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 *x*_{0} 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, vectorize import 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*12 ystar = 201*feet_to_meter x0 = 207*feet_to_meter height = 984*feet_to_meter # Solve for where to cut off curve to match height of the tower. # - ystar log xmin/x0 = height xmin = 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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The St. Louis arch is approximately a catenary, i.e. a hyperbolic cosine.

My studies show Eiffel Tower to exactly follow a full hyperbolic curve, from its origin upward, with the E limiting axis turned vertical.. Any comment?