I remember watching a video a few years ago on YouTube about packing circles in a 2D container. I think it was on a Maths channel similar to 3Blue1Brown or Numberphile but 8 haven't had any luck on the ones I've searched through.
The video goes into exploring a feature of this box of circles whereby the top line of circles in the box always stays perfectly aligned with each other despite the circles underneath being arranged in weird, random ways. I'm pretty sure it also proves why it happens and explores some other properties of this setup.
Thanks in advance. I really want to rewatch it but can't find it anywhere!
Hi, I am trying to find optimal ways a circle can be packed into various rectangles, such as this example:
https://www.wolframalpha.com/input/?i=pack+circles+of+radius+.096+in+a+square+of+side+1.3
However, this is a square, but I need the 2 sides to be different, a rectangle, and Wolfram cant seem to accept that... Any ideas?
I need to pack 5 circles into a single circle.
Wikipedia says that this Formula can be applied to make the calculation, however, I lack the know-how to apply it.
The radius for the circle I want to fit 5 other circles into is 22cm.
Wolfram Alpha gives me This but I don't understand it.
I'd appreciate any help, including pointers to a resource I perhaps missed while Googling.
This site has been extremely helpful in designing battery packs to fit in circular spaces. I was wondering if something similar exists that demonstrates the optimal packing for equal sized circles in an N-sided regular polygon, or where to begin mathematically generating these optimal scenarios myself.
This is an odd question, but figured was worth a shot. I need to make quite a few images that depict various sets of tangent circles with disjoint interiors. This can be pretty damn annoying to do, after you place the first few tangent circles, you have to be super precise with the following ones to keep the image consistent. The papers I'm reading have these beautiful graphics, but i should really be doing my own. Any thoughts on how they did it? Any program they used?
Tools like Tikz would be a nightmare unless I created a program that would generate the coordinates for a Tikz circle..It would be much simpler to simply make the images in paint or some other image editor, but most of those draw circles by just having you select a center and a size, which again can be really hard to get right. Any thoughts?
And sorry if it wasn't clear, I don't mean theoretically what sort of approach would you use. I mean literally I just need something to generate images to include in my research!
I was reading this article about a very simple and cool proof of Thue's Theorem. I understood almost everything, but there's one part that i really couldn't. When the author says that the density of an ABC triangle is equal to (A/2+B/2+C/2)/The triangle's area (page 3) , why's that? Here's the article link: https://arxiv.org/abs/1009.4322
function p = circle1(m,n,r,s)
origin = [ m n ] ;
radius = r ;
a = origin(1) ;
b = origin(2) ;
segments = s ;
x = linspace(a-radius,a+radius,segments) ;
y1 = sqrt(abs(radius.*radius-(x-a).*(x-a))) + b ;
y2 = -sqrt(abs(radius.*radius-(x-a).*(x-a))) + b ;
p = plot(x,y1,'k-',x,y2,'k-',a,b,'k.');
end