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Journal for Geometry and Graphics 25 (2021), No. 1, 071--078
Copyright Heldermann Verlag 2021

On Pepe Trapezoids

Ting Hon Stanford Li
M7 - Queen Elizabeth Hospital, 30 Gascoigne Road, Kowloon, Hong Kong

We explore a special geometric figure, consisting of a trapezoid, the Pepe trapezoid, and an ellipse. The trapezoid is non-rectangular and has integer side lengths. The ellipse is non-circular, inscribed into the trapezoid, and has integer semi-axis lengths. We prove that there are infinitely many non-similar isosceles Pepe trapezoids, right-angled Pepe trapezoids and Pepe trapezoids in the form of parallelogram.

Keywords: Trapezoid, ellipse.

MSC: 51M04

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