Next message: Jeff Bole: "Re: lv-ab: Question"
Wow, its a bunch of years since I did this stuff, like 50!
This may not be the simplest solution and I could have an error but this is
what I came up with.
Assume the length of the straight line is x
Assume the height of the curve in the middle is y.
Since I can't show superscripts here, squared is shown as ^2
I get the radius of the circle as r = (x^2 + 4*y^2)/8*y
So the total circumfrence is (pi*x^2 + 4*pi*y^2)/4*y
The angle between sides of the whole pizza slice is ArcSin(x/r)
= ArcSin{(4*x*y)/(x^2 + 4*y^2)}
So the length of the arc is angle/360 * circumfrence
= ArcSin{(4*x*y)/(x^2 + 4*y^2)} * (pi*x^2 + 4*pi*y^2)/1440*y
Plug some actual numbers in and see if it comes close. If its wrong it will
be radically wrong.
Colin Foster,
I have a geometry problem.
Imagine two horizontal lines, one straight and one curved, a few inches
long, sorta parallel with the ends of each line touching the other. Like
you sliced a piece of the crust of a pizza off and the sliced-off piece is
lying on the table.
I know the length of the straight line that the knife cut, and I know the
distance apart the lines are in the middle of the sliced off pizza crust,
how do I find the length of the curved line?
Norm
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