All the Ways of Defining e | Is Euler's Number Geometric? -- Part 1

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Part 2:    • What is algebra and geometry? | Is Eu...  

The full series on Euler's number:
Part 1:    • All the Ways of Defining e | Is Euler...  
Part 2:    • What is algebra and geometry? | Is Eu...  
Part 3:    • What are geometric numbers? | Is Eule...  
Part 4:    • Conservative Vector Fields and Euler'...  
Part 5:    • Is Euler's Number a Geometric Number?...  

Given any conversation between two mathematicians in which π is discussed, sooner or later, Euler’s number e comes up. In this video, we want to address the question of whether Euler’s number admits a geometric interpretation. That is, in the sense that π is geometric, is Euler’s number geometric?

Timestamps
0:00 Introductory Chit Chat
1:22 Reminder of Euler's number
6:44 Calculus definition of Euler's number
7:37 Integral definition of Euler's number
8:05 Summary and comparison of Euler definitions
8:55 Are these geometric characterisations?


This is part 1 of a short series of videos in which we address what makes a number geometric, and whether Euler's number is such a geometric number. The answer turns out to be surprisingly non-trivial, and such an elementary question turns out to be an active area of mathematical research.

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Hi, my name is Kyle and I'm currently doing my doctoral mathematics degree in complex differential geometry under the supervision of Professor Gang Tian and Professor Ben Andrews.