An Interesting contstant showed up one day.

The area of a circle of radius one can be computed with an integral. Similarly, the volume of a three dimensional sphere of radius one can be found with a double

integral. It is well known that one can generalize the concept of a sphere volume (and a circle area) into a higher or lower number of spatial dimensions. These

hypothetical objects are called n-balls. The “n” represents the number of dimensions. For, example a four dimensional sphere of radius one has a


I used Mathematica to evaluate the infinite sum of the volume of all even numbered n-balls of radius one (starting at n equals zero) and got a very fun answer.


The above answer is kind of hard to read. It is supposed to be "e to the pi".

If anyone wants to know the details just comment or email me.


Patrick R.

Twenty Five Years Experience Math and Physics Tutoring

10+ hours
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