42 lines
1.1 KiB
Plaintext
42 lines
1.1 KiB
Plaintext
# Appendix
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```{julia}
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#| hold: true
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#| echo: false
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gr()
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## For **some reason** having this in the natural place messes up the plots.
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## {{{approximate_surface_area}}}
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xs,ys = range(-1, stop=1, length=50), range(-1, stop=1, length=50)
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f(x,y)= 2 - (x^2 + y^2)
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dr = [1/2, 3/4]
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df = [f(dr[1],0), f(dr[2],0)]
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function sa_approx_graph(i)
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p = plot(xs, ys, f, st=[:surface], legend=false)
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for theta in range(0, stop=i/10*2pi, length=10*i )
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path3d!(p,sin(theta)*dr, cos(theta)*dr, df)
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end
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p
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end
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n = 10
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anim = @animate for i=1:n
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sa_approx_graph(i)
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end
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imgfile = tempname() * ".gif"
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gif(anim, imgfile, fps = 1)
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caption = L"""
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Surface of revolution of $f(x) = 2 - x^2$ about the $y$ axis. The lines segments are the images of rotating the secant line connecting $(1/2, f(1/2))$ and $(3/4, f(3/4))$. These trace out the frustum of a cone which approximates the corresponding surface area of the surface of revolution. In the limit, this approximation becomes exact and a formula for the surface area of surfaces of revolution can be used to compute the value.
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"""
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plotly()
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ImageFile(imgfile, caption)
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```
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