Planting Trees 1
You are a landscape gardener working on a project for a mathematics professor. She has an unusual request: she wants you to plant four trees in her garden such that each tree is exactly the same distance from every other tree.
How can you arrange the four trees to satisfy this requirement?
Solution
Place the four trees at the vertices of a regular tetrahedron.
If we restrict ourselves to placing trees on a flat surface, we cannot arrange four points such that each is equidistant from all others. Three points can form an equilateral triangle where each point is the same distance from the other two, but adding a fourth point on the same plane cannot maintain equal distances to all three existing points.
Thankfully, reality is 3-dimensional. We can place a mound in the middle of this triangle and plant the 4th tree on top of it. At the right height, it will form a regular tetrahedron, and all 4 trees will be equidistant from each other.
Next puzzle in this series
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