The Hidden Hexagons Inside Bananas

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  • Опубліковано 27 гру 2024

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  • @ComboClass
    @ComboClass  Рік тому +26

    Hope you enjoy this combo of a "snack break" and math lesson! I'll hopefully have a new episode out here every Sunday in May. I've also begun putting occasional "shorts" on this channel, but won't make them alert notifications or subscription feeds like full episodes do. This channel's focus will always be full episodes, but my previous shorts did so well at introducing people to my other @Domotro channel that I'm going to post some of my future shorts from this channel instead. See this video's description if you want more details. And check out the first short I've put out on this channel so far here: ua-cam.com/users/shortszhOiUNQtGF4?feature=share

  • @joshflynnvoice
    @joshflynnvoice Рік тому +26

    Love these vids, Domotro. Please keep this aesthetic for as long as you can! It makes it feel like its own style : fire, bubbles, clocks, and dice in some crazy science guy's garden! :)

  • @TheGoldenTankTGTgoldisawesome
    @TheGoldenTankTGTgoldisawesome Рік тому +92

    Hexagons are the bestagons!

    • @sdspivey
      @sdspivey Рік тому +4

      Flexigons are the bestagons.

    • @Easonium
      @Easonium Рік тому +2

      No, hexagons are the bestagons.

    • @Pangui008
      @Pangui008 Рік тому +4

      I was coming to the comment section to say the same! :D

    • @sdspivey
      @sdspivey Рік тому +4

      @@Easonium Vi hart says otherwise.

    • @histrion2
      @histrion2 Рік тому +1

      ​@@sdspivey Then let her come here and say it!

  • @areadenial2343
    @areadenial2343 Рік тому +15

    I call the "full rotation" unit a revolution, some people simply call it a turn. Revolution makes the most sense to me, after all the most common unit of rotation frequency is revolutions per minute!

    • @mikecaetano
      @mikecaetano Рік тому +1

      But a calling one rotation a turn allows for semantically isolating the phase. Edit -- leading to a linear expression for a rotation that resembles a complex number, eg. s = wt+p, where w is turns and p is phase. Also what about Hertz? Hz -- cycles per second -- is very common too, especially vis-a-vis computers and signal processing (where s=wt+p figures in).

    • @MrCheeze
      @MrCheeze Рік тому +1

      I never understood why rotations/revolutions/turns aren't the default unit talking about angles... They're more natural than both degrees and radians.

    • @codahighland
      @codahighland Рік тому +1

      ​@@MrCheeze Because it lacks some nice properties that are useful -- namely, you can't as easily combine fractions of a revolution; you have to find a common denominator in order to combine fractions. And if you were to choose a consistent denominator to make things easier for that... Wait a minute, those are degrees!

  • @jackb7685
    @jackb7685 9 місяців тому +1

    I just tried to peel my banana in sections and realized that the bottom is a hexagon. This is the only answer I could find online!

  • @GamerSquiddy
    @GamerSquiddy Рік тому +18

    I found your channel the other day and have been watching a bunch. Really love the stuff! I've always loved math and really love the chaotic nature of the videos. Thanks for putting so much passion into your channel man!

  • @DanDart
    @DanDart Рік тому +2

    What a lovely smile when he drops character when he drops something he didn't expect to drop.

  • @bobboby4869
    @bobboby4869 Рік тому +2

    My guess is that the hexagonal pattern emerges because the bananas try to fit as much meat per unit of area of peel. Which would be a circle as you said, but then pressure from surrounding bananas has brought them to grown in hexagonal formations on the outside, similar to the bee situation you mentioned. The result is that the inside is precisely the intersection point of 3 surrounding implied hexagons, like it would if you overlaid two hexagon grids slightly offset. Hopefully that makes sense? But its probably not really relevant because this 3 partition pattern shows up in so many other fruits, watermelons, cucumbers etc. I also noticed that if you took apart the three sections you can form a hexagon by putting the rounded sides all at the center, maybe that is somehow indicative of some further pattern?

  • @ComDenox
    @ComDenox Рік тому +3

    There's 360°, the common way
    There's 2 pi radians, the mathematical way
    And then there's 1 tau radians, the enlightened way

  • @HipsterShiningArmor
    @HipsterShiningArmor Рік тому +4

    gradians are basically someone going "what if there was a system of measuring angles that had all of the drawbacks of degrees but also lacked almost all of its benefits." the only reason i can even imagine it exists is because someone really wanted right angles to be 100 for some reason and were willing to throw everything else into the meat grinder to achieve that

    • @ComboClass
      @ComboClass  Рік тому +3

      Yeah they are “.01 of a right angle” which at first looks nice in base ten, but loses all the good divisibility that 360 has. For example, 400 isn’t threeven!

    • @stickfiftyfive
      @stickfiftyfive Рік тому +2

      They could've at least gone with a 420 unit full rotation to keep an equal number of divisors (and gain 7 divisability, but lose 8 and 9, which is definitely not worth it IMO).

    • @HipsterShiningArmor
      @HipsterShiningArmor Рік тому +1

      @@ComboClass it looks nice right up until you have to contend with the fact that the internal angle of an equilateral triangle in gradians is 66 1/3. awful

    • @monhi64
      @monhi64 5 місяців тому

      @@HipsterShiningArmorso that’s it though? It just has less divisors, mostly all those multiples of three. That’s a bad quality for sure but not catastrophic, I could see a world where they thought of 400 first and settled for it

    • @monhi64
      @monhi64 5 місяців тому

      @@ComboClassI’d be really curious for your opinion on Celsius vs Fahrenheit. I ya know obviously prefer metric for a lot but the more I think about Celsius I don’t really see much advantage. Makes remembering the phase changes for one specific substance (water) ever so slightly easier but comes at the cost of making each degree huge, less precise meaning more decimals with Celsius to describe a temp with accuracy. Not sure how Celsius helps with calculations since you rarely convert degrees to anything else

  • @Idekaks
    @Idekaks Рік тому +1

    Domotro have you heard of Tau and the Tau manifesto? I thought you were about to introduce it at around 3:00 but you didn't.
    Keep up the great work ma man!

  • @stickfiftyfive
    @stickfiftyfive Рік тому +4

    The polygon math videos are some of my favorites without fail, and now with fruit math sharing that space I think you've found a top-tier niche with this one.
    I love bananas and hexagons so much. Thank you for bringing this question of implied spatial geometries up. I've been thinking about this one a lot in regards to specifically nature, polygons and circles, and efficient packing so this topic is weirdly synchronous with my fascinations right now.

  • @TheMagicFellow
    @TheMagicFellow Рік тому +5

    Loved the 360 degree relationship with angles and shapes and that outro shot was really smooth 👌

  • @publiconions6313
    @publiconions6313 Рік тому +3

    Love the vid -- props to Carlo as well!!! He does a great job

  • @lotta414
    @lotta414 Рік тому +1

    this felt like a fever dream... in the absolute best way possible! definitely going to subscribe!

  • @jvsonyt
    @jvsonyt Рік тому +1

    I love this channel so much haha

  • @CMDRunematti
    @CMDRunematti Рік тому +2

    i mean...the bananabunch is a beehive, if you cut all the bananas at once by a plane...the hexagons are probably hiding in the start of the growth where theyre very close together.

  • @KarlAckerman
    @KarlAckerman Рік тому +3

    Broke: Khan Academy- Area of a Regular Hexagon
    Woke: CGP Grey- Hexagons are the Bestagons
    Bespoke: Combo Class- Hidden Hexagons Inside Bananas

  • @georgesamaras2922
    @georgesamaras2922 Рік тому

    What a gem .. Im reposting on twitter .. Can we get a chaitin's constant video ?

  • @thomasadami9549
    @thomasadami9549 Рік тому +2

    the shape that you find inside of a banana is also present in heart valves!!

    • @thomasadami9549
      @thomasadami9549 Рік тому

      so maybe we also are part of a bigger hexagon pattern!! I'm joking but it's clearly a recurring pattern in nature.

  • @dman-tm
    @dman-tm Рік тому

    Hey Man, just found your channel. i'm starting to watch all your channels.
    One thing! I would love to hear your input and thought on SET THEORY. I find it extremely fascinating, especially in the world of Sudoku! Do you think you could share any knowledge on the topic or any experiences you have had with it?
    You have to make an episode on it! thanks for your awesome content!

  • @aer0a
    @aer0a Рік тому +1

    Fun fact: The tilings are also regular polyhedra

  • @anieldayyanelday1771
    @anieldayyanelday1771 Рік тому

    12:34 I'm no botanist but you might want to check the banana flowers (early fruit development)

  • @tejassingh4745
    @tejassingh4745 Рік тому +1

    saturn also has a hexagon on it

    • @stickfiftyfive
      @stickfiftyfive Рік тому

      This one is cool. I refer to the reason as the "squished concentric rubber bands" model.

  • @alikaperdue
    @alikaperdue Рік тому

    The full circle unit measure is "turns".
    Nobody uses "rights", but I like them a lot, because then e^-i(rads) = i^(rights)

  • @danielrhouck
    @danielrhouck Рік тому

    I think you might have been on to something in the beginning, with talking about the outside shape. How do bananas fit together in a bunch? Do they line up so that those “implied hexagons” all join in an interesting way?
    Also, there are too few letters in the Latin and Greek alphabets combined, and torque is already using one of them and related to circles, so ↻ is a better symbol for a full turn than the usual one.

  • @tegxi
    @tegxi Рік тому +12

    fun episode!
    also, I noticed you using a little cycle symbol for fractions of a full circle. Tau (τ) (equal to 2 pi and its proposed replacement) actually lets you notate that the same way! (In addition to its many other benefits)
    This channel has done a lot on stuff like base 6 and 12 and other math things we take for granted, and if you haven't read it yet I highly recommend the Tau Manifesto. Pi itself turns out to be a pretty silly choice for a circle constant!

    • @ComboClass
      @ComboClass  Рік тому +13

      In this circumstance, yeah my squiggly symbol is also equivalent to “tau radians”. As far as that “manifesto”, I’ve read it, but honestly somewhat disagree with it. I think that pi and tau are both pretty similar in terms of how many equations/contexts one is neater than the other. Some cases tau is neater, but there are various other equations/contexts that author left out where tau is way harder to deal with than pi. I don’t mind having names for both. In terms of describing radians I agree it is useful.

    • @thomaskn1012
      @thomaskn1012 Рік тому

      It can’t get any more perfect than 1 = e^(tau*i). No need for a silly “+ 1 = 0” fudge factor.

    • @ComboClass
      @ComboClass  Рік тому +6

      @@thomaskn1012 I like the form that has = 0 on one side, like many properly formatted equations are put in. So e^(tau*i) - 1 = 0, or e^(pi*i) + 1 = 0 are both equally cool to me. They are even cooler in conjunction with each other, so there's no need to make tau "replace" pi in that equation, when they both are just different sides of it

    • @stickfiftyfive
      @stickfiftyfive Рік тому +1

      Totally agree Domotro. I've come to the conclusion that either can end up being the more elegant choice simply depending on context, purpose, and personal ease of use/preference.

    • @thomaskn1012
      @thomaskn1012 Рік тому

      @@ComboClass Then why not write “e^(tau*i) = 1 + 0”?

  • @evandrofilipe1526
    @evandrofilipe1526 Рік тому +2

    casual tau reference. >:)

  • @X3MgamePlays
    @X3MgamePlays Рік тому

    I love hexagons too!
    Check out the inside of a cucumber.
    You also might find the surface of a pineapple interesting.
    Some fruits however, decided to have the number 5 instead.

  • @FirstLast-oe2jm
    @FirstLast-oe2jm Рік тому

    No that's 110% a hexagon. Fascinating! if I had to guess this might have something to do with the sugar that starts the growth seed of the fruit, given most fruit are simply sugars to feed seeds, maybe the whole hexagonal pattern stems from a polysaccharide chain.

    • @TalsBadKidney
      @TalsBadKidney Рік тому

      Dunno if i agree with your police work there, Norm

  • @rjhealey
    @rjhealey Рік тому

    This is just bananas ❤. You are onto something! I see it

  • @daniel_77.
    @daniel_77. Рік тому

    at the beginning tip of a banana bunch, i think that is a hexagon tiling

  • @OLAFBONDD
    @OLAFBONDD Рік тому

    Next time we may discuss a cucumber!

  • @jitteryhands16
    @jitteryhands16 Рік тому

    Never stop being chaotic!

  • @ChongFrisbee
    @ChongFrisbee Рік тому

    That round arrow symbol is quite similar to the greek letter tau. Maybe we could use that.. just an idea ;-)

    • @ComboClass
      @ComboClass  Рік тому

      If you are speaking in terms of radians, yes, but it also “equals” other things under other measurements

    • @ChongFrisbee
      @ChongFrisbee Рік тому

      @@ComboClass I really mean just use it as a symbol. Mathematicians did this with pi as "the relevant circle constant for this particular problem". Pi is now tainted for it, but no one cares about tau, so is game on

  • @westleywest7259
    @westleywest7259 22 дні тому

    So a triangle is a should be a triagon and a square should be called a tesseragon?

  • @masonduarte8001
    @masonduarte8001 Рік тому

    Cones! not enough info on cones

  • @spirttomb
    @spirttomb Рік тому

    I noticed this once and googled it, the answer i got was a lot less satisfying than this video, wish i found it then!

  • @bayzul7405
    @bayzul7405 Рік тому

    Bananas stronk

  • @RobertShippey
    @RobertShippey Рік тому +1

    cellular modular interactiveodular

    • @TalsBadKidney
      @TalsBadKidney Рік тому

      its a real live mama and a papa phone, a brother and a sister and a dogaphone, grandpaphone and a GRAMOPHOOOOONE

  • @FenrizNNN
    @FenrizNNN Рік тому

    8:55 - 9:17 no wonder graphene is so strong.

  • @RedLuigi235
    @RedLuigi235 Рік тому +1

    after all hexagons ARE the bestagons

  • @guidetogaming6911
    @guidetogaming6911 Рік тому

    COMBO CLASS goes beastie ham on in it, necessarily! finna will to be next 3Blue1Brown on moms,brother,love,&ghost

  • @CaedmonOS
    @CaedmonOS Рік тому

    Hexagons are the bestagons

  • @DanDart
    @DanDart Рік тому

    I love turns as a unit, yes...
    tau radians = 1 turn
    tau = t

  • @TalsBadKidney
    @TalsBadKidney Рік тому

    Banonagon

  • @Marc-Tu
    @Marc-Tu Рік тому

    This is bananas.

  • @JR13751
    @JR13751 Рік тому

    Round arrow. New symbol for tou.

    • @ComboClass
      @ComboClass  Рік тому

      If you are comparing it to tau, it has to be in the measurement radians, so moreso it could be said to be equivalent to “tau radians”. And would be equivalent to other numbers if using other measurements than radians

  • @litigioussociety4249
    @litigioussociety4249 Рік тому

    We got a banana video, maybe we'll get an eggplant one next.

  • @doctorsabado2792
    @doctorsabado2792 Рік тому

    Cucumbers have something similar. I see the Biohazard symbol in cross section.

  • @soninhodev7851
    @soninhodev7851 Рік тому

    hexagons, the bestagons

  • @emilyrln
    @emilyrln Рік тому

    Hexagon, heptagon, octagon, banonagon 😂

  • @DeWillpower
    @DeWillpower Рік тому

    beautiful

  • @buckleysangel7019
    @buckleysangel7019 Рік тому

    This video is bananas 🍌

  • @abe-danger
    @abe-danger Рік тому

    math, math everywhere

  • @thomaskn1012
    @thomaskn1012 Рік тому

    There are three segments because bananas are one of the few organisms that are triploid in their genes.

    • @ComboClass
      @ComboClass  Рік тому +2

      Not all bananas have triploid genes. The types I have in this video do (I think), although a banana-like fruit could have evolved from a different genetic structure, and I’m curious about diving deeper into why a three-based genetic structure ended up evolving successfully into this common form of bananas and survived that way for many years (as opposed to the possibility that triploid genes historically never managed to evolve something like this, while a banana-esque fruit became successful from others different genetic structure)

    • @theneoreformationist
      @theneoreformationist Рік тому

      threeven*

  • @BaseSixBasics
    @BaseSixBasics 11 місяців тому

    Tomatos are Hexagons

  • @WDCallahan
    @WDCallahan Рік тому

    Dude...
    τ rad
    please.

    • @FenrizNNN
      @FenrizNNN Рік тому

      Most people don't even know what Tau is, and he didn't want to explain what it was

  • @debblez
    @debblez Рік тому

    engle

  • @xardiodrack1798
    @xardiodrack1798 Рік тому

    There is an error in the title it should be "The bestagones hidden inside bananas" common mistake

  • @daniel_77.
    @daniel_77. Рік тому

    at the beginning tip of a banana bunch, i think that is a hexagon tiling

  • @willamgaines
    @willamgaines Рік тому

    hexagons are the bestagons