5
votes
2answers
150 views

What is the flaw in this proof that all triangles are isosceles?

What is the flaw in this "proof" that all triangles are isosceles? From the linked page: One well-known illustration of the logical fallacies to which Euclid's methods are vulnerable (or at least ...
3
votes
0answers
83 views

Why is this proof false? (Why is $e^i \neq 1$?) [duplicate]

I found this on MathOverflow: $$e^i = (e^i)^{(2\pi/2\pi)} = (e^{2\pi i})^{1/2\pi} = 1^{1/2\pi} = > 1.$$ I first saw this one many years ago, written on the wall of a bathroom stall in ...
3
votes
3answers
457 views

number of points on two circles

(sorry I don't know how to add pictures) Two friends argue if larger circles have more points than smaller circles Friend number 1 (a well known argument) Say the circles are concentric. you cannot ...
6
votes
4answers
872 views

Proof That $1=0$ — Why is it False?

So I devised this proof that $1=0$. Of course it is false, but I don't know why. Why? $$\begin{align*} x+1&=y\\ \frac{x+1}{y}&=1\\ \frac{x+1}{y}-1&=0\\ \frac{x+1}{y}-\frac{y}{y}&=0\\ ...
27
votes
6answers
3k views

Where is the flaw in this argument of a proof that 1=2? (Derivative of repeated addition)

Consider the following: $1 = 1^2$ $2 + 2 = 2^2$ $3 + 3 + 3 = 3^2$ Therefore, $\underbrace{x + x + x + \ldots + x}_{x \textrm{ times}}= x^2$ Take the derivative of lhs and rhs and we get: ...
41
votes
6answers
5k views

How come $32.5 = 31.5$?

Below is a visual proof (!) that $32.5 = 31.5$. How could that be?