Cyclic Lattice Points
For any positive integer \(N \geq 2\), let \(D(N)\) denote the diameter of the smallest circle which passes through exactly \(N\) different lattice points. For example:
- \(D(2) = 1.0\)
- \(D(3) = \frac{5}{3}\sqrt{2} = 2.3570226039551585\ldots\)
- \(D(4) = \sqrt{2} = 1.4142135623730951\ldots\)
| Part A | What are the first \(6\) digits of \(D(8)\) after the decimal point? | |
|---|---|---|
| Part B | What are the first \(6\) digits of \(D(5)\) after the decimal point? |