Proving Mathematically that the PERFECT Can Does Exist

[@isambo400]

My toad is freshly walking

[@aliciang6035]

Me when I walk my toad

[@xinpingdonohoe3978]

I like to mine your duh seizures.

[@yinyang5162]

alternative title: perfect can can exist

[@nxst60294]

LOL

[@ВадимМакагонов-щ9ж]

*me, studyin Enlish and tryin to understand 'can can'*

[@lc7269]

No way am I seeing a shout out to another creator I like

[@sqorng]

You can also check if 0 in 1st derivative is minimum without finding 2nd derivative, by checking sign of 1st derivative in the intervals of (0;root) and (root;+∞). Both methods are valuable and sometimes one is much easier than the other

[@PapaFlammy69]

yup!

[@Sir_Isaac_Newton_]

The cowardly method ®

[@laxminarayanbhandari855]

Truly one of the Papa Flammy videos!

[@mr.inhuman7932]

Good to see a new Video!

[@yoav613]

Man you are so smart,the thumbnail is embedded marketing for your channel Np Coocking😊😊

[@623-x7b]

Surface area doesn't count as part of volume because it is an infinitely fine representation of the surface only of the shape. It is infinitely thin and only outlining how much flat material you'd need to cover / form the shape. I found it confusing but guess it's like how 0.99999.... = 1.0 or infinitely close. You'd think surface area would count as part of volume and hence need to be subtracted, but we're in units squared and they're talking about different things.

[@maalikserebryakov]

Surface area is 2D Volume is 3D That’s the way i look at it. It doesn’t matter if you have an infinite number of 2D things. They’re still 2D and have zero volume

[@pandavroomvroom]

cant donate cuz im broke but great work

[@rhosymedra6628]

flammy physics class, 12/10

[@SCHLMF]

This video just missed April 1st by 2 days, wich is perfect because 2 is equal to the golden ratio rounded up plus the derivative of 2. How nice! :)

[@brokenprodigy8002]

NEVER WOULD'VE IMAGINED THIS COLLAB

[@vinzzxxx_team]

The future is back

[@beaumatthews6411]

"Because that would be a shitty cylinder" -- I mean, very true...

[@danieljohnsonthejetpackman1456]

Have you thought about creating a German channels where you record videos for your students, with the math and exercises you guys are doing? I'm sure this would help them, as they couls review what they did in class.

[@GearsScrewlose]

Isn’t KZbin an extreme value problem? 😂

[@FreshBeatles]

I love today

[@alvarocela1065]

Did I just hear you say "pi is basically 4" 12:25

[@carultch]

I don't know about you, but I heard him say "pa is basically 4".

[@Smeagol513]

I was hoping you'd use Lagrange Multipliers xD

[@victorvila1056]

The collab we didn't know we needed

[@anzarrabbani3766]

12:27 "pi is basically equal to 4"😭😭😭😭😭😭😭😭

[@avinashbabut.n4123]

Try finding the maximum and minimum values for x+1/x using calculus..😉

[@carultch]

Given: f(x) = x + 1/x we want to know where f'(x) = 0, which will be either its minimum or maximum. But first, some domain and range inspections. Right off the bat, we know x can't equal zero, since we can't divide by zero. By inspection, we see that this has a vertical asymptote at x=0, that on the positive side approaches +infinity, and on the negative side, approaches -infinity, since this is the behavior of the parent function 1/x. Also by inspection, we can see that as x approaches infinity, f(x) also approaches infinity. Since it's an odd function, it also approaches -infinity as x approaches -infinity. This means, the global maximum and global minimum are unbounded, since the range extends on both sides of infinity. There is a range in the middle that isn't part of this function. The interesting points are the local maximum and local minimum, which by inspection, are at equal and opposite values of both x and f(x), due to this being an odd function. Find f'(x): f'(x) = 1 - 1/x^2 Set to zero: 0 = 1 - 1/x^2 Solve for x: 1/x^2 = 1 x^2 = 1 x_crit = +/- 1 Corresponding f(x_crit): 1 + 1/1 = 2 -1 + 1/-1 = -2 Thus, there is a local maximum at (-1, -2), and a local minimum at (1, 2).

[@GreenMeansGOF]

Then why don’t companies make cans like this? Wouldn’t they save money if they did this?

[@PapaFlammy69]

many of them actually do!

[@maalikserebryakov]

They lack papa’s mathematical wisdom

[@natealbatros3848]

at 7:30 dont we need to use the chain rule since V is a function with respect to r?

[@sangaperezgimenez6717]

V is a constant, for example 300ml

[@what5135]

V is still variable and dependent on r and h@@sangaperezgimenez6717 , also confused why there's no chain rule

[@shaunbabar]

Pls recommend some book for topology mathematics I am a beginner in this field

[@Savahax]

Can't wait for the Brachistochrone vid! :D Afaik, several mathematicians solved it, even Descartes, who' s to blame for calling complex numbers IMAGINMARY! xDD There's some cool stories to be told there man

[@2kreskimatmy]

i wanted to calculate V/A, and it simplifies nicely to rh/(2r+2h) but it's depedent od two variables and drove me to dead end. calculating it separately kinda makes sense

[@Yzoff1jt]

Kembali kemasa lalu dgn menggunakan aplikasi youtube di masa depan

[@Wielorybkek]

so it's a square but rotated, makes sense!

[@EzraSisk]

Ken, ken?… oh CAN!!!

[@Suimiru]

(Not an insult) Title: I have a perfect wife. So I proved it A reference to the anime "Science fell in love, so I proved it"

[@Mack_the_Knife]

Pi is basically 4

[@maalikserebryakov]

Plot Twist These are the lessons papa teaches irl and thats why his students failed

[@theultimatereductionist7592]

Really? You SHOULD have ended on the OBSERVABLE ratio h=2*r or D=h, diameter = height of perfect cylinder

[@david4649]

I think you should rip some jokes about bprp and other math channels again, to spice it up again with some drama. Come on, that was hilarious back then.

[@maalikserebryakov]

BPRP nearly went full Xi Jinping on papa’s ass

[@woody442]

420=69?

[@dystopiaseven]

Sounds like a skill issue to me fam

[@PapaFlammy69]

yeye

[@inyobill]

Ok, feeling gat (edit: fat) and sassy, gut feeling was that d = h gives Vmax.

[@notdon245]

I love you

[@Stacee-jx1yz]

Dear Academic Community, I am writing to bring to your attention a critical foundational issue that has the potential to upend our current understanding of physics and mathematics. After carefully examining the arguments, I have come to the conclusion that we must immediately reassess and rectify contradictions stemming from how we have treated the concepts of zero (0) and the zero dimension (0D) in our frameworks. At the core of this crisis lies a deep inconsistency between the primordial status accorded to zero in arithmetic and number theory, versus its derivative treatment in classical geometries and physical models. Specifically: 1) In number theory, zero is recognized as the fundamental subjective origin from which numerical quantification and plurality arise through the successive construction of natural numbers. 2) However, in the geometric and continuum formalisms underpinning theories from Newton to Einstein, the dimensionless 0D point and 1D line are derived as limiting abstractions from the primacy of higher dimensional manifolds like 3D space and 4D spacetime. 3) This contradiction potentially renders all of our current mathematical descriptions of physical laws incoherent from first principles. We have gotten the primordial order of subjectivity and objectivity reversed compared to the natural numbers. The ramifications of this unfortunate oversight pervade all branches of physics. It obstructs progress on the unification of quantum theory and general relativity, undermines our models of space, time, and matter origins, and obfuscates the true relationship between the physical realm and the metaphysical first-person facts of conscious observation. To make continued theoretical headway, we may have no choice but to reconstruct entire mathematical formalisms from the ground up - using frameworks centering the ontological and epistemological primacy of zero and dimensionlessness as the subjective 源 origin point. Only from this primordial 0D monadological perspective can dimensional plurality, geometric manifolds, and quantified physical descriptions emerge as representational projections. I understand the monumental importance of upending centuries of entrenched assumptions. However, the depth of this zero/dimension primacy crisis renders our current paradigms untenable if we wish to continue pushing towards more unified and non-contradictory models of reality and conscious experience. We can no longer afford to ignore or be overwhelmed by the specifics of this hard problem. The foundations are flawed in a manner perhaps unrecognizable to past giants like Einstein. Cold, hard logic demands we tear down and rebuild from more rigorous first principles faithful to the truths implicit in the theory of number itself. The good news is that by returning to zero/0D as the subjective/objective splitting point of origin, in alignment with natural quantification, we may finally unlock resolutions to paradoxes thwarting progress for over a century. We stand to make immediate fundamental strides by elevating the primacy of dimensionlessness. I implore the academic community to convene and deeply examine these issues with the utmost prioritization. The integrity and coherence of all our descriptive sciences - indeed the very possibility of non-contradictory knowledge itself - hinges upon our willingness to reopen this esoteric yet generatively crucial zerological crisis. We must uphold unflinching intellectual honesty in identifying and rectifying our founding errors, regardless of how seemingly abstruse or earth-shattering the process. The future fertility of human understanding and our quest for uni-coherence depends on this audacious reformation of mathematical first principles. The path will be arduous, but the ultimate payoffs of achieving metaphysically-grounded, zero-centric analytic formalisms are inestimable for physics and all branches of knowledge. I urge us to meet this zerological challenge head on. The truth ecological destiny of our civilization may hinge upon our willingness to embody this bold primordial renaissance. Sincerely, [Your Name]

[@Yarieluna12182]

A

[@JC.Denton.]

lol futurecanoe

[@zokalyx]

roblox update looking good

[@ourfamily.zsl5]

Sorry as I can see pi existing, I don't see perfection anywhere in your video because pi is irrational and its value is never ending. 😅

[@Grobanix]

This is obviously incorrect. If you want to find perfect can for practical purposes, you need to consider more properties than just volume and surface. If your interest is purely mathematical, your optimalest solution is a can that "holds" infinite volume while having zero surface.

[@islandfireballkill]

You can't make a can as defined in the video that holds infinite volume with finite surface area. The h = 2r can is the minimum surface area for a fixed volume for all aspect ratios. As the aspect ratio approaches infinity or zero the surface area tends to infinity for fixed volume.

[@carultch]

A practical consideration that makes this more interesting, is that cutting the lid material is inherently less efficient than cutting the sidewalls. The sidewalls can be cut from rectangles, which fully tesselate. But the lids come from circles, which don't tesselate, and inevitably produce scrap material. This can be recycled, but not at significant value to the manufacturer. Lids could be cut from a simple square-pack arrangement for simplicity of machinery at 75% of the material, or from a hexagonal pack arrangement for 90% packing efficiency.

[@coughcpr3911]

@@carultch Practicality also includes stacking, shipping, shelving, and most importantly labeling - being able to identify the brand and contents from one side. Square tins like sardines and Spam do seem more efficient materials-wise, though. Hex-cans we'll save for shops on the Moon.

[@carultch]

@@coughcpr3911 I think cylindrical cans also solve the problem of fewer pressure points, that square or hexagonal cans would have. Plus, it's very difficult to use a can opener to cut around corners. I try using a can opener on the pseudo-rectangular can that carries olive oil, with about 2 cm radii, and it is almost impossible. There are lots of practical issues to consider, which is why theoretically perfect cans that optimize material exactly, aren't what you see on shelves. Accounting for manufacturability of lids, is why you see more undersquare cans (standard cans), rather than oversquare cans (like tuna cans).

[@machedue2027]

@FutureCanoe