# Plateau Curve

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Contents:

1. The Plateau curve (of Joseph Plateau).
2. Plateau of a curve (physics).

## The Plateau Curve

The Plateau curve is also called the curve of Joseph Plateau, after the blind Belgian physicist who discovered that a curved wire frame dipped in a soap solution forms “beautiful curved surfaces” [1].

The Cartesian equation for the Plateau curve is:

Where m ≠ n. If m = 2n, the curve degenerates to a circle centered at (1, 0) with radius 2 [2].

## The Plateau of a Curve

A plateau curve (no capitalization) refers to a curve with a rapid rise, followed by a leveling off; the flat region that follows is called the plateau of the curve. Roughly speaking, curves with this form have the equation [3]

A plateau curve representing the variation of counting rate with voltage.

This type of curve has many uses in science and engineering. Plateau curves are often seen in models of high voltage, where they can help determine optimal input voltage [4]; The section of a Geiger Counter is characterized by the plateau curve [5]; there is a sharp ramp up when a Geiger tube turns on, followed by a plateau. In mechanics, the curve can model a flow curve of steady shear stress vs. shear-rate [6]. In biochemistry, the plateau curve models an enzyme-catalyzed reaction rate of a substrate as a function of the concentration of the substrate [7].

## References

Image of curves: Hellingspaul, ,CC BY-SA 3.0 via Wikimedia Commons
[1] Britannica. Joseph Antoine Ferdinand Plateau. Retrieved February 24, 2022 from: https://www.britannica.com/biography/Joseph-Antoine-Ferdinand-Plateau
[2] Plateau Curves. Retrieved February 22, 2022 from: https://archive.lib.msu.edu/crcmath/math/math/p/p351.htm
[3] Billo, E. (2007). Excel for Scientists and Engineers: Numerical Methods. Wiley & Sons.
[4] Lab 1 – Rough HV Plateau Curve. Retrieved February 24, 2022 from: http://atlas.physics.arizona.edu/~shupe/Physics_Courses/Phys_586_S2015_S2016_S2017/Lab%201%20write%20up%20Gia.pdf
[5] Lee, R. Plateau characteristics of Geiger Counters with respect to different gas mixtures and pressures. Masters Thesis. Retrieved February 24, 2022 from: https://scholarsmine.mst.edu/masters_theses/4836/
[6] Slippage and migration in Taylor–Couette flow of a model for dilute wormlike micellar solutions.

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Stephanie Glen. "Plateau Curve" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/plateau-curve/
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