Mark Equidistant Points on a Spiral

This story sounds totally implausible, so I'm going to give it in exact details (while leaving out the name of the second party, until they want to confirm it from their point of view)

I had a dinner date with my wife's parents. I was running ahead of schedule and I stopped at House of Shields, hoping to find a barstool where I could sit and read. 5:30. No stools. No booths. Standing room only. On to the next spot, Novella. Despite the full bar, I ordered a drink and leaned against a pillar to read. After ten minutes or so I asked a woman if the second seat at her table was taken. I slowly, silently pick through A Burglar's Guide to the City for the next half hour or so. She closes her tab and I thank her for letting me sit at her table.

She says "Oh sure, Actually there's something I've been wanting to ask you. How's your math?"

Curious question.

That could mean everything from "I just wanted somebody to check if this was an appropriate tip" (sure thing) to "Could you verify this work on braid theory" (I can't).

I think I tried to give a shrug and a nod, as if to suggest "Well, I'm no Euler, and I never learned arithmetic, but my trig is pretty on-pointe"

Close enough. She asks "How about calc?". I think I furrowed my brow, grimmaced, wiggled my left hand side to side, shook my head "no" and said "Iffy, what do you need?". I know enough calc to convince a computer to tell me what I want, not enough to do it on pencil and paper after a manhattan.

"I do data visualizations. I want to mark points equidistant from each other along a spiral. I found one answer, but I've forgotten most of my calc and I'm stuck on the integral". I scratched some notes, we chatted for a bit. I was also stuck on the integral. I don't think I've done anything in polar coordinates since High School but enough of what Mr Hohman said was still stuck in the cobwebs to make some sketches before I had to run to dinner.

I asked what she was visualizing. I won't spoil it here because it sounds pretty neat, and that part isn't my story to tell.

I had to bail, which was excellent timing, because I needed some time to work through the problem, and I got to save a bit of face. I start tripping over my words a bit on the way out.

"I'm going to... uh... Hi, I'm a strange man at a bar, I'm going to give you my email address because I'm not going to stop thinking about this until I figure it out, this isn't me making a pass at you". I gestured at my wedding band. I might be slightly-too-frank with people sometimes.

We traded emails. It was a good story to tell over dinner. I like San Francisco when strangers at the swanky lounge ask me about algebra. I say algebra because I could only solve it with algebra, I brute-forced the calc.

I poked around at it a bit after dinner, it was too late to do anything useful with my brain but I emailed my new math friend and got the useful links.

When I got up this morning I started poking around at some Javascript. I came up with my answer.

If you want to figure out your own answer to this, now is a great time to stop reading.

Here's my main trick: When you're drawing the spiral, you need to generate every X and Y point on the spiral. If you keep track of the last point you can track the distance between each point. If you sum the distances, and put a marker every time the sum reaches a certain point, you're set.

Here's my code

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After a few more emails, it turns out that she doesn't actually want equidistant points, she wants to know where to put the point given a distance. I still brute-forced that, but there's an updated gist which reflects marks at specific distances along the spiral.

20th January 2017