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how far is a klick - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \((\pm 5, 0)\) gives 2 points: \((8, 4), (-2, 4)\)

📌 Total integer points: \(2 + 8 + 8 + 2 = 20\).

📌 Thus, the number of integer coordinate points on the circle is:

📌 \boxed{20}

📌 Question:** A biologist studying the genetic diversity of plants is analyzing a regular tetrahedron with vertices at \((0, 0, 0)\), \((1, 0, 0)\), \((0, 1, 0)\), and a fourth vertex \((x, y, z)\) where \(x, y, z\) are integers. Find the coordinates of the fourth vertex.

📌 A regular tetrahedron has equal edge lengths. The given vertices are \((0, 0, 0)\), \((1, 0, 0)\), \((0, 1, 0)\). The side length is 1.

📌 The distance from \((0, 0, 0)\) to \((x, y, z)\) is:

📌 \sqrt{x^2 + y^2 + z^2} = 1 \quad \Rightarrow \quad x^2 + y^2 + z^2 = 1

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