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 Equal Maxes (Posted on 2007-06-12)
Find a shape for which the area of the largest inscribed triangle is equal to the area of the largest inscribed square.

No doubt there are an infinity of such shapes, but you must find one that can be expressed by a simple equation of order 2 or less, combined with constraints on the domain and range.

 See The Solution Submitted by Larry Rating: 3.0000 (1 votes)

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 Solution | Comment 3 of 6 |
`How about the interior of the unit circleintersected with the first quadrant. Thesquare has one vertex at the origin, sidesaligned with the x an y axes, and the opposite vertex on the circle. The triangleis an isosceles right triangle with the rightangle vertex at the origin, the legs alignedwith the x an y axes, and the other twovertices on the circle. The area of the squareand the triangle is 1/2.`
` `

 Posted by Bractals on 2007-06-12 13:19:27

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