Comments on: A Quadrilateral in a Rectangle
https://blog.tanyakhovanova.com/2023/11/a-quadrilateral-in-a-rectangle/
Mathematics, applications of mathematics to life in general, and my life as a mathematician.Tue, 05 Dec 2023 14:28:35 +0000
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By: Carnival 170: A Plethora of Playful Math – Denise Gaskins' Let's Play Math
https://blog.tanyakhovanova.com/2023/11/a-quadrilateral-in-a-rectangle/#comment-13854
Tue, 05 Dec 2023 14:28:35 +0000https://blog.tanyakhovanova.com/?p=1985#comment-13854[…] Khovanova poses a nice Quadrilateral in a Rectangle puzzle (solution […]
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By: Tanya Khovanova's Math Blog » Blog Archive » A Quadrilateral in a Rectangle Solution
https://blog.tanyakhovanova.com/2023/11/a-quadrilateral-in-a-rectangle/#comment-13853
Sat, 02 Dec 2023 21:43:36 +0000https://blog.tanyakhovanova.com/?p=1985#comment-13853[…] recently posted A Quadrilateral in a Rectangle […]
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By: Lazar Ilic
https://blog.tanyakhovanova.com/2023/11/a-quadrilateral-in-a-rectangle/#comment-13848
Wed, 29 Nov 2023 09:54:33 +0000https://blog.tanyakhovanova.com/?p=1985#comment-13848If a diagonal is parallel then it follows by drawing the triangles and bh/2 area splitting each subrectangle in half. The other direction follows from a relatively simple smoothing argument. If BD is not parallel then the area function is monotone and nonconstant linear as we shift point A along its edge and in particular obtains its unique 1/2 valuation when AC is parallel. More formally this can be observed in the literal definitional derivative d/da of the area (a*(1-b)+b*(1-c)+c*(1-d)+d*(1-a))/2 in terms of their locations along their respective edges.
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