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  "body": "\n## Summary\n\nA Busemann G-space is a [[metric space|0VKD1TP7F3]] in which shortest paths exist and extend a little past their ends in exactly one way.\nThese axioms, due to Herbert Busemann, capture the behaviour of [[geodesics|NSYMQMHPDN]] with no smoothness assumed.\nComplete [[Riemannian manifolds|7CBT4SM83Y]] and many [[Finsler manifolds|5R6QZ388BB]] are examples, so G-spaces give a common synthetic frame for their geometry.\n\n## Explanations\n\n### L1 human\n\nIn a G-space you can always walk from one point to another along a shortest route.\nYou can also keep walking straight a bit past the end, and there is only one way to do so.\nThe round sphere has this property: a great circle arc continues as a unique great circle.\nThe plane with the taxicab distance fails it, because a shortest route can be continued straight on or bent at a corner with the same length.\n",
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