in terms of the length of the side of the white triangle.
The formula for (a+b)2 is, of course, also demonstrated by fig 2. Those for (a-b)2 (fig 3) and (a+b)(a-b) (fig 4) can also be demonstrated using the fact that the area of cardboard is a2+b2 (The triangles have been turned over so all are the same colour).
3aaa~a
2~~~~:::~iiiiiiii
1
Fig. 1 Fig. 2
Fig. 3 Fig. 4
But the most fun has been in discovering patterns of rotational symmetry of order four, and speculating as to how many there are. (The need to formulate some restrictive rules to prevent an infinite number adds spice to the arguments!) F*
Author Roger Baker, ex Abingdon School e-mail: [email protected]
Mathematics in School, March 1997 27
This content downloaded from 92.239.129.104 on Mon, 7 Apr 2014 14:19:36 PMAll use subject to JSTOR Terms and Conditions