Melody

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pi is an irrational number and cannot be expressed as a fraction or as a decimal.  When expressed as  a decimal the digits keep going for ever without any pattern.  Hence whenever it is expressed as a fraction or a decimal it is always an approximation.

This may be of interest to some people it is from Wikipedia.

Pi can be calculated in ta number of ways.  Here are a couple.

Hi Heureka,

You have an excellent argument.

BUT

what if you start with   $$x=\dfrac{40}{(\frac{-1}{10})}\\\\$$    and then continue with a similar argument to yours.

I think that you end up with $$\frac{40}{0}=\:-\infty$$  

It can't equal   $$-\infty \quad and \quad +\infty$$   at the same time therefore it is undefined.

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I really need to learn to write limits using Latex! 

also

\frac{40}{(1/10)}

$$\frac{40}{(1/10)}$$

How did you get it to write the fraction upright on the bottom more neatly than mine?

I had to go into display mode else it was too squashy.

Thank you.

What did you use to get your answers?

All great answers  

Where is your working Chris?

A rectangle can't have 4 different length sides!

Congratulations Zegroes!   

I'm sorry blaster0 but I don't think it makes sense to me either.  Sorry.

Monday 18/5/14

This one is up for discussion: