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Consider a lit candle placed on a cylinder. If the candle is placed at the center of the top surface, let the distance from the origin (center of the surface) to the end of the shadow be $r$. In this case the area of the shadow can easily be calculated by the difference of 2 circular areas ie:- $\pi r^2-$ Area of cylinder's base.

Now suppose we shift the candle from the origin & place it at some point $(x,y)$ on the circular surface, how do we calculate the area of the shadow? The dimensions of the cylinder are known. The length of the candle at the particular instant is known.

Further, what is the equation the shape of the shadow?

Thanks in advance.

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    I think this may be interesting. http://www.math.utah.edu/~treiberg/Perspect/Perspect.htm2012-07-06
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    I think the shape of the shadow doesn't change at all, but I don't have the time to go through a proper working.2012-07-06
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    @BenMillwood I'm sure the shape changes but the area might be constant.2012-07-06
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    Why are you sure? It's possible I've misunderstood the question, but the mental picture I have in my head is just a cone of light with a shear (i.e. a linear transformation) applied.2012-07-06

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