Can you teach a mathematical Luddite to do something reallly clever in math?

Question

People consider those good at math to be clever people, but my challenge will find out if this is true. Teach me some complicated looking mathmatical art and if I can understand it, you get 10 points and a big thank you from this dunce.

I could teach you how to play dueling banjos on the guitar, you would no little about music, but i could do that, can anyone do the same wit math?

Answer 1

Well, I'm a bit of a mathematical dunce myself, but how about demonstrating that 2=1?

there are two ways of doing this, one using irrational numbers / vulgar fractions, and one using algebra. Here is the algebra; (The thing is to keep track of the fact that at each stage, both sides of the equals sign really do match up. This means that the proof is mathematically valid, even though nonsensical in reality!)

Let a and b be equal non-zero quantities
a = b
Multiply through by a
a2 = ab
Subtract b2
a2 − b2 = ab − b2
Factor both sides
(a − b)(a + b) = b(a − b)
Divide out (a − b)
a + b = b
Observing that a = b
b + b = b
Combine like terms on the left
2b = b
Divide by the non-zero b
2 = 1

The 'Clever' bit comes in then disproving your own proof. The fallacy is the division by (a-b) - this is actually a division by zero, which as any Excel user can verify, is an error.
The other method looks more impressive, but frankly is a bit scary to me. There are quite a few sites devoted to it, try http://www.math.toronto.edu/mathnet/falseProofs/second1eq2.html

Answer 2

I've been sitting here for 10 minutes trying to think of something for you, but all the "clever" I can think of requires a fair amount of prior knowledge!
I know it may sounds silly, but why don't you pick up an A Level / difficult GCSE book on ebay and actually learn some Mathematics? Having studied Theoretical Physics right up to and including degree standard, I can assure you than A Level Maths really isn't that tough, some of the concepts might take a little while to sink in, is all. Plus you'll have the added bonus of having bettered yourself in a small way.

Answer 3

An easy trick is to ask someone what is the square root of minus one. But make sure the people you are asking haven't gone beyond GCSE Mathematics.

There is no number that is the correct answer, and sometimes you can get people guessing for hours.

The answer is i. This is dealt with in more detail at A Level.

Answer 4

Math is like art; it's not really clever unless you already appreciate it.
I know a bunch of interesting things about math, but if you're not into math, you probably wouldn't find those things all that fascinating.

Answer 5

Demonstrate that all mathematical functions are modifictions of addition by demonstrating them on a numberline.
E-mail me if you think you need more info.