...proves to be less of a pain than you might originally think. In
fact, it's no problem at all to unravel millennia of careful mathematical
postulation with just one simple trick. Can you spot it?
Given: a=b
(1) pi*a^2 = pi*a*b
(multiplying pi*a)
(2) 3*a*b = 3*b^2
(multiplying by 3*b)
(3) pi*a^2 - 3*a*b = pi*a*b - 3*b^2
(subtracting (2) from (1))
(4) pi*a^2 - pi*a*b = 3*a*b - 3*b^2
(adding 3*a*b and subtracting pi*a*b on both
sides)
(5) pi*a^2 - pi*a*b + a*b - b^2 = 4*a*b - 4*b^2
(adding a*b and subtracting b^2 on both
sides)
(6) pi*a*(a-b) + b*(a-b) = 4b*(a-b)
(factoring out common terms)
(7) pi*a + b = 4*b
(removing common terms)
(8) pi*a = 3*b
(subtracting b)
(9) pi*b = 3*b
(substituting a for b since a =
b)
(10) pi = 3
(removing
common terms)
Therefore pi=3.
Spoiler ahead! If you want to figure it out yourself, then don't read on
just yet!
The trick is actually the same employed over and over to prove
all kinds of things in math, including that 1 = -1 and 1 = 2, among the more
famous. Take a look at step 7. This is where the error is.
In order to remove the terms, we must divide, right? Well, if a = b, then a
- b = 0, thus we are dividing by zero, which is a big math
no-no. Aside from being a fun trick to throw at your math
students, it is a great example of why we can't divide by zero.
Indeed, if we allowed it, then we can prove all kinds of false statements in
our system!
Try your own hand at it for a minute. What other "convenient"
conclusions can you come to? Can you prove that the world is like this
math
t-shirt? Maybe prove that e = 2 or that sqrt(2) = 1.5 or, if you're
really adventurous, prove that pi = e!
Now, consider branching out into other illegal areas of math. :)
How about negative square roots? What kind of false statements can you
arrive at using that loop hole?
Just for fun, here is another fake proof. See if you can find
the error:
(1) John = Time * Money
(or anyone that you want to stick it
to...)
(2) Time = Money
(Time is Money)
(3) John = Money * Money
(substitution)
(4) Evil = sqrt(Money)
(Money is the Root of Evil)
(5) John = Evil
Of course, here the problem is in (4) because Paul said that the
love
of money was the root of all evil...har-de-har-har...oh, well, it was funny
to me...
By the way, here si a good link for a fun twist on this topic:
How
to Become An Irrational Number Liberator and Prove That Pi Equals 3
