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A beautiful related result is the Crofton Formula [0], which says that you can measure the length of any curve by appropriately counting the number of straight
by samsamoa 7y ago
A beautiful related result is the Crofton Formula [0], which says that you can measure the length of any curve by appropriately counting the number of straight lines that intersect it.
(My co-authors and I discovered a generalization of the formula that also holds in curved space [1].)
[0] https://en.wikipedia.org/wiki/Crofton_formula https://en.wikipedia.org/wiki/Crofton_formula
[1] https://arxiv.org/pdf/1505.05515.pdf https://arxiv.org/pdf/1505.05515.pdf
- sova 7y agoI'm especially intrigued by the "Timelike, Spacelike, and Lightlike" diagram on Page 10 of the linked paper where "lightlike" phenomena share an endpoint. Fascinating.
- srean 7y agoInteresting as the paper is, please link to the arxiv abstract rather than the pdf as that's more web friendly. Reader can always click on he pdf link there. https://arxiv.org/abs/1505.05515 https://arxiv.org/abs/1505.05515