This is quite mesmerizing ...
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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...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.
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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.
circles
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@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.
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@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.
@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.
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@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.
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@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.
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.
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@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.
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@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.
@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
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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.
circles
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Desmos (www.desmos.com)
@futurebird Fascinating! 🤩 Here's a slowed down version of the interesting part. It's jumpy, which indirectly shows the speed up in the middle: more distance drawn between frames. Of course, the hand has to start and end with zero speed, but it's not clear to me how close to perfect sinusoidal one needs to be to get the appearance of a circle. Probably getting the speed profile symmetric is already quite a challenge? Would love to try this! @lienrag
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@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
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.
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@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.
The orange line is linear in time (steps of angle), and the green line is plotted with just the radial component of the orange line.
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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.
circles
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Desmos (www.desmos.com)
@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.
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