That's the one

That's the one

Why should that squiggle represent 98765932 rather than 98765933? 

If a squiggle is going to be able to represent an arbitrary natural number of up to 8 digits, then there must be at least 10^8  different  possible squiggles, distinguishable both to us (the makers of the squiggle) and to the machine.  I think for most people, accurate squiggle-making at the required level of precision would turn out to be more difficult than typing it on a keypad.

Thanks for that.  I think I'll leave the link as is, though: it's better to read the thread from the beginning, as my comment isn't completely self-contained.

Thanks for that.  I think I'll leave the link as is, though: it's better to read the thread from the beginning, as my comment isn't completely self-contained.

The confusion stems from the fact that you said "polynomial" and this is not a polynomial: it is piecewise polynomial.  The distinction is important.  The fsolve function does find all real roots of a polynomial in a given interval, but not of a piecewise polynomial.  However, you can use fsolve separately on each of the pieces in its own interval, as I did in my reply to your question on "Local maxima and minima of piecewise polynomials".

The confusion stems from the fact that you said "polynomial" and this is not a polynomial: it is piecewise polynomial.  The distinction is important.  The fsolve function does find all real roots of a polynomial in a given interval, but not of a piecewise polynomial.  However, you can use fsolve separately on each of the pieces in its own interval, as I did in my reply to your question on "Local maxima and minima of piecewise polynomials".

The command is polygonplot in the plots package.  But the vertices should be in a list, not a set.

The command is polygonplot in the plots package.  But the vertices should be in a list, not a set.

I was confused by your statement

Depending on whether the domain of the piecewise function is bounded, the first entry of the list may be a function or a bound.

I've never seen an example where the first entry of the list is a bound.  It seems to me that if an interval is not covered by any of the conditionals, and there is no "otherwise" clause, the pwlist makes the function 0 there.  For example:

convert( piecewise(1 <= x and x < 2, f1(x), 
    x>=2 and x < 3, f2(x)), pwlist);

[0, 1, f1(x), 2, f2(x), 3, 0]

I was confused by your statement

Depending on whether the domain of the piecewise function is bounded, the first entry of the list may be a function or a bound.

I've never seen an example where the first entry of the list is a bound.  It seems to me that if an interval is not covered by any of the conditionals, and there is no "otherwise" clause, the pwlist makes the function 0 there.  For example:

convert( piecewise(1 <= x and x < 2, f1(x), 
    x>=2 and x < 3, f2(x)), pwlist);

[0, 1, f1(x), 2, f2(x), 3, 0]

But that's exactly what Mariner told you how to do!

Your equation is this:

P = 2.666845389*10^(-12)*Pi^2/(1.450695744*10^(-11)*Pi

+6.406272405*10^(-13)*Pi*(0.10e-1*tan(0.5637758661e-1*sqrt(P))

*sin(0.5637758660e-1*sqrt(P))+0.10e-1*cos(0.5637758660e-1*sqrt(P))))

Call it eq.  So all you have to do is

 fsolve(eq);

and you get the answer

.5772706213

If you want to give fsolve a little more help, you could specify an interval, e.g.

fsolve(eq, P = 0 .. 2);

But that's not necessary in this case.

But that's exactly what Mariner told you how to do!

Your equation is this:

P = 2.666845389*10^(-12)*Pi^2/(1.450695744*10^(-11)*Pi

+6.406272405*10^(-13)*Pi*(0.10e-1*tan(0.5637758661e-1*sqrt(P))

*sin(0.5637758660e-1*sqrt(P))+0.10e-1*cos(0.5637758660e-1*sqrt(P))))

Call it eq.  So all you have to do is

 fsolve(eq);

and you get the answer

.5772706213

If you want to give fsolve a little more help, you could specify an interval, e.g.

fsolve(eq, P = 0 .. 2);

But that's not necessary in this case.

Like this:

 display([pointplot(data1),pointplot(data2),
    plot([f1(1/t),f2(1/t)],t=0..1/8)],labels=[1/N,f(N)]);

Like this:

 display([pointplot(data1),pointplot(data2),
    plot([f1(1/t),f2(1/t)],t=0..1/8)],labels=[1/N,f(N)]);