Chapter 1: Using dimensional analysis to quickly pull correct-ish equations out of thin air!
Chapter 2: Focusing on easy cases. It’s amazing how many problems become simpler when you set some variables equal to 1, 0, or ∞.
Chapter 3: An awful lot of things look like rectangles if you squint at them hard enough. Rectangles are nice.
Chapter 4: Drawing pictures can help. Humans are good at looking at shapes.
Chapter 5: Approximate arithmetic in which all numbers are either 1, a power of 10, or “a few”—roughly 3, which is close to the geometric mean of 1 and 10. A few times a few is ten, for small values of “is”. Multiply and divide large numbers on your fingers!
… And there’s some more stuff, too, and some more chapters, but that’ll do for an approximate summary.
There’s a free book on this sort of thing, under a Creative Commons license, called Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving. Among the fun things in it:
Chapter 1: Using dimensional analysis to quickly pull correct-ish equations out of thin air!
Chapter 2: Focusing on easy cases. It’s amazing how many problems become simpler when you set some variables equal to 1, 0, or ∞.
Chapter 3: An awful lot of things look like rectangles if you squint at them hard enough. Rectangles are nice.
Chapter 4: Drawing pictures can help. Humans are good at looking at shapes.
Chapter 5: Approximate arithmetic in which all numbers are either 1, a power of 10, or “a few”—roughly 3, which is close to the geometric mean of 1 and 10. A few times a few is ten, for small values of “is”. Multiply and divide large numbers on your fingers!
… And there’s some more stuff, too, and some more chapters, but that’ll do for an approximate summary.