# Straight line is the shortest of curves, who proved?

I am curious, when and by whom it was proved that straight line is the shortest of measurable curves connecting two given points.

• To me this sounds more like a basic assumption than something that had to be proved. – aventurin Jul 21 '16 at 17:31
• There is no way to answer this because it depends on what set of axioms and definitions you use. It could be a definition, or it could be something you prove. – Ben Crowell Jul 21 '16 at 19:19
• As pointed out in the above comment by Ben Crowell, it's important to state what kind of framework you're expecting. Modern axioms? Ancient Greece-style mathematics? – Danu Jul 21 '16 at 21:51
• Say curves in $\mathbb{R}^n$ for natural $n$, as defined in modern math – porton Jul 21 '16 at 22:37
• @porton: "as defined in modern math" doesn't mean anything. – Ben Crowell Jul 26 '16 at 16:55