On Sunday, June 8, 2014 9:40:42 AM UTC-7, Андрей Ширшов wrote:
>
> TypeError: unable to convert x (=floor(tan(abs(1/2*pi + 
> alpha)^0.220000000000000))) to an integer
>

The problem is that "fibonacci" isn't a symbolic function, so when you give 
it an argument, it wants to evaluate it to an integer immediately. The 
polar-plot thing never comes in:

 sage: fibonacci(floor(tan((abs(alpha+pi/2)^0.22))))
TypeError: unable to convert x (=floor(tan(abs(1/2*pi + 
alpha)^0.220000000000000))) to an integer

Plot functions also accept python-callables as arguments (as long as they 
have a way of getting their data points, they're happy), so the following 
does work:

sage: polar_plot(lambda 
alpha:(1+cos(fibonacci(floor(tan((abs(alpha+pi/2)^0.22)))))), (alpha, 
-pi/2, pi/2))

Alternatively, you could use the closed formula for the fibonacci sequence 
as a symbolic expression and work with that:

sage: fib(n)=(((1+sqrt(5))/2)^n-((1-sqrt(5))/2)^n)/sqrt(5)
sage: polar_plot((1+cos(fib(floor(tan((abs(alpha+pi/2)^0.22)))))), (alpha, 
-pi/2, pi/2))

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