rotation geometry rules counterclockwise

#Rotation geometry rules counterclockwise how to#
#Rotation geometry rules counterclockwise full#

If you're confused by my bad drawing skills, we start measuring the first angle from the black line, not the grey line.

For example (assuming the red point is your original position, and the black point is where you end up):

#Rotation geometry rules counterclockwise full#

It's okay if you end up making more than a full 360° rotation, just keep on going around the circle until you've doubled the initial angle.I would apologize for my terrible MS Paint skills, but I'm not sorry at all. Rotate yourself counterclockwise by that same angle, maintaining your distance from the center, like so:.Yes, I may have used Microsoft Paint on the previous image for this one because I didn't want to bother coding.what of it? Find the orienting line we drew on the floor earlier, and measure, counterclockwise, the angle between it and your new imaginary line.Imagine a line connecting your current position to the center of the circle:.Remember this position-or jot it down on a notepad if your memory is bad-for later. Choose a starting point anywhere you want in the room.Note that drawing on the floor is totally optional if you can keep this all in your head, good for you. It should look something like this:Ī bird's-eye view of a dance hall, all decked out for a Mandelbrot Waltz. Now, draw a circle around the room's center, such that it intersects the 'orienting line' halfway through.This line is to help orient the dancers, so we'll refer to it as the 'orienting line' moving forward.

Setup: Draw a line from the center of the room to the nearest part of the wall, like so:.

You will need: Yourself, an empty room, and a drawing tool (like chalk or tape).

#Rotation geometry rules counterclockwise how to#

How To Perform The Mandelbrot Waltz: A Step-By-Step Guide In case you don't already know the moves, I'll describe how to do the dance yourself (if given an arbitrary starting point on the dance floor) step-by-step. You will unfortunately be cursed to dance forever (there's always a catch to these dance invitations!), but if you ever touch the edges of the dance floor, the curse will be lifted and your part in the dance ends, so it's really not all that bad. This dance follows very simple rules, with the quirk that your starting location will influence your part in the dance. I call this dance the Mandelbrot Waltz, but you can call it whatever you'd like. Since we're (presumably) both cool, hip people, let's go with a somewhat avant-garde dance that's popular with the kids these days. My goal is for this post to (theoretically) be acceptable to the historical René Descartes, who coined the term 'Imaginary number' because he did not believe such things could possibly exist. Instead of helping you understand the relevant math like a reasonable person would, I'm just going to pretend the concept doesn't exist, and try to explain how to generate the Mandelbrot set anyway. the square root of negative one) a bit mystifying and counterintuitive. Note: This post assumes you've heard of the Mandelbrot set before, and you want to know more about it, but that you find imaginary and complex numbers (e.g.