Monday, 14 May 2018

big list - 2=1 Paradoxes repository

I really like to use paradoxes in my math classes, in order to awaken the interest of my students. Concretely, these last weeks I am proposing paradoxes that achieve the conclusion that 2=1. After one week, I explain the solution in the blackboard and I propose a new one. For example, I posted the following one some months ago: What is wrong with the sum of these two series?
I would like to increase my repertoire of fake-proofs. I would be glad to read your proposals and discuss them! My students are 18 years old, so don't be too cruel :) Here is my own contribution:



y(x)=tanx


y=1cos2x


y=2sinxcos3x

This can be rewritten as:
y=2sinxcos3x=2sinxcosxcos2x=2tanx1cos2x=2yy=(y2)

Integrating both sides of the equation y=(y2):
y=y2

And therefore
1cos2x=tan2x

Now, evalueting this equation at x=π/4
1(2/2)2=12

2=1

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