Equation for the Eiffel Tower

Robert Banks's book Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics describes the Eiffel Tower's shape as approximately the logarithmic curve

where y_* and x₀ are chosen to match the tower's dimensions.

Here's a plot of the curve:

And here's the code that produced the plot:

from numpy import log, exp, linspace, vectorizeimport matplotlib.pyplot as plt# Taken from "Towing Icebergs, Falling Dominoes,# and Other Adventures in Applied Mathematics"# by Robert B. Banks# Constants given in Banks in feet. Convert to meters.feet_to_meter = 0.0254*12ystar = 201*feet_to_meterx0 = 207*feet_to_meterheight = 984*feet_to_meter# Solve for where to cut off curve to match height of the tower.# - ystar log xmin/x0 = heightxmin = x0 * exp(-height/ystar)def f(x): if -xmin < x < xmin: return height else: return -ystar*log(abs(x/x0))curve = vectorize(f) x = linspace(-x0, x0, 400)plt.plot(x, curve(x))plt.xlim(-2*x0, 2*x0)plt.xlabel("Meters")plt.ylabel("Meters")plt.title("Eiffel Tower")plt.axes().set_aspect(1)plt.savefig("eiffel_tower.svg")

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