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2016•Mathematics MagazineRequires access

Proof Without Words: The Parallelogram With Maximum Perimeter for Given Diagonals Is the Rhombus

Ángel Plaza

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Abstract

SummaryBy using the ellipse with foci at the extreme points of the shortest diagonal and the minor axis being the longest diagonal, it is proved without words that the parallelogram with maximum perimeter for given diagonals is the rhombus.

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SummaryBy using the ellipse with foci at the extreme points of the shortest diagonal and the minor axis being the longest diagonal, it is proved without words that the parallelogram with maximum perimeter for given diagonals is the rhombus.

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Available abstract

SummaryBy using the ellipse with foci at the extreme points of the shortest diagonal and the minor axis being the longest diagonal, it is proved without words that the parallelogram with maximum perimeter for given diagonals is the rhombus.

Key concepts: Rhombus, Parallelogram, Diagonal, Perimeter, Mathematics, Ellipse, Combinatorics, Geometry

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