Post B1uJSvLreMEXilqTdA by oschonrock@mastodon.social
(DIR) More posts by oschonrock@mastodon.social
(DIR) Post #B1sJsvWJG1kzSND6H2 by futurebird@sauropods.win
2026-01-02T13:02:12Z
0 likes, 1 repeats
@lienrag I don't know about the younger kids, but ever since I saw this I have been thinking about the second circle they draw. It's driving me nuts. How do they draw a circle off center?It looks like they simply move the pen in a line. I think you must move it at a speed that would vary like a sinusoidal curve.They do it *so* quickly and nothing else in the video is nearly as interesting as that moment. https://www.desmos.com/calculator/if9r9uirtl
(DIR) Post #B1sKdT8KcHO51kBhZo by lienrag@mastodon.tedomum.net
2026-01-02T13:04:52Z
0 likes, 0 repeats
@futurebird I mean, it's obviously mesmerizing, so kids would absolutely be interested by it.And they would absolutely love to learn how to do it themselves.Which is certainly a good way to teach them some fundamental mathematical principles.I just don't know which nor how...
(DIR) Post #B1sKdU4T87tLw3O8C8 by futurebird@sauropods.win
2026-01-02T13:10:42Z
0 likes, 0 repeats
@lienrag Well one is that a circle is set of points a fixed distance from a center. And a spiral is when you change the radius as you draw it.
(DIR) Post #B1sKk68uUf3jkYcT2W by veronica@mastodon.online
2026-01-02T13:11:52Z
0 likes, 0 repeats
@futurebird @lienrag Yeah, that's the big "what" moment for me as well. I think all you need is to draw a straight line through the centre, but it would have to be timed with the rotation speed. Otherwise you'd end up with a spiral.
(DIR) Post #B1sL3wl360PYR1vIFk by veronica@mastodon.online
2026-01-02T13:14:09Z
0 likes, 0 repeats
@futurebird @lienrag Ok, it's definitely off-centre, looking at the looped video. But the offset to the centre seems to determine the radius of the inner circle.
(DIR) Post #B1sL3xql2GZVp1bMn2 by futurebird@sauropods.win
2026-01-02T13:15:29Z
0 likes, 0 repeats
@veronica @lienrag "But the offset to the centre seems to determine the radius of the inner circle."Do you mean the whole thing is centered on the small circle? I thought the whole thing was centered on the large circle... the small one is an anomaly.
(DIR) Post #B1sLBn8EljjStgVfs0 by futurebird@sauropods.win
2026-01-02T13:16:55Z
0 likes, 0 repeats
@veronica @lienrag Moving the pen at a constant speed won't work I think? I feel like I'm missing something obvious. I have a clay wheel I'm going to bring it out. Hold. on.
(DIR) Post #B1sLF9xUMAJoYs5XdI by veronica@mastodon.online
2026-01-02T13:17:29Z
0 likes, 0 repeats
@futurebird @lienrag What I mean is that the straight line doesn't go through the centre, it goes slightly above it from the perspective of the camera, and it seems to determine the "highest" point of the inner circle relative to the inner edge of bigger one. If that made sense 😅
(DIR) Post #B1sLLYVXzmrIRB4KhM by lienrag@mastodon.tedomum.net
2026-01-02T13:18:34Z
0 likes, 0 repeats
@futurebird I was quite confident that I could nerdsnipe you here.Hope some wonderful math lesson (that you'll put under some copyleft license) comes out of it !@veronica
(DIR) Post #B1sLPjJnkCM97kZ6qe by veronica@mastodon.online
2026-01-02T13:19:24Z
0 likes, 0 repeats
@futurebird @lienrag Yeah, this calls for an experiment. I don't have anything I can test on.When I was a kid, my grandma gave me her old record player, and I did play around with drawing patterns on paper I sticky-taped to it, but nothing like this.(It was great though, because it had 16, 33, 45 and 78 speed.)
(DIR) Post #B1sMAhI36RDKRa8pP6 by ptmesis@writing.exchange
2026-01-02T13:27:52Z
0 likes, 0 repeats
@futurebird @veronica @lienrag I think if you move it at constant speed across the middle (with a speed of 2r per revolution time) you get a cardioid.
(DIR) Post #B1sMELSUDLqdtOlM36 by veronica@mastodon.online
2026-01-02T13:28:33Z
0 likes, 0 repeats
@futurebird @lienrag Thinking about it, I think constant speed is the key. This is a radial/rotating coordinate system after all, and all they're doing is creating a constant motion in r. The cosine/sine comes into play when working in a Cartesian coordinate system.
(DIR) Post #B1sNpwIOJjqkoGWz7Q by veronica@mastodon.online
2026-01-02T13:30:37Z
0 likes, 1 repeats
@ptmesis @futurebird @lienrag I think it would be a cardioid if r was outside the first circle, but again, not sure.Radial geometry always messes with my head 😅
(DIR) Post #B1sNvTcRqghLbnYLVA by futurebird@sauropods.win
2026-01-02T13:47:35Z
0 likes, 0 repeats
@veronica @ptmesis @lienrag I think you may be right about the cardioid it seems the easiest thing to make from playing around just a bit with it. Also it's easier if it's moving faster. I wish I had a motor.
(DIR) Post #B1sO5kDJ0Q53yHglFY by futurebird@sauropods.win
2026-01-02T13:49:26Z
0 likes, 1 repeats
@veronica @ptmesis @lienrag Ok that was the wrong video hold on.
(DIR) Post #B1sOFHQsrr6VbXaRxw by futurebird@sauropods.win
2026-01-02T13:51:09Z
0 likes, 0 repeats
@veronica @ptmesis @lienrag Working slowly makes the errors causes by moving the pen worse. Speed is your friend for this. The wheel in the video must have a motor or she's kicking it. My wheel is just for hand building and won't spin for long at all.
(DIR) Post #B1sQ6G54iwaOiLDCE4 by log@mastodon.sdf.org
2026-01-02T14:11:54Z
0 likes, 0 repeats
@futurebird @lienrag As with most magic tricks, watch the other hand. Is it affecting the speed of the paper's rotation?
(DIR) Post #B1sT5aQzrdHJPdpwbg by veronica@mastodon.online
2026-01-02T14:45:22Z
0 likes, 0 repeats
@futurebird @ptmesis @lienrag I just plotted it, and as far as I can figure out, if you stay inside the radius of the outer circle, the "cardioid" is a drop-shape, but if you move the pen a little slower at the start and end, it should be pretty circular. I think this would be a pretty natural consequence of drawing on paper given the friction.
(DIR) Post #B1sTKdgs2ZLdr3RINk by veronica@mastodon.online
2026-01-02T14:48:03Z
0 likes, 1 repeats
@futurebird @ptmesis @lienrag I just plotted it, and as far as I can figure out, if you stay inside the radius of the outer circle, the "cardioid" is a drop-shape, but if you move the pen a little slower at the start and end, it should be pretty circular. I think this would be a natural consequence of drawing on paper given the friction between pen and paper.
(DIR) Post #B1sTaAXcBV8s5DW09Y by quizzicus@mastodon.online
2026-01-02T14:50:56Z
0 likes, 0 repeats
@futurebird @lienrag An intuitive demonstration of cartesian to polar mapping!
(DIR) Post #B1sYZ03CCcDT1oY59E by AlexaFontanilla2024@mastodon.social
2026-01-02T15:44:15Z
0 likes, 0 repeats
@futurebird #PostOfTheWeek (season 3):Ways to draw the circle off center:
(DIR) Post #B1sZEqgDQsjo80ks6a by llewelly@sauropods.win
2026-01-02T15:28:37Z
0 likes, 0 repeats
@futurebird @lienrag when I play it at half speed, it does look like there's some variation in the velocity of the marker. Not sure what kind of variation, but it might be sinusoidal , which is what would make sense to me as well.
(DIR) Post #B1sa39wM65u4LHIImu by stilescrisis@mastodon.gamedev.place
2026-01-02T16:03:23Z
0 likes, 0 repeats
@futurebird @veronica @ptmesis @lienrag If I were at home I think this is something I could try in an HTML canvas trivially. Just plot a point and rotate in a loop
(DIR) Post #B1sqybIidrHCyNAOQq by twipped@twipped.social
2026-01-02T19:13:01Z
0 likes, 0 repeats
@futurebird @lienrag
(DIR) Post #B1uJSvLreMEXilqTdA by oschonrock@mastodon.social
2026-01-03T12:06:59Z
0 likes, 0 repeats
@futurebird @lienrag It is a constant linear speed in the observers reference frame. And your desmos supports that. Because the r= sin (theta) is exactly that, because (theta) is increasing linearly with time, because you are using it like that to draw the outer circle. so t proportional to thetaand thereforer(small_circle) proportional to time. and r(small circle) is the position of the pen?Video shows the pen running a long a line offset from centre of big circle = similar.