The AM-GM Inequality (also: rectangles, discriminants, identities, blenders and thermodynamics)
Автор: Way Tan
Загружено: 2025-08-15
Просмотров: 491
Описание:
For a new topical series, here's another (almost) unscripted introduction to AM-GM. We want to understand that:
0) We use AM-GM, not solve it
1) It conforms to our existing intuition
2) For 2/3 variables, it is consistent with the algebra that we know
3) It minimises a sum given a fixed product, or maximises a product given a fixed sum
4) It tells you when the optimum happens - or if it can't happen at all!
5) It can be made more flexible by 'weighting' the terms going into AM-GM
6) It gives high-level intuition that less 'mixed-up' algebraic expressions are larger than more mixed-up ones.
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