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# Tag Archives: Recreation

## On the Rope Boys are Tau and Girls Are Pi

Cartoon of

Today, in the morning when I was teaching my sister about numbers, viz. rational numbers and irrational numbers, this one was created. My sister, Kavita Tiwari, is in Vth grade and mainly study Math ,Science and Social Science. On last wednesday we visited a Circus show. We all liked that very much. And she became a fan of a girl acrobat. She always says that female acrobats are far better than male acrobats in circus-shows having rope-walk show. Male acrobats look like they are about to fall, but female ones are frank in this work. When I discussed with her about some constants like $\pi, \, \tau, \, e$ etc., she asked me to stop for a while, and started making this cartoon. Her thoughts were mingled with math. I was surprized by the meaning this cartoon had. I really liked her stuff, and thought to post it on the web.

Notes:

• I have searched everywhere, but couldn’t find same topic/idea like this.
• For those who don’t know:

[ My english is also weaker than her. ]

## Derivative of x squared is 2x or x ? Where is the fallacy?

As we know that the derivative of $x^2$ , with respect to $x$ , is $2x$.

i.e., $\dfrac{d}{dx} x^2 = 2x$

However, suppose we write $x^2$ as the sum of $x$ ‘s written up $x$ times..

i.e.,

$x^2 = \displaystyle {\underbrace {x+x+x+ \ldots +x}_{x \ times}}$

Now let

$f(x) = \displaystyle {\underbrace {x+x+x+ \ldots +x}_{x \ times}}$

then,

$f'(x) = \dfrac{d}{dx} \left( \displaystyle {\underbrace {x+x+x+ \ldots +x}_{x \ times}} \right)$

$f'(x)=\displaystyle {\underbrace {\dfrac{d}{dx} x + \dfrac{d}{dx} x + \ldots + \dfrac{d}{dx} x}_{x \ times}}$
$f'(x)=\displaystyle {\underbrace {1 + 1 + \ldots + 1 }_{x \ times}}$
$f'(x) = x$

This argument appears to show that the derivative of $x^2$ , with respect to $x$, is actually x, not 2x..

Where is the error?