Math Teasers: Drive your Non-Scientist Friends Crazy
An old joke asks, ‘how to drive a miser nuts?’, with the answer being, ‘put a dime in a round room and tell him to look in the corner.’ Over the years, I’ve noticed non-scientists are very easy to fool since they’re not experienced and can’t detect mathematical and other fallacies your argument holds. Here are a few ‘practical math jokes’ for you to try on your friends or family. Some won’t care, but some will just get extremely frustrated as they try to figure out the catch, which should provide you with some quality entertainment.
The Dollar-to-Cent Illusion
Convince your friends that 1$ = 1 cent. This is great since almost everyone’s interest gets piqued when money is involved! Here’s how to do it:
1$ = 100 cents = (10 cents)² = (0.1$)² = 0.01$ = 1 cent
Any freshman will immediately tell you you’ve got your units wrong - you can’t square the cents. However non-physicists will puzzle over this for hours.
The i² = 1 Trick
This is best used on highschool pupils or college freshmen just taking a course with complex numbers:
1/i = 1/√(-1) = √(1/-1) = √(-1) = i.
Multiplying both sides by i you get i² = 1 (instead of the true form, i² = -1). (Can you spot the fallacy?)
How to Prove that 1=2
Suppose a=b. Then a*b=a². Subtracting b² from both sides, one gets:
a*b - b² = a² - b²
Using algebraic identities, we can factor it as follows:
b(a-b) = (a-b)(a+b)
Dividing by a-b, we get: b = a+b = 2b (since a=b). Dividing once again by b, one obtains 1=2.
The error hides in the division by a-b, which (by the assumption a=b) is zero. Division by zero is forbidden. You can use this to prove 1$ = 2$ - as before, anything having to do with money will attract a bigger audience.
