pythagoras Mike Askew

the ppt here shows that pythagoras' result can be viewed as a boundary...

pythagoras proofs

a collection

the usual proof (below) involves some relatively easy algebra
a ppt for this is here

a ppt put together by Pete Griffin

pythagoras visuals

a ppt is here

Byrne's Euclid here

pythagoras 8 proofs

a ppt is here

8 fairly different justifications/proofs

pythagore

based on Herve Lehning's work

Herve Lehning's posters of Pythagoras by means of dissections
(are the same, apart from the central one)

make into a square

show how this hexagon can be transformed into a square
by cutting and fitting
with as few lines as possible

it's a tilted one, obviously...

make the pentomino/hexagon into the square
by cutting and fitting

with as few lines as possible

pythagoras

James Garfield 'Pythagoras' proof

James Garfield was the 20th president of the USA
for a brief period of time (he was assassinated)

he worked on a proof of the theorem with colleagues, five years before he became president

first, establish that the isosceles triangle is right-angled

then find the area of the trapezium (trapezoid)

relate this to the sum of the three triangles (two of which are congruent):

this involves squaring (a + b)

pythagoras justification

when shapes are similar their areas are in proportion to the squares of corresponding sides

drop a perpendicular from the apex at the right angle to form two similar triangles (relatively straightforward to justify) which are similar to the original triangle

k(5^2) = k(4^2) + k(3^2)
and this generalises...

not that helpful as a means of justifying the theorem maybe, but a neat enough way of tying in the area property of similar shapes

[ from the website betterexplained ]