It’s Time to Reexamine Euclid’s Definition of a Point

In the delightful and informative Veritasium video <a href="https://youtu.be/lFlu60qs7_4?t=18m58s" rel="noopener ugc nofollow" target="_blank">How One Line in the Oldest Math Text Hinted at Hidden Universes</a>, physicists Alex Kontorovich and Derek Muller discuss how the mathematics of General Relativity emerged from careful examination of Euclid’s millennia-old Fifth Postulate about parallel lines never intersecting. The far-ranging discussion also addressed the twenty-three Definitions that preceded Euclid’s five Postulates: <a href="https://youtu.be/lFlu60qs7_4?t=17m26s" rel="noopener ugc nofollow" target="_blank">17:26</a> AK: “[Euclid’s] Definition 1: ‘A point is that which has no part.’ What does it mean to have a part? What is a part? What does it mean not to have a part?” <a href="https://youtu.be/lFlu60qs7_4?t=18m58s" rel="noopener ugc nofollow" target="_blank">18:58</a> DM: “You can think of geometry as a game. The first four postulates, [which in turn are based on 23 definitions,] are like the minimum rules required to play.” <a href="https://medium.com/@terrybollinger/its-time-to-reexamine-euclid-s-definition-of-a-point-9024cfe5f446">Visit Now</a>