I'm currently studying to be a maths teacher and i have to present the answer to this problem in two days to other student teachers:
manufacturer who makes replica norman windows. A norman window can be modelled as a rectangle surmounted by a semicircle. The length of framing for the heavy outside of th window is limited to 12m.
a) Find the dimensions of the window so that the maximum amount of light will be allowed into the building that has the window fitted.
b) The window maker did not use the optimum design. Why not?
So there are a couple of ways i'm solving it, algebraically and graphically. My problem is that i don't have decent software (besides excel) to get some decent graphs going on.
Would anyone please find it in their hearts to send me a couple of jpeg's of some graphs.
the two graphs i'm looking for are
Area = 12x - 2x^2 - (PI/2)x^2
A' = 12 - 4x - PIx
those two graphs would be great.
Also, if anyone has any interesting insights into problems like this, or even this one in particular, i'd love to hear it. It ends up being the optimum height of the rectangle is half the base of the rectangle, which i thought was interesting, but i can't explain why that is instinctively.
Thanks so much for your time