Pythagoras rule proved by geometry
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Pythagoras rule proved by geometry - Presentation Transcript
- Proving Pythagoras’s theorem (by geometry)
(This technique comes from Jacob Bronowski’s book, The Ascent of Man.)
C
A
i.e., C2 = A2 + B2
B - Arrange four identical triangles in a square as shown.
C
C
A
C
C
B
C - Fill the gap in the middle with a square.
C
C
A
B-A
C
C
B
B-A
B-A
B-A
C - Fill the gap in the middle with a square.
The area of all five shapes put together is C2.
C
C
A
B-A
C
C
B
B-A
B-A
B-A
C - The area of all five shapes put together is C2.
Rearrange the shapes.
C
A
B
B-A
A
B
B-A
B-A
B-A - The area of all five shapes put together is C2.
Can you see that this is the same as B2 + A2 ?
B
B-A
C
A
A
B-A
B-A
B
B-A - END
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David Coulson, 5 months ago
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How Pythagoras himself might have derived the trian more
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