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A Norman Window

Date: 16 Jan 1995 14:42:05 -0500
From: Jon Tienhaara
Subject: calc quest.

        Dr. Math:

        My calculus teacher wanted me to give you this problem to see how 
you would do it.  He says there are many ways:

        A Norman window is a window in the shape of a rectangle with a 
semicircle attached to the top.  Assuming that the perimeter of the 
window is 12 feet, find the dimensions that allow the maximum amount of 
light to enter.

Thank you!

Date: 17 Jan 1995 00:52:18 GMT 
From: Dr. Math
Subject: Re: calc quest.

Hello there!

Well, probably the reason your _calculus_ teacher gave you this question
is that it's a question that's ideally suited for calculus.  So what I
would do is first assign some variable r to the radius of the semicircular
portion of the window.  Then I would find an expression for the area of
the window as a function of r.  Then, as in most max/min problems, I'd
take the derivative with respect to r of this function, set it equal to
zero, and figure out what that gives me for r.  Then, of course, you
really have to figure out whether what you've found really is a maximum
value, perhaps using the second derivative test.

Anyway, give this a shot, and write back if you have difficulty.

-Ken "Dr." Math
Associated Topics:
High School Calculus

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