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\[ \lim_{n \to \infty} n \left( \frac{1}{1^2 + n^2} + \frac{1}{2^2 + n^2} + \ldots + \frac{1}{n^2 + n^2} \right) =?\]

Consider rotating a unit cube about the axis passing through two opposing vertices.

What is the volume of the revolution solid?

If the answer can be expressed as ...

Hint: Each digit is ...

The dartboard in the diagram consists of an infinite number of concentric circles. Each successively smaller circle has half the radius of the preceding, larger circle. The colors of the ...

Solve the following diophantine equation: \[y^2 + 2 = x^3\]

Let \(A\) be the set \(A = \{(x,y) \in \mathbb{Z}^2 \text{ / } y^2 + 2 = x^3\}\) which is ...

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