teaching:topics:number:euler_number
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
teaching:topics:number:euler_number [2020/09/12 13:04] simon |
teaching:topics:number:euler_number [2020/12/17 12:01] (current) simon |
||
|---|---|---|---|
| Line 11: | Line 11: | ||
| \[\large{\rm e}^x=\sum_{n=0}^\infty\frac{x^n}{n!}\] | \[\large{\rm e}^x=\sum_{n=0}^\infty\frac{x^n}{n!}\] | ||
| Which, using the properties of \(\rm i\) along with the power series for `cos x` and `sin x`, gave the formula named after him. There are other approaches to that formula, and this combination of different ways to get there shows how deeply it crosses many areas of mathematics --- bringing algebra, trigonometry, geometry and number together when we embrace complex numbers as our underlying set of numbers. | Which, using the properties of \(\rm i\) along with the power series for `cos x` and `sin x`, gave the formula named after him. There are other approaches to that formula, and this combination of different ways to get there shows how deeply it crosses many areas of mathematics --- bringing algebra, trigonometry, geometry and number together when we embrace complex numbers as our underlying set of numbers. | ||
| + | |||
| + | This notation, and some ideas around these infinite series, are discussed here: **=>[[teaching:topics:calculus:limits#limits]]** | ||
| + | |||
| + | [[https://m.youtube.com/watch?v=-dhHrg-KbJ0|the mathologer]] talks of this using examples and patterns first, then [[https://m.youtube.com/watch?v=DoAbA6rXrwA|extends]] this | ||
teaching/topics/number/euler_number.1599879884.txt.gz · Last modified: 2020/09/12 13:04 by simon
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported
