Results 1 to 7 of 7
Thread: Circles, waves and triangles.
-
2023-01-04, 06:49 AM (ISO 8601)
- Join Date
- Jun 2013
- Location
- Bristol, UK
Circles, waves and triangles.
I was trying to get to sleep.
So, if a circle rotates at the same speed as a sheet of paper (or whatever, so long as it can be drawn on), is passing it, and a marker marks the surface (the speed of rotation of the circle being such that when the marker is moving exactly in the direction of the paper, the speed of the marker is static with respect to the paper), what is the line that is drawn called?
It's not a sine wave, because in that the marker doesn't move forward or back with respect to the world the paper is passing through. It's not a series of semi-circles, because the angle of the line reaches 45 degrees at the middle height, which isn't true of a semi-corcle.The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.
-
2023-01-04, 07:32 AM (ISO 8601)
- Join Date
- Jan 2007
Re: Circles, waves and triangles.
Not sure if this shape has a specific name or can be described with a simple function aside from a parametric curve like (here skipping a few adjustable parameters for simplicity)
x = cos(t) + t
y = -sin(t)
Update before I actually posted: I did some search and the shape is called a cycloid. There are some proper equations for the shape given in the link along with some other properties.In a war it doesn't matter who's right, only who's left.
-
2023-01-04, 07:52 AM (ISO 8601)
- Join Date
- Jun 2013
- Location
- Bristol, UK
-
2023-01-04, 10:09 AM (ISO 8601)
- Join Date
- Dec 2015
-
2023-01-05, 05:52 AM (ISO 8601)
- Join Date
- Jan 2007
-
2023-01-05, 10:00 PM (ISO 8601)
- Join Date
- Nov 2006
- Location
- Watching the world go by
- Gender
Re: Circles, waves and triangles.
It is the shape a point on a wheel makes as the wheel rolls. When I put that in a search engine the Wikipedia page for "cycloid" shows up.
Now I am not sure I would have leapt to that without seeing "cycloid", so thanks to Radar.
One of the interesting things about cycloids is that ropes naturally form them when allowed to hang from their ends.
-
2023-01-06, 08:15 PM (ISO 8601)
- Join Date
- Jun 2013
- Location
- Bristol, UK
Re: Circles, waves and triangles.
Last edited by halfeye; 2023-01-06 at 08:18 PM.
The end of what Son? The story? There is no end. There's just the point where the storytellers stop talking.