Infinitely Many Touching Circles - Numberphile
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Date: 2022-04-09
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Comments and reviews: 9
sur-taka
technically what he is doing is not sphere inversion. with sphere inversion the original point and the image are on a straight line through the center of the circle. in his construction they are on two different lines, which are orthogonal to each other (corresponding to the different sides of the rectangle. so its a sphere inversion, combined with a rotation. however, a rotation is just the composition of two reflections, which are sphere inversions on a sphere with infinite radius (i. e a straight line.
so it is in fact the composition of multiple sphere inversions, thus the properties are preserved.
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technically what he is doing is not sphere inversion. with sphere inversion the original point and the image are on a straight line through the center of the circle. in his construction they are on two different lines, which are orthogonal to each other (corresponding to the different sides of the rectangle. so its a sphere inversion, combined with a rotation. however, a rotation is just the composition of two reflections, which are sphere inversions on a sphere with infinite radius (i. e a straight line.
so it is in fact the composition of multiple sphere inversions, thus the properties are preserved.
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MrVipitis
I love the beauty of those visualization.
Perhaps one could use all of their code to training a neural network that does text generation. And see what comes up. The dataset is probably way to small - and even larger datasets probably don't do enough for current methods.
I am trying the same with webGL shaders from Shadertoy and that has 22k shaders, which might not be enough either.
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I love the beauty of those visualization.
Perhaps one could use all of their code to training a neural network that does text generation. And see what comes up. The dataset is probably way to small - and even larger datasets probably don't do enough for current methods.
I am trying the same with webGL shaders from Shadertoy and that has 22k shaders, which might not be enough either.
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Caleigh
The circle and it's eversion/inversion is a perfect model for the structure of our manifold. Circle is event horizon. Inside the circle is antimatter universe, our inversion. And we are the infinite plain outside the circle. The numeric field of outside is like gravity and the inside with intense negative pressure in center is similar to proton density imaging.
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The circle and it's eversion/inversion is a perfect model for the structure of our manifold. Circle is event horizon. Inside the circle is antimatter universe, our inversion. And we are the infinite plain outside the circle. The numeric field of outside is like gravity and the inside with intense negative pressure in center is similar to proton density imaging.
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Jonathan
There are 4 corners to the rectangle. One corner is fixed; one corner is drawing circles above the line; and one corner is drawing circles in the circle below the line. Is the 4th corner doing anything meaningful or artistic?
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There are 4 corners to the rectangle. One corner is fixed; one corner is drawing circles above the line; and one corner is drawing circles in the circle below the line. Is the 4th corner doing anything meaningful or artistic?
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Stephen
I was actually thinking that rectangle drawing points inside a circle using points outside the circle reminded me of Ptolemy's theorem and circle inversion, glad to know my instincts were onto something.
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I was actually thinking that rectangle drawing points inside a circle using points outside the circle reminded me of Ptolemy's theorem and circle inversion, glad to know my instincts were onto something.
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chickenmonger123
In the many circles, what happens if you start mapping another one of the infinitely many circle (sets, inside one of the circles that corresponds to the original mapped infinite circle (set.
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In the many circles, what happens if you start mapping another one of the infinitely many circle (sets, inside one of the circles that corresponds to the original mapped infinite circle (set.
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Certainly
When I saw this line drawing a circle, my brain immediately shouted -PTOLEMY'S THEOREM! - with Prof. Stankova's voice. Oh, that one, it's still my favorite video I've watched in my whole life!
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When I saw this line drawing a circle, my brain immediately shouted -PTOLEMY'S THEOREM! - with Prof. Stankova's voice. Oh, that one, it's still my favorite video I've watched in my whole life!
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Plads
I don't understand why there is a hole to the right of the circle. Doesn't this region gets mapped too when r is really big and the x component is relatively small compared to the y component?
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I don't understand why there is a hole to the right of the circle. Doesn't this region gets mapped too when r is really big and the x component is relatively small compared to the y component?
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Not
The pattern when rotated 90 of the touching circles reminds me of a spiders eyes. Not quites but it is the closest thing i can think of and these panthers usually have a resemblance in nature
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The pattern when rotated 90 of the touching circles reminds me of a spiders eyes. Not quites but it is the closest thing i can think of and these panthers usually have a resemblance in nature
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