Polygons with Increasing Sides, Inscribed in Circles

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def display_polyarc(n,r):

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    A=[0]; L=[]; st='$\\tiny{P=%s}$<br/>$P=%.4f$'

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    [A.append(A[i-1]+4*pi*i/(n*(n+1))) 

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     for i in [1..n]]

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    pretty_print(html('$A=%s$'%latex(A)))

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    ar=sum([arc((0,0),r,sector=(A[i],A[i+1]),

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                color=hue(i/n)) for i in range(n)])

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    for i in range(n+1):

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        x=1-2*sin(A[i]/2)^2

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        y=sqrt(1-x^2)*sign(cos(A[i]/2))

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        L.append([r*x,r*y])

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    l=sum([line((L[i],L[i+1]),color=hue(i/n)) 

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           for i in range(n)])

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    p=sum([2*r*sin((A[i+1]-A[i])/2) 

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           for i in range(n)])

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    pretty_print(html(st%(latex(p),p.n())))

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    (ar+l).show(gridlines=True)

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display_polyarc(7,3)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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