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3 Mathematical Conundrums
I stubled across 3 false proofs, see if you can find the errors.
- X=Y
- X^2=X*Y
- X^2-Y^2=X*Y-Y^2
- (X+Y)*(X-Y)=Y*(X-Y)
- X+Y=Y
- 2Y=Y
- 2=1
- X=0.99999...
- 10X=9.99999...
- 10X-X=9.99999...-X
- 9X=9
- X=1
- 0.99999...=1
This one is a word problem. Imagine a square with sides of 4, and therefore a perimiter of 16. Cut corners, and the perimiter stays the same. See below for a visual.
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
- HHHHHHHHHH
The perimeter of the above shape is equal to the perimeter of the shape below.
(_ equals negative space)
- ____HHHH____
- ____HHHH____
- HHHHHHHHHH
- HHHHHHHHHH
- ____HHHH____
- ____HHHH____
Repeat to infinity. Square becomes a circle
- 16=Pi*(2)^2
Therefore, Pi equals 4
That's all folks!
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