Proportions of the Golden Section

Copyright (C) 2020 Andreas Kloeckner

MIT License

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import matplotlib.pyplot as pt
from math import sqrt

a = 0
b = 1

#tau = .3
tau = (sqrt(5)-1)/2

m1 = a + (1-tau) * (b-a)
m2 = a + tau * (b-a)

pt.xlim([a-0.5, b+0.5])
pt.ylim([-0.1, 0.2])
pt.grid()
pt.plot([a,b], [0,0], "ob")
pt.plot([m1, m2], [0,0], "or")

[<matplotlib.lines.Line2D at 0x7f4072f19ca0>]

Now see if any function evaluations can be reused if we move to the "left" subinterval:

pt.xlim([a-0.5, b+0.5])
pt.ylim([-0.1, 0.2])
pt.grid()
pt.plot([a,b], [0,0], "ob")
pt.plot([m1, m2], [0,0], "or")
# Same as above up to this point

pt.plot([0, m2*m1, m2*m2, m2*b], [0.1]*4, "og")

[<matplotlib.lines.Line2D at 0x7f4072b23b20>]

Check numerically:

m1 - m2**2

-1.1102230246251565e-16