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From: David Vrona (no email)
Date: Sun Mar 02 2003 - 23:13:51 EST
I've outlined two methods for calculating it. The second method is
probably what you want.
(1)
Assuming you know the radius....
You want to determine the angle of the "pizza slice" as if you cut a
traditional wedge in the pizza which coincides with the slice as you
described. Does that make any sense?
Once you have that angle, the partial circumference you are are looking for
is the ratio of the angle to be determined over 360 degrees.
pC = 2 Pi r ( angle / 360 )
Now, the angle is:
angle = 2 ( 90 - cos(-1) (1/2 L / r) )
L is the lenth of the straight cut you mentioned (this would be called the
chord of the segment you cut)
r is the radius of the pizza (assuming you know r)
Would someone double check this?
(2)
So, for not knowing the radius. You know the chord length and the height.
The answer is:
r = (c2+4h2)/(8h),
theta = 2 arcsin(c/[2r]),
s = r theta
c = chord length
h = height at the midpoint
s = the arc length you want
Theta is an angle you calculate in radians. That's the angle subtending
the arc.
I did not go to the trouble of figuring out this second formula. Instead,
I took the easy way out and found it at the following web site:
http://mathforum.org/dr.math/faq/faq.circle.segment.html#8
Dave
--On Sunday, March 02, 2003 10:01 PM -0500 ""
<> wrote:
>
>
> 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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