Talk:Largest Rectangle Contained in Triangle

In its current form, this page does not fully answer Dudeney's Puzzle 132.

There needs to be an argument shown that if the rectangle is simply contained, not inscribed, in the triangle, its area still cannot exceed half the area of the triangle.


 * That was sort of what I was trying to say in the first part of the question. --prime mover (talk) 06:47, 15 February 2022 (UTC)


 * I believe I have finished everything I outlined. All that remains is to rename the page (and add a book page for the reference book of Niven's, perhaps)
 * --RandomUndergrad (talk) 12:19, 15 February 2022 (UTC)
 * Good job well done.
 * For books we don't cite pages, in case a subsequent printing has a different pagination, thereby rendering the citation inaccurate. --prime mover (talk) 18:13, 15 February 2022 (UTC)

This blog post, citing I. Niven, Maxima and Minima without Calculus (p. 58-61), does this by dividing the triangle into two parts with a line parallel to some side of the contained parallelogram.

I suggest creating a new page "Largest Parallelogram Contained in Triangle", moving the bulk of this proof there.

Then for this page, show that the midpoint method can create a rectangle half the area of the triangle, and link the new page to show the area is maximized.

--RandomUndergrad (talk) 03:52, 15 February 2022 (UTC)