The Double Bubble Theorem 

who cares? nerd

holy shit i never knew that. thanks for sharing

They settle into hexagons, because of course they're the bestagons!

@@faytaliti why do you hate nonagons?

I was under the impression that they got that shape because the bees will push the wax outwards as they work, and so over time, as many bees push the perimeters of the wax outwards, they behave a lot like bubbles being pushed by air pressure.

@@channelknightfadran7901 they are just billionaire propaganda, sorry bro

Kurtzegat is really depressing, hopeless and inhuman.

​@@kashu7691 The response to the 'Billionaire Propaganda' allegations was quite interesting, I'm not sure if you've seen it. Kurzgesagt opened up on how they are funded and money from the Gates fundation came down to only 4% I think. Not sure if that changes your mind or anything but I think it's worth a read. Being skeptical is of course not a bad thing no matter who is talking.

@@nive7299 thank you for the info =)

@@EliStettner That's like... the exact opposite of their content though? All of their space technology content is the definition of 'Here's cool shit we could perhaps do one day' or 'heres a cool way the world will definitely never end'. All of their videos on real world problems tend to take cautiously positive stances, always ending with the message that although things aren't perfect we can definitely make a difference and that we can come out the other side. The recent immune system videos are just 'Hey look at how cool our human bodies are'. Hell, go watch the The Human Era

Lol "however, because in a gravitational field the preferred direction of......"

But I get what you mean tho, and that's really cool actually

168th like

Thanks. What should I look for with/involving water bubbles?

Gotta be careful with the definition of "bubble". There are *solid* bubbles (air bubble rising in a glass of water; also a drop of water in air (while falling). There are *hollow* bubbles (a soap bubble drifting in air; also a rare "anti-bubble", a hollow shell of air that sits underwater with water inside it). There are solid bubbles of water that "float" on top of water (tricky to produce; they don't last long; an electrostatic field helps). There are solid bubbles of air that sit just under the surface in your glass of water (they don't last long). It's hard or impossible to "blow" *a hollow bubble of water in air;* it breaks before it forms. You can't even make a film by lifting the bubble wand out. Things might change if the wand is very small (microscopic films and microscopic bubbles?) or in *zero-g.* It all depends what is really happening. In *zero-g,* released water sticks together as a blob. The blob tends toward the shape of a solid sphere (a *ball* ). At first it will be oscillating, but in time the waves damp out (unless you blow on it). (A spinning blob will tend toward an ellipsoid.) With a straw, you can blow a solid air bubble inside the water bubble, yielding a thick-walled *hollow bubble of water in air.* What happens next? (Assume the air bubble is not centered.) Without forces, the air bubble will stay where it is. Do forces like surface tension exert a directional force on the air bubble? If forces push the air bubble to the center, you got it right. If forces push the air bubble to the edge and then the air bubble exits the water bubble, you got it wrong. In *zero-g,* an anti-bubble *(a hollow bubble of air in water)* might persist longer, because there is no buoyancy to drive it to the surface.

I feel like getting compared to 3b1b is every math ed channels dream come true. This channel is truly marvelous.

The internal pressure of the bubble scales inversely with radius (crude idea: smaller bubble = higher SA/vol ratio = more surface tension per volume = higher pressure; more exactly: P = 4*gamma/R) so a smaller bubble will bulge slightly into a connected larger bubble. But that bulge may be difficult to see because two bubbles of similar size will have a minimal pressure difference (minimal bulge) while a duo of widely different sizes may have more of a bulge but less of a connecting surface to see it (unless one of the bubbles is huge)

@@alberthung6191 Yes, the radius of the face between two bubbles is dictated by the difference in the pressures on either side of it. Let P be pressure, T surface tension, R1 ,R2, and R3 the radii of the smaller bubble, the bigger bubble, and connecting or intermediate surface respectively. The pressures are 4T/R1 and 4T/R2. So P3 = 4T/R3 = 4T/R2 - 4T/R1. So finally 1/R3 = 1/R2 - 1/R1. Must be tricky to verify in some cases though. Photographs?

Here's something about curvature. P is pressure, T is surface tension, R₂ and R₁ are the radii of the larger and smaller bubble respectively, R₃ is the radius of the wall or intermediate film between them. "The pressure in a bubble is inversely proportional to its radius since P = 4T/R. The radius of the intermediate film is dictated by the difference in the pressures on either side of it. These pressures are 4T/R₁ and 4T/R₂ respectively. It immediately follows that P₃ = 4TR₃ = 4T/R₂ - 4T/R₁. So finally we have the simple equation 1/R₃ = 1/R₃ - 1/R₁." (From Gems of Geometry by John Barnes)

In theory it should be as close as possible, but there is a finite smallest edge size due to the minimal distance between molecules in the Lennard Jones potential. But they are arguably the closest things to a sphere we have on Earth

@@rafaelalmada723 “in theory” that’s why we should actually measure it, maybe learn some new stuff by how much it is off from a real sphere

@@crsmith6226 there may be some way of measuring it through Mie scattering, but I am not an experimentalist so it's out of my expertise 😔😔

With no wind or external forces, bubbles should be as close to perfect spheres as protons I’m sure in real life, the bubbles are slightly bottom-heavy due to gravity. You could confirm this experimentally through high-optic photography from multiple angles

Well you can “see” the thickness of a bubble from the diffracted colors, so it must be aspherical by at least a couple 100nm

unproven conjecture

@@vespuccini feels right tho

Triptophobia?

@@douggaudiosi14 no, only specifically for bubble clusters, but other so called 'tryptophobia' images or settings still don't scare me. If i'm in the shower and see such bubble clusters i wil literally scream my lungs out and i have to carefully wash myself to avoid making these soap bubbles. Especially if they're big, uneven and there are a lot of them. Like for me, going into a bubble bath is like the purest form of torture and i'll probably pass out from fear drown and die.

Do you have any idea what started this phobia?

Yep, I graduated from Cal's physics department. Go Bears!

Don't think they don't know how to weed 'em out

what? why? how? what did you even fear about them? the complex mathematics behind their existence?

And perhaps, the person that made the chain of 87 bubbles is ahead of the math and physics