Why the Number 1,000,000 Should Be 1,081,080
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- Опубліковано 3 чер 2022
- What do clocks, calendars, and eggs have to do with the number 1,081,080? Get ready to learn about an exclusive family of special numbers....
Stay tuned for next class when we'll prove things about prime numbers and infinity!
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Combo Class, taught by Domotro, is an unconventional learning experience where anybody (whether they're a fan of normal school or not) can become excited to learn rare things about math, science, language, and more. Also check out the shorter videos on the Combo Class Shorts channel (and TikTok page). Thanks for coming to Combo Class!
DISCLAIMER: The burning clock in the intro (and any other uses of fire, tools, or science experiments in this series) was done in a professional and safe way. Don't try to copy anything you see in this series yourself.
I love you jack harrlow
I can not tell you how much I love that there is enough overlap between people who watch content like this and those who like rap in general and at least know who jack Harlow is to make this the top comment lmao
@@monhi64 I agree
@@monhi64 Last time I checked rap is the most popular genre in the US and Jack Harlow has made several hit songs
Better Jack Harlow.
@@Omlet221rap is not that popular
The reason for all the duplicated numbers is that 1001 is 11 * 13 * 7 which adds a lot of potential new combinations.
I was searching for exactly this comment.
First thought was it to be some cousin of 11 like 101 or 1001 which it is.
and 10010 is 11*13*7*5*2 which is really good too
Can we appreciate him writing "Highly Composite Numbers" while simultaneously explaining some context verbally?
Had a school acquaintance demonstrate saying a sentence while writing a completely different one and my mind was blown. You don't realize how hard that is to do until you try it.
Like numberphile writing out a 20 digit number.
Yeah right! That was insane
Its really cool I think you could achieve it reasonably with practice
Timestamp?
@@2P9PR 2:54
Admittedly, he pauses to explain some things before writing "Numbers", but he still did it for most of it so it was cool.
You’re incredible Dimitri!! I love this!!
Thanks! More coming soon :)
Your tetration video was the first one of yours that I saw. When you brought up factorial, I immediately thought, is there a higher and lower operation than factorial? I don't think there is. Most of what I found just used sigma.
Either way, I enjoy the detail that you go into. It forces me to wonder what happen if ___. You'll have a Practical Million subscribers in no time!
I just watched your video about primes. Once you said the word "factorial," I knew you had to be answering what google didn't show me in my searches. lol
There's double factorial, counterintuitively named
cool that’s also my first vid of his!
@Chip Wiseman arent these the triangle numbers
@@muskyoxeseah, it should have been called half factorial
I can't help but smile while watching this. Your love of math really speaks in this video. This is the kind of attitude we need for teaching maths!
I think what kills school teachers is that they have to explain the same thing over and over again and they are also constrained on what they must teach. Being on youtube on the other hand gives you much more freedom on what YOU want to present, which also means you are more than likely excited to talk about it
@@MCreeper-eg9xy Oh yea, definitely! This is more of a systematic problem than a problem with individual teachers. I've had lots of inspirational teachers who loved math but were stuck teaching the same dry, boring material year after year. It might have been more accurate to say, "This is the kind of attitude our system needs for teaching maths!"
I originally thought this was a numberphile video because of the enthusiastic looking man with a marker in the thumbnail and a very interesting title that seems to make no sense lol
I like 45045, like an "odd highly composite", has a sweet palindromic binary form, and can just bit shift to get to 720720. (Of course, 7*11*13=1001 is how we get clones)
I’m guessing all the “clones” in the later Highly Composite Numbers are because they all have 11 as one of their many factors. With the lower ones, it looks like every highly composite number except 1 is divisible by 2, every highly composite number starting with 6 is divisible by 3, highly composite numbers starting with 60 are divisible by 5, and 840 is where they start being divisible by 7, so it makes sense that 11 joins later on.
Yes for 11 and also 7x11x13 = 1001 might be a factor (ha!) in why the pattern/clone numbers are highly composite.
@@Rack979 Came here to say this.
Good point! I didn’t even consider 1,001, but those numbers look a lot more like multiples of 1,001 than just 11, so you’re probably right!
I'm getting back into all the math and STEM fun that I used to love as a kid, and you're becoming such an inspiration to me on this path! I can tell you're having a blast with it too, a like a new Bill Nye!
When you said “for some reason [4324320] is superior” I laughed out loud. Very nice
10:31 that exclamation mark after the 9 threw me theough the loop for a good 20 seconds thinking it meant 9 factorial and I was trying to figure out how that could possibly make sense, you gotta be careful with that especially after just talking about factorials and such in the video
this channel is something really special. can't wait to see you get bigger! the music feels really nostalgic for some reason, and makes me happy :)
There actually exists a duodecimal system with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, dek, el and do. This would be way more useful to modern-day mathematics, because fractions in this system are more often visually appealing and easier to work with. For example: 1/3 = 0.4, 1/4 = 0.3 and 1/6 = 0.2. These fractions are 0.3333..., 0.25 and 0.1666... in our decimal system, which is way more inconvenient.
There's also base six, officially named senary but also called seximal. It's got a lot of the same benefits of dozenal, while requiring no new symbols and having better representations for a fifth (0.11111...) and a seventh (0.05050505....) than the corresponding ones in dozenal (0.24972497..., 0.186X35186X35...). But it does have a downside of having numbers get long somewhat quickly.
it's far easier to just work with fractions instead of converting them to numerical form
Great video!
A tip for the videographer (who is doing a great job btw) and for you, would be to make sure the sun is not behind you or in front of the camera. It looks like you lost a fair bit of contrast.
Now, I bought a polarizing filter, and a mattebox to solve this for when I had to put my subjects between me and the sun, and that works really well!
Looking forward seeing more of your stuff!
Found this channel from a UA-cam short you posted, you're doing awesome work.
Hey, I love your cheerfulness, and the fact that when you don't know something you nonchalantly admit it.
This highly composite numbers' video was a gem! Thank you very much for the mathematical enthusiasm, your channel is the most mathematical creative one I've seen so far. I hope to watch more videos where you show the beauty in math for us starving for it.
The title had my curiosity. The information/content within had my subscription. Very well done
I can't wait to see how this channel grows. New subscriber!
These videos always amaze me, keep doing these
My favorite quirk of numbers is talking with people who think Base 10 is somehow better than other Bases. Like the only reason Base 10 means Base (9+1) is because we all agree that it does. Every base system would call itself Base 10. Count using 6? That's now Base 10. Counting using 100? 100 is now Base 10. So next time someone says Base [anything with more than 1 digit] poke a little fun at how ambiguous their phrasing is.
I really love this channel
Amazing video man
Great show, always loved 7!
I think it's interesting that most fair dice (aside from the infinite dihedral families) have a number of faces which is a highly composite number. The exceptions being the d8, d20, and d30, and the lack of a d36 existing
8, 20, and 30 are part of the "largely composite" family, where the number of divisors are greater than or equal to, rather than just greater than the numbers less than them that the highly composite numbers abide by.
The old pre decimal British pound used to have 240 pence to the pound. 240 being one of your numbers and highly divisible.
I sugest the 'Equaly Highy Composite Numbers' this will include all the Highly Composite Numbers and all the numbers that have the same amout of divisible factors than the last Highly Composite Numbers. 3, 8 and 16 will be the first of these, We could also call these 'Strictly Highy Composite Numbers' by just takeing the away the Highly COmposite Numbers from the list
I also though about ' factor dense numbers '
I like your inspiring videos!
"What do all these items have in common?"
me: they're all measurment tools. Measure time, measure weeks, measure length, measure eggs
"They all have the number 12"
me: oh yeah totally I was gonna say that
You're not that far off though!
we liked using 12s to measure things because it was divisible, so 12 worked it's way into a lot of early measurements
my guess was that they were all related to time
you make this so interesting!!
I never knew I needed this but this is actually highly practical.
2520 is a nice number since it's the smallest number that can be divided by all numbers up to 10
27720 is also nice since it has the same property but goes up to 12
I wonder if there's a name for numbers whose factors can form a sequence from 1 to n. They're very factorial-esque.
"Hey, can I please buy exactly 1,260 grains of rice?"
excellent video. very fun numbers!
Cant wait for this channel to well and truly blow up.
The Practical Million makes the whole video worthwhile.
This is cool!
So cool, I wish my teachers made math this interesting when I was in school
2:08 Yes but then it could get a bit confusing when someone says “three tenths past/till” some hour. Memorizing all the possible fractions would be difficult when there are many ways to divide the hour. If, for example, I saw “14.42” on a clock I might not immediately read it as “three tenths till three.”
I do like using "a third past" or "a third to" though, mostly just to see people's reaction.
That was awesome
I recently decided I was going to express time in scores. 4:40 would be 4 'n' 2 score. Though now I'm not sure if you should say "2 score" or "2 scores" but I think the prior sounds better.
Yooo this video just blew my mind
we love highly composite numbers! such neat and handy lil guys
if you look up what superior highly compossite numbers are. you'll get a very technical definition which doesn't make much sense. so, as i was comparing them i realised shcn are those numbers whose divisors are a highly composite number example, the number of divisors for 12 is 6 which is highly composite. idk if it's an exact rule but it's fairly accurate.
Yes! Spread the good word of dozenal/doudecimal!
6:44 Plato was not worrying about dividing up votes
Explain
@@honeytubs Plato was not a democracy enjoyer
I shall propose a number system based on 24 called tetraseximal (Sub base of 8 )
10 -24 (24×1)
20-48 (24×2)
100-576 ( 24×24)
1000-1728 ( 72×24)
10000 - 8640 ( 360 x 24 )
Basically this system is more of Roman numeral style where instead of exponents it's more of an addition subtraction thingy hence the lack of uniformity. It goes like this in our base 10 system
24 , 48 , 576 , 1728 ,8640 , 13824 , 46456 ... and then back to 24 ^n to the beyond
Here's a couple of examples
To write 33 (DEC ) in base 24 (TSM).
All you need to do is find if it's close enough to 24 and no more than 8 spaces away from 24 .
Now 33 is 9 spaces away , so this sub base of 8 comes in handy and it's right next to 8×4 so this is how how write 33 in this system
(8×4)+1 =33 ,so everything from one to 0-7 is written as the same and from 8-15 is written with the same numbers from 1 to 7 but with a dash above them and 16 -23 is written with 2 dots
_
So 33 is 1 ×4 +1 = . .
11
If anyone cares what the equivalent antiprimes would be when accounting for the same number of divisors:
10 -> 6
100 -> 36
1,000 ->120
10,000 -> 360 (1 less divisor than 10,000)
100,000 -> 1,260
1,000,000 -> 2,520 (1 less divisor than 1,000,000)
I think if you start throwing "largely composite numbers" into the mix I think one could potentially come up with a system that divides much nicer into the next orders of magnitude upward.
I don’t know if it was intentional to shoot into the sun but it totally works for this channel and ONLY this channel lol
This feels like a combination of explosions and fire and vsauce 2
That's so cool! So that means Tau=6! degrees which is superior to 6!/2
13: one shall rise and one shall fall
14: the one that shall fall is you, PRIME!
I wonder if you were to sort all the natural numbers by this formula (numberOfFactors(N) / N) what that list would look like. I wonder if you could prove what the Nth element was in that list without looking at all of the infinite possible natural numbers first.
Call your formula f(n). There is no Nth member, because for any number n, there are infinitely many m_i where f(m_i) > f(n). As n goes up, there will always be numbers n with larger and larger f(n). For example, if we take numbers 1..120, the leaders are: 120:3 60:14/5 72:65/24 84:8/3 96:21/8 90:13/5 108:70/27 48:31/12 36:91/36 24:5/2. If we go up to 1000: 840:24/7 720:403/120 360:13/4 420:16/5 960:127/40 480:63/20 900:2821/900 540:28/9 600:31/10 240:31/10 504:65/21. If we go up to 10000: 5040:403/105 7560:80/21 9240:288/77 2520:26/7 7920:403/110 8400:1922/525 6720:127/35 9360:217/60 3360:18/5. If we go up to 1081080: 720720:248/55 1081080:640/143 831600:15376/3465 942480:29016/6545 1053360:6448/1463 997920:22/5.
The only highly composite number is zero, since it has infinite factors. Every larger number has fewer factors.
Amazing
What a stoatally awesome calendar
I propose that we call these anti-prime numbers, Amibote Number. Yes, the name is intentionally similar to Amicable Numbers which comes in pairs.
A bit of Classical Latin, "Amabo te" is dirrectly translate as "please", although it is less ambiguous than the English phrase "please". It has additional meaning of pleasing. So, Amibote Numbers are Pleasing Numbers! In the event that you use these numbers, you ("te") will love it ("ami" or genitive "ama") and it is good for you ("bonum").
This video is the worthy successor to Numberphile's base 12 video
Very fun video
12 and 60 are dicisible by 2,3,4,5(for 60) and 6.
This channel makes the math area of my brain spin fast
720720, 1081080, 1441440, 2162160, those are all video resolutions with the first three digits repeated!
I think you may have shown why the metric system is not the most desirable system for many applications.
For me, the biggest pro of SI is the fact all of the units are experimentally derived (though US Customary are legally defined in terms of SI units, and thus physical constants, now). Order of magnitude prefixes are just shorthand for scientific notation, so they aren't really as big of an advantage as is often touted.
Another thing is that scientists have to deal with floating point precision, so in the end base 2 reigns supreme.
this is so cool! i have to know why the copies are there though…
Time to crack open that dusty old box of primorials in my attic. I'm not exactly sure what they'll do, but they seem about right.
1,081,080 should be a baker's million.
9:29
Correction:
10,080! is not a highly composite number.
9:34 Woah, 10,080! That's a big number
5:00 lmao that ugly 12 cracked me up
Whew! You got the gift of gab! I loved
your dancing me through all that math; that was fun and instructive! Sign me up for combo class!
Incredible. Johnny Carson of mathematics!
This was very cool in a weird way
when asking for wrench sizes gonna start saying like 6/12ths
I had to look twice before I realised that this is not Explosions&Fire
I like 720720 = 7! • 11 • 13
Made me see that 1001 is 7•11•13 which explains why the highly composite numbers around a million all look like clones, because 1001 just contains a succession of primes - or I'm looking too much into this
It would be more compelling to also write them in their most appropriate numeral base.
I just can't repeat that 12 eggs falling down moment! 0:49
Why did he have to look in his notes to write down the factorials though?😅
"Anti Prime" - missed opportunity for a Megatron pun. 😁
If evolution had contrived to give us six fingers on each hand we would likely have adopted base 12 as our everyday number system.
I like to imagine that humanity would be a type 3 civilization by now if that was the case.
Apparently one or more of our ancient civilisations used base 60 for counting, using knuckles rather than fingers. I think it was the baylonians or sumarians but can't remember off the top of my head.
as soon as I looked at the description and title, I thought he was gonna talk about Base 12. But nope, Highly Composite Numbers (anti-primes).
Yes, those Number are so interesting : )
Your "practical million" is pretty close to what one might call a baker's million, if you will. 1000000×13÷12 = 1083333.3333333333.
I'd be curious to see what these numbers look like in a duodecimal system. Whether the patterns start to make more sense...
Why not convert them yourself?
@@michaelcherokee8906 I have, and they do, but not many people watching me.
@@jamescarruthers1967 Even in context, that sentence was nearly unintelligible.
@@michaelcherokee8906 I have converted them myself, and the patterns are quite interesting / seem less "random", but no-one is watching me, I don't have a UA-cam channel.
@@michaelcherokee8906 idk what you're on about, the sentence is fine in context, chill out
Could there be a prime before or after (-1 or +1) highly composite number?
Yes! In fact all primes except 2 and 3 are right next to multiples of 6, granted some of these aren't HCN numbers but still have a lot of factors
Every time I see these type of exercises, I want to see them in binary.
Let's write these in nice bases!
The best number is 0, because it can be divided by anything, except zero
I think I like "nice thousand" and "nice million" for these.
Actually maybe "neat million" feels just slightly more measurement-like.
Fractions are useful! Have people forgotten? Yes...thank you electronic calculators.
what's your opinion on the "dosonal" ( base 12 ) number system as opposed to the decimal (base 10) since the dosonal system is more devisable???
it's dozenal or doudecimal, not dosonal
@@gljames24 *duodecimal
@@amayans4230 no alot of ppl nicknamed it dozenal
@@tristantheoofer2 yeah, it can be called dozenal or duodecimal, i was just correcting spelling of duodecimal
Is there a symbol for lcmUpTo n = lcm [1..n] ? E.g. lcmUpTo 10 = 2³ × 3² × 5 × 7 = 2520?
0:29
No we didn't decide 12 was important. The Romans did. They probably got it from the Etruscans or the lucanians since they still counted in base 10. The Babylons decided that 60 was an important number that's why we have 60 seconds in a minute and 60 minutes in an hour, and why we have 360 degrees in a circle and calendars used to have 360 days a year before Julius Caesar standardized it.
??? He clearly was talking about the human race when he said "we."
And he was going to say "we decided that 12 eggs [fit good in a carton?]" or something like that, not that 12 was important.
@@mickeyrube6623 that's my point. [We] who made the decision was the Romans and the use of the number 12 in European culture is just a vestige of their empire. Like why breaking mirrors gives 7 years bad luck, or why we call the monthly money we make a salary while if you are paid per week it's called wages, or why people used to measure distance in miles, leagues and feet before the metric system. It's kind of like if you travel to East Asia the number 4 is seen as extremely unlucky. It's because of the influence of the Chinese empire. [We] didn't "decide" that it's just a vestige of history.
@@tnk4me4 ???? Your first comment literally says "No we didn't decide 12 was important. The Romans did."
What do you mean when you said "No?"
@@mickeyrube6623 Dude I'm not even sure about what you're confused about here. My comment was just me voicing that for more than 4 billion people the number 12 isn't as special as it is to western society and that it is only because of Roman imperialism that 12 is important at all.
@@tnk4me4 It was your timestamp. It's at 29 seconds. He doesn't say "we decided" until he starts talking about the carton of eggs, so I thought that was your only problem with the video. He doesn't even finish the sentence, so I thought you were being ridiculous. You should have put the timestamp at 28 secs.
Your argument makes no sense anyways.
When he says "we decided to divide the year into 12 months" it's because we have. We could only mean a few things here.
1. Literally him and at least one other person.
When you say "no, we didn't decide," are you literally saying you and the UA-camr didn't decide that? I think not. (I hope not!)
2. He means the whole human race. This is true. The entire human race has decided to officially adopt some form of calendar that has 12 months.
If you bring up some tribes in the Amazon or some shit I swear I will find you.
3. He means western civilization, which includes him, his culture, and basically ever one who is watching the vid who speaks English.
2 and 3 are interchangeable.
When he says "decided" he mean accepted as basic reality, or or come to an agreement that that is what we are going to go with.
If a philosophy professor said in a classroom "we decided that murder is immoral" would you say "No, we didn't decide that. The Sumerians decided that."
If you would, then I'm sorry. Either English is not your first language, you are an idiot, or you are being a pendantic troll.
"1080×1001", I thought.
Also, 720720 is a nice one.
Lets just go to a Metric clock and a Metric Calendar.
Can we also call 10080 a "Practical Myriad?"
About 180, you forgot its importance in geometry with respect to angle measurements of all triangles (vertices, that is).
hi! i think you wrote a number towards the end of the list wrong, because if as you said all of these are divisible by 9, 17297290 should not be on the list. very interesting video regardless, thank you for making this.
edit: okay i checked the list and turns out you only have a digit wrong, it should be 17297280.
Thanks for noticing that. I must have written a digit wrong by accident. I’ll add a correction in the video description
Highly Composite Numers... you could just multiply primes, right?