How many ways can circles overlap? - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users cite it as the origin of the circle-arrangement counting problem when they pose related questions about kissing circles and unit-circle sections.
Recommended by 0 people across 0 different months, 2021 to 2022.
What it is
A Numberphile video in which Neil Sloane of the OEIS explains the sequence counting distinct arrangements of n overlapping circles in the plane, with tangent circles forbidden. It shows how the counts grow for 1, 2, 3 and 4 circles and links to OEIS A250001. Filmed and produced by Brady Haran with animation by Pete McPartlan.
What people said
Cites Jens · 2021-03 · Mathematics Stack Exchange · on “On the number of ways to draw kissing circles”
So I was watching Numberphile with Neil Sloane [this video] of OEIS fame on the number of ways to make circles intersect. During the intro, he explicitly forbid kissing (touching, tangent) circles. This made me think about the number of ways to draw circles that must all kiss, where intersections are not allowed . Kind of the dual problem, if you will. So in a nutshell: Circles in the affine plane can be of any finite size Circles must kiss at least one other (no separate circles, all must be connected) Solutions that can be transformed into each other through mirroring, rotation, stretching, moving circles without making new tangent points, are considered the same For $n=2$ circles there are two
Cites Joako · 2022-05 · Mathematics Stack Exchange · on “Does Lipschitz-kind "non-scalar ODEs" and PDEs could stand having finite-duration solutions?”
@mathcounterexamples.net ... the other one is more trivial, but I still didn't find any video on Youtube that explain probability independence with Venn Diagrams, always hidding that is a relation within the related meassurable-areas of their intersection (if I am not mistaken), which is a mess because is just one case of continuous possibilities of area mixing (so zero probability). Also it is never touched this difficulties when making Venn diagrams: video1 [this video] and video 2 [LINK]
Cites mdahlman · 2022-11 · Mathematics Stack Exchange · on “Smallest overlapping circles containing unit circles in each section”
This is a question inspired by the number of arrangements of n circles in the affine plane [LINK] which was discussed on Numberphile [this video] . One way of overlapping 3 circles looks like this: [LINK] My informal question is: what are the sizes of the 3 smallest circles for this arrangement subject to the limitation that each section is large enough to enclose a unit circle? The answer perhaps looks like this: [LINK] That is approximate (and possibly wrong!). In my drawing the 2 lower circles have radius 2, which is clearly the smallest they can be and still enclose 2 distinct unit circles. The upper circle has a radius of... a bit more than 2. I think that to be well-defined, we must specify