A trick to eliminate 2π (sometimes)

Re:A trick to eliminate 2π (sometimes) by jameshart on Wednesday June 28, 2023 @03:09PM (#36511109)

Seems like an odd choice when talking about the cross product, since the cross product is only a thing in 3D. You can define analogous things in other dimensions but it becomes clearer and clearer that it’s not meaningfully a ‘product’.

So it doesn’t matter if your visual intuition for a cross product breaks down in higher dimensions - a cross product is only a thing in three.

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Re:A trick to eliminate 2π (sometimes) by jacobolus on Wednesday June 28, 2023 @04:12PM (#36511916)

This is very off topic, but the wedge product absolutely is "meaningfully a product", generalizes fine to arbitrary dimension, and has a perfectly reasonable visual/spatial/geometric interpretation.

(Indeed, we should entirely scrap the cross product in undergraduate level technical instruction and replace it with the wedge product; one happy effect will be replacing students' misleading spatial intuitions with better ones.)

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Re:A trick to eliminate 2π (sometimes) by jameshart on Wednesday June 28, 2023 @05:08PM (#36512633)

Or bivectors, or k-vectors, or blades…

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Re:A trick to eliminate 2π (sometimes) by nilstycho on Wednesday June 28, 2023 @06:06PM (#36513306)

Good point; you're right. I might be misremembering the cross product. I do remember that he didn't even teach the geometric interpretation of vector addition.

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