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
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! :)
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!
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 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!
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!
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?
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
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!
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).
@@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
@@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
@@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
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!
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.
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.
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!
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.
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!
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 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
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.
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.
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.
@@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
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
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)
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
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! :)
Hexagons are the bestagons!
Flexigons are the bestagons.
No, hexagons are the bestagons.
I was coming to the comment section to say the same! :D
@@Easonium Vi hart says otherwise.
@@sdspivey Then let her come here and say it!
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!
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).
I never understood why rotations/revolutions/turns aren't the default unit talking about angles... They're more natural than both degrees and radians.
@@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!
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!
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!
What a lovely smile when he drops character when he drops something he didn't expect to drop.
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?
There's 360°, the common way
There's 2 pi radians, the mathematical way
And then there's 1 tau radians, the enlightened way
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
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!
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).
@@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
@@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
@@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
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!
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.
Loved the 360 degree relationship with angles and shapes and that outro shot was really smooth 👌
Love the vid -- props to Carlo as well!!! He does a great job
this felt like a fever dream... in the absolute best way possible! definitely going to subscribe!
I love this channel so much haha
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.
Broke: Khan Academy- Area of a Regular Hexagon
Woke: CGP Grey- Hexagons are the Bestagons
Bespoke: Combo Class- Hidden Hexagons Inside Bananas
What a gem .. Im reposting on twitter .. Can we get a chaitin's constant video ?
the shape that you find inside of a banana is also present in heart valves!!
so maybe we also are part of a bigger hexagon pattern!! I'm joking but it's clearly a recurring pattern in nature.
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!
Fun fact: The tilings are also regular polyhedra
12:34 I'm no botanist but you might want to check the banana flowers (early fruit development)
saturn also has a hexagon on it
This one is cool. I refer to the reason as the "squished concentric rubber bands" model.
The full circle unit measure is "turns".
Nobody uses "rights", but I like them a lot, because then e^-i(rads) = i^(rights)
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.
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!
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.
It can’t get any more perfect than 1 = e^(tau*i). No need for a silly “+ 1 = 0” fudge factor.
@@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
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.
@@ComboClass Then why not write “e^(tau*i) = 1 + 0”?
casual tau reference. >:)
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.
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.
Dunno if i agree with your police work there, Norm
This is just bananas ❤. You are onto something! I see it
at the beginning tip of a banana bunch, i think that is a hexagon tiling
Next time we may discuss a cucumber!
Never stop being chaotic!
That round arrow symbol is quite similar to the greek letter tau. Maybe we could use that.. just an idea ;-)
If you are speaking in terms of radians, yes, but it also “equals” other things under other measurements
@@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
So a triangle is a should be a triagon and a square should be called a tesseragon?
Cones! not enough info on cones
I noticed this once and googled it, the answer i got was a lot less satisfying than this video, wish i found it then!
Bananas stronk
cellular modular interactiveodular
its a real live mama and a papa phone, a brother and a sister and a dogaphone, grandpaphone and a GRAMOPHOOOOONE
8:55 - 9:17 no wonder graphene is so strong.
after all hexagons ARE the bestagons
COMBO CLASS goes beastie ham on in it, necessarily! finna will to be next 3Blue1Brown on moms,brother,love,&ghost
Hexagons are the bestagons
I love turns as a unit, yes...
tau radians = 1 turn
tau = t
Banonagon
This is bananas.
Round arrow. New symbol for tou.
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
We got a banana video, maybe we'll get an eggplant one next.
Cucumbers have something similar. I see the Biohazard symbol in cross section.
hexagons, the bestagons
Hexagons are the bestagons.
Hexagon, heptagon, octagon, banonagon 😂
beautiful
This video is bananas 🍌
math, math everywhere
There are three segments because bananas are one of the few organisms that are triploid in their genes.
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)
threeven*
Tomatos are Hexagons
Dude...
τ rad
please.
Most people don't even know what Tau is, and he didn't want to explain what it was
engle
There is an error in the title it should be "The bestagones hidden inside bananas" common mistake
at the beginning tip of a banana bunch, i think that is a hexagon tiling
hexagons are the bestagons