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I can still picture it: the rack of newspapers, magazines, and comic books; the ice-cream treats in the back corner; the long counter with stools, where I used to sit and spin until I was told to stop. It was about a mile-long walk, reserved for special occasions. On that bright fall morning, we strolled up Spring Street—a beautiful street lined with huge oak trees—and talked about fractions, though I wouldn’t have known to call them that. We were puzzling over—or, rather, I was puzzling over—how to fairly divide a pie (probably one of the Corner Confectionery’s apple pies).

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*Where do ideas come from? That’s a big question. Here’s a smaller one: Where do mathematical ideas come from? I’ve wondered about this from the time I first contemplated being a mathematician until long after I officially became one.*

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How do Eureka moments happen? They do feel contingent & magical, arising in consciousness on their own. But looking at the history of breakthrough ideas there seem to be a rough 2-phase process:

- An initial period of
**concentration**, study, tinkering aka “worrying” abou...

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Ideas come to us when we have a specific problem but we do not focus on solving the problem directly.

It’s not at all obvious how to go about thinking up some new twist on these things. A new idea can feel like a remarkable discovery

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There is a lot of math behind how the Golden Ratio is calculated. But designers, artists, and photographers aren’t usually high-level mathematicians. To benefit the algebraically disinclined, let’s keep it simple.

The Ratio is approximately **1.618 to 1**. It’s approximate bec...

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