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Undergraduate Posters

Undergraduate Poster Session #21

Subevent of Undergraduate Poster Session

Phillips Lobby

Eastern Time (US & Canada)

Starts at: 2025-03-01 10:45AM

Ends at: 2025-03-01 12:00PM

Area Under a Rolling Ellipse

Nancy Scherich ⟨nscherich@elon.edu⟩

Abstract:

The ElonU Tangential’s student group solved the AMM problem 12476 which states: Let $C$ be one arch of the elliptic cycloid generated by the ellipse $x^2+\frac{1}{4}(y-2)^2=1$. That is, let $C$ be the curve traced by the vertex at the origin as the ellipse rolls without slipping along the $x$-axis for one revolution. What is the area under $C$ and above the $x$-axis? Our solution uses a clever change of perspective letting a tangent line roll around the ellipse, instead of the ellipse roll along the $x$-axis. The desired area turns out to be a surprisingly simple number.

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