The Seven Magic Theorems of Mathematics
-by Pawan Rama Mali
# Theorem 1.
=> 3=4.
Proof =>
Suppose a + b = c.
i. e. (4a - 3a) + (4b - 3b) = (4c - 3c)
i. e. 4a + 4b - 4c = 3a + 3b - 3c [ After reorganising ]
i. e. 4*(a+b-c) = 3*(a+b-c) [ Taking constants out of brackets ]
i. e. 4 = 3
Hence the proof.
# Theorem 2.
=> All numbers are equal to zero.
Proof =>
Suppose a = b.
Let sqr = square.
Let sqrt = square root of.
As a = b,
therefore ( a sqr 2 ) = ab
i. e. ( a sqr 2 ) - ( b sqr 2 ) = ab - ( b sqr 2 )
i. e. ( a + b ) * ( a - b ) = b*( a - b )
i. e. a + b = b
i. e. a = 0 ( zero )
Hence the proof.
# Theorem 3.
=> 1$(dollor) = 1c(cent)
Proof =>
And another that gives you a sense of money disappearing...
1$ = 100c
= (10c) sqr 2
= (0.1$) sqr 2
= 0.01$
1$ = 1c
Hence the proof.
# Theorem 4.
=> 1 = -1.
Proof =>
We know 1 = 1.
1 -1
i. e. -- = --
-1 1
_____ _____
[ / 1 ] [ / -1 ]
i.e. [ / -- ] sqr = [ / -- ] sqr
[ \/ -1 ] [ \/ 1 ]
___ _____
( \/ 1 ) sqr ( \/ -1 ) sqr
i.e. ------------- = --------------
____ ____
( \/ -1 ) sqr ( \/ 1 ) sqr
___ ___ ____ ____
i. e. [ ( \/ 1 ) sqr ] * [ ( \/ 1 ) sqr ] = [ ( \/ -1 ) sqr ] * [ ( \/ -1 ) sqr ]
___ ____
i. e. [ [ ( \/ 1 ) sqr ] sqr ] = [ [ ( \/ -1 ) sqr ] sqr ]
___ ____
i. e. \/ 1 = \/ -1
i. e. 1 = -1 [ Squaring both the sides ]
Hence the proof.
# Theorem 5.
=> 4=5.
Proof =>
We know -20 = -20
i. e. 16 - 36 = 25 - 45
i. e. ( 4 sqr 2 ) - ( 9 * 4 ) = ( 5 sqr 2 ) - ( 9 * 5 )
Now add the term (81/4) on both of the sides.
i. e. ( 4 sqr 2 )-( 9 * 4 )+( 81/4 ) = ( 5 sqr 2 )-( 9 * 5 )+( 81/4 )
i. e. ( 4 - ( 9/2 ) ) sqr = ( 5 - ( 9/2 ) ) sqr
i. e. ( 4 - ( 9/2 ) ) = ( 5 - ( 9/2 ) )
i. e. 4 = 5.
Hence the proof.
# Theorem 6.
=> A cat has nine tails.
Proof =>
No cat has eight tails. But a cat has one tail more than no cat.
Therefore a cat has nine tails.
Hence the proof.
# Theorem 7.
=> sin x = 6n.
Proof =>
To prove that sinx = 6n
sinx
i.e. to prove that ------ = 6
n
Canceling n from upper & lower sides, we get
six = 6
which is always true.
Hence the proof.
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