#7. Are These Distances Euclidean?

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Link to Slides · Link to recording

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Prompts for discussion:

1. Confirm that the positive semidefinite criteria indeed turns out to be the familiar triangle inequality constraints when n = 2.

2. Can you explain the criteria of the theorem in geometric terms for higher dimensions?

Here’s the link to the Geogebra applet showing the triangle inequality, and here’s a slightly nicer one that lets you set the three distances and see the two circles come together or become disjoint depending on whether or not you violate one of the triangle inequalities.