Can Pi be Constructed on a Number Line Using Non-Traditional Tools?

[vaishakh]

how to plot the irrational number pi on a number line. i know the procedure for square roots of different non-perfecr square number. it is by drawing a perpendicular at a suitable integral length again at suitable integral length such that the hypotenuse is of required length as per the pythagoras theorem. then measuring the hypotenuse with compass and plotting it on number line

 

[hypermorphism]

While square roots can be constructed, a line with length corresponding to pi cannot be constructed, due to pi being transcendental. You can, however, construct a circle of unit diameter whose circumference will be pi.
If you just want the decimal value of pi, many numerical algorithms exist that converge to multiples of pi, including the Newton-Raphson method, or Taylor series of trigonometric functions.

 

[Zurtex]

Ask your self, what is a number line and how do you plot 1 on it?
For example:

0        Pi
__________

There I've plotted Pi on that number line.

 

[HallsofIvy]

Ask your self, what is a number line and how do you plot 1 on it?
For example:

0        Pi
__________

There I've plotted Pi on that number line.

Perhaps you should ask yourself those questions. It was clear from the original post that he meant "constructing" a line segment of length pi, using compass and straightedge, given a line segment of length 1.

 

[Zurtex]

Perhaps you should ask yourself those questions. It was clear from the original post that he meant "constructing" a line segment of length pi, using compass and straightedge, given a line segment of length 1.

Oh I see, sorry, I read the post only very quickly and that kind of request didn't seem to belong in a Numer Theory forum...

 

[vaishakh]

please explain Newton Raphson method.

this the not the place forsuch request- Zurtex.
which is the riht place then. i thought number theor page would help me more because this subject would have moretheorems and formulae to deal with such problems

i think the plotting of e is also done with Taylor series. please briefly explain the procedure for both of these cases

 

[hypermorphism]

please explain Newton Raphson method.
...
i think the plotting of e is also done with Taylor series. please briefly explain the procedure for both of these cases

A basic calculus course would cover both algorithms. The Newton-Raphson method is a simple way of finding roots of equations, while Taylor series are infinite series expansions of analytic functions. They both deal with derivatives and can be found in the first few chapters of any (beginning) calculus text.
As an example, we know that sin(pi) = 0, so the root of the equation sin(x)=0 in the neighborhood around pi should yield pi if Newton-Raphson is applied. Use http://planetmath.org/encyclopedia/NewtonsMethod.html . Note the domain of convergence; you'll have to choose a fractional multiple of pi, then multiply your calculation by the denominator.
More number theoretic approaches to calculating pi can be found on the page linked to in your other post.

 

[Aditya89]

Pi can not be constructed by ruler and compass.But,Pi may be constructed with the help of some other things other than compass and non-marked ruler.