Formula for Area of Overlapping Rings?

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Could anyone direct me to a formula for the area enclosed by two overlapping rings? Sketch below...

area.jpg


Thanks...
-jg
 
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I realize my question was a little bit ambiguous... specifically, the area in terms of the radius of the two circles and the distance between their centers. The rings are identical.

Sorry about that.
-jg
 
Also, looking at your attachment appears to require a password.
 
OK, should be fixed now. Sorry, once again.
-jg
 

Thread 'Injective immersion and embedding'

Hello! There is a simple line in the textbook. If ##S## is a manifold, an injectively immersed submanifold ##M## of ##S## is embedded if and only if ##M## is locally closed in ##S##. Recall the definition. M is locally closed if for each point ##x\in M## there open ##U\subset S## such that ##M\cap U## is closed in ##U##. Embedding to injective immesion is simple. The opposite direction is hard. Suppose I have ##N## as source manifold and ##f:N\rightarrow S## is the injective...
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