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teaching:topics:number:euler_number [2020/09/13 18:50] simon |
teaching:topics:number:euler_number [2020/12/17 12:01] (current) simon |
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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: **=>[[limits#limits]]** | + | This notation, and some ideas around these infinite series, are discussed here: **=>[[teaching:topics:calculus:limits#limits]]** |
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+ | [[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 | ||