overlapping circles

Circle packing theorem

Recently I heard about this surprising theorem. I already knew about Fáry’s theorem: if a simple graph can be drawn on the plane without crossing edges (i.e. if the graph is planar), then it can always be drawn in such a way that all edges are non-crossing straight lines. Hence, restricting to straight-line edges doesn’t give a strictly smaller class of planar graphs. I found this to be quite surprising already.

However, much more is true: you can always draw a simple planar graph in the plane in such a way that you can place non-overlapping circles on the vertices, such that two circles touch if and only if the corresponding vertices are joined by an edge. In particular, the drawing clearly satisfies the result of Fáry’s theorem. This result is called the circle packing theorem.

A stereo image of Jupiter’s atmosphere, derived from data collected by the Juno spacecraft during perijove 3.  These images, taken at different point in the orbit, can be combined to reveal the 3D structure and relief of clouds in the southern atmosphere.  To see the image in 3D, relax the eyes until the white circles overlap, then look at the image.  Alternatively the image can be viewed with Google Cardboard or another VR device.

Image source: NASA

Processing: James Tyrwhitt-Drake

what a strange fruit:
kernels in chessboard pattern,
circles overlapping,
a non-Euclidian geometry,
a planet with rings
turned inside out,
in miniature;
would you risk

the size of a lion cub’s head,
heavy as metal,
lead in color.
why is it so cold?
is it a fruit at all?

The Flower of Life is the modern name given to a geometrical figure composed of multiple evenly-spaced, overlapping circles. They are arranged to form a flower-like pattern with a sixfold symmetry.

Within the Flower Of Life’s concentric circle pattern lies another pattern - the Fruit of Life. This symbol is composed of 13 circles taken from the design of the Flower of Life. The Fruit of Life is said to be the blueprint of the Universe, containing the basis for the design for atoms, molecular structures, life forms, in short everything in existence.

Sociocracy - Wikipedia
Governance by consent

After years of experimentation and application, Endenburg developed a formal organizational method named the “Sociocratische Kringorganisatie Methode” (Sociocratic Circle Organizing Method). Endenburg’s method was based on the circular feedback process then called the “circular causal feedback process,” now referred to commonly as the circular process and feedback loops. The Sociocratic Circle Organization Method uses a hierarchy of circles corresponding to units or departments of an organization, but it is a circular hierarchy—the links between each circle combine to form feedback loops up and down the organization. Because representatives overlap the circle with a linked circle and each circle makes policy decisions by consent this forms a strong and integrated structure of communications and control. Feedback moves up and down the organization and can’t be ignored.

All policy decisions, those that pertain to the allocation of resources and constrain operational decisions, require the consent of all members of a circle. Day-to-day operational decisions are made by the operations leader within the policies established in circle meetings. Policy decisions affecting more than one circle’s domain are made by a higher circle formed by representatives from each circle. This structure of linked circles that make decisions by consent maintains the efficiency of a hierarchy while preserving the equivalence of the circles and their members.

Decisions are made when there are no remaining “paramount objections”, that is, when there is informed consent from all participants. Objections must be reasoned and argued and based on the ability of the objector to work productively toward the goals of the organization. All policy decisions are made by consent although the group may consent to use another decision-making method. Within these policies, day-to-day operational decisions are normally made in the traditional manner. Generally, objections are highly valued to hear every stakeholder’s concern. Many call this process “objection harvesting”.[10] It is emphasized that focusing on objections first leads to more efficient decision making.[11]


A question I’d like to put out to the world: has anyone else been feeling like the catch rates have been nerfed again? I’ve been playing all night and feel like 4 break outs are happening way too much. Maybe it’s just me tho.

Also, I really don’t think my eyes were lying to me, but there was one single catch tonight, a Krabby, where I threw the ball at it, and it insta-caught. And it didn’t seem like a glitch, because the catch animation was different, with the stars that come out being bigger and more golden. I’d really love if anyone could confirm I’m not crazy. It may have something to do with throwing the ball when the timer circle overlaps the inner circle perfectly.

i feel like since i started style experimenting with miri, i’ve gotten better at defining characters by simple shapes while sketching them; skelix is much rounder and pudgier now because her body just starts off as two overlapping circles with ovals slapped on as her titties


Art Crowns Newly Opened Subway Station

Xenobia Bailey’s “Funktional Vibratons” is a highlight of the new NYC subway station at 34 St. – Hudson Yards which opens today and brings New Yorkers to the Javits Center, the High Line and Chelsea via the 7 line’s extension. Majestic mosaics are suspended above the main entrance and feature overlapping mandala-like circles and patterns against a cobalt blue background. Starbursts and rays of light fill the space creating a vibrant and joyous attraction. Bailey is a fiber artist and her art for the station began as crocheted pieces, which were transferred to digital images, enlarged and interpreted into mosaic by Miotto Mosaic Art Studio. Take a ride and see it for yourself! #MTAArts
#XenobiaBailey #FunctionalVibrations #7


“Emma swallowed. She was remembering Julian, two years ago, standing in the overlapping circles of fire where the parabatai ritual was performed. The look on his face as they each stepped into the central circle and the fire rose up around them, and he unbuttoned his shirt to let her touch the stele to his skin and carve the rune that would bind them together for their whole lives. She knew if she just reached out now, she could touch it, touch the rune cut into his shoulder, the rune she had put there …”

Is it just me or has the secret life of pets been released several times over the past few years? How many times have I seen it coming soon to cinemas? 3? I feel like I’m in this universe where time is circling and overlapping itself and although I live each day differently the secret life of pets is perpetually coming soon, never arriving but always looming in the future, a future that will never be

why is there such an overlap with dorky circles of friends and lgbt people…like specifically in high school it was strange just to see how many of the Nerdy ™ kids were all questioning their gender/sexuality

FYI, I’ve completely forgotten about you....

I haven’t forgotten you
Though I’d like you to think I have
I think about you pretty often
Just about every other song alludes to you
And how I felt back in the day
And the secrets we thought we kept hidden away

Isn’t it funny how time heals all wounds
But I can’t stop picking at all of them
So I am open and weeping nostalgia
For the times when you were important

I haven’t forgotten you
Though I’d like you to think I have
Because I wish you didn’t mean a thing
So that I wouldn’t think fondly of you

So I tell them I’ve forgotten about you
Because if they knew the truth
It’d get back to you somehow
Becuase we dance overlapping circles around one another
[In closer proximity than one would think]
Avoiding the truth they always knew
That we could never just be friends

inspired by this post by @merseawaves