The Hidden Patterns Inside Spiky Shapes
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- Опубліковано 28 вер 2024
- Let's look at some spiky star-like shapes (including original animations of them moving) and see their cool connections to clocks, prime numbers, and more. Thanks for watching! Leave a comment with your favorite shape.
Combo Class links:
Bonus Channel with more videos: / @domotro
Discord: / discord
Reddit: / comboclass
Patreon: (coming in December)
Some topics in this video include: coprime numbers, shapes (similar to what's known as "star polygons" although sometimes those are defined slightly differently), other numerical bases such as Base 6 and Base 12, the last digit of prime numbers, modular arithmetic, clocks, broken desks, and more.
Disclaimer: Do not copy any actions you see in this video. This is for educational purposes.
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 Bonus channel. Thanks for coming to Combo Class!
Hey, since a lot of people requested that I make a Patreon, here is it (with various cool rewards for different tiers) www.patreon.com/comboclass
Make a grade -0.5 of you showing us cleaning up and get everything put together and setting out the fires, it wouldn’t do as well but that’d be interesting
fr
No way, this set up is perfect
Yes
base 12 and prime numbers? Dango this class is EXTRA combo'd
So a base-prime system (base-3, base-5, base-7, base-11, base-13, … base-769, etc.) would actually be a major headache for prime hunters, since any number not ending in zero is potentially prime.
The whole numbers less than and coprime to 24 are 1, 5, 7, 11, 13, 17, 19, and 23. Their squares are 1, 25, 49, 121, 169, 289, 361, and 529. Each of these are congruent to 1 mod 24. That means that for all primes greater than 24 (in fact, all primes greater than 3), the prime's square will be 1 greater than a multiple of 24.
Love your content and this is easily one of your best videos, I wish you had more subscribers, I recommend you whenever relevant
Underrated channel, u just earned a new sub, I'm literally watching this at 3 AM
I love your vids! I’ve been showing my friends them because your energy is just *perfection*. Keep doing what you’re doing! :)
This video made my day! Great content!!
I've come to a really similar set of discoveries analyzing the twelve tone system in music! This is amazing!
I love the comedy that's built into your videos what with everything falling and collapsing and stuff, but make sure that nothing hurts you super badly! 😆😆😆
And keep up the good work!!
this guy never ceases to amaze us
Dimotro do you live in an area where its always pretty warm outside because otherwise I fear Combo Class may have to be moved indoors for the next few months
No snow in my area so apart from when it rains my outdoor classroom should still be ok :)
@@ComboClass ok awesome, that's good to hear
lmao "mod 11 - just imagine these ones" cracked me up
Imagine winning a messed up desk competition against scott the woz only to find out this guy is the final boss
OMGoodness
I went to high school with Scott the Woz! I didn't know him super well, but some of his friends in his skits I knew better.
Amazing.
Cant wait till your entire fence is just clocks 🤝💯
love the credits scene
Is this what a mad scientist would be for math?
Either way, good stuff.
Only 4 days late! good job UA-cam algo! Guess I'll keep dinging the bell until it gets the picture lmao
This is the one UA-camr I would want to meet in real life
very spooky, the wilson's theorem
3:19 an odd hour like 2 in the morning? really any time in the middle of the night would be an odd hour to film this. but i dont see how that would affect the math.
Is there any way to make a base 1? because then that wouldn't have any primes
Dude this is crazy
Do you realize that any prime / 6 will have a .166 or .833 ?!?!?! Having those don't guarantee that the number is prime, but not having those guarantees that it's not prime... Mind blown
There is a formula which will give you all results in the last column, testing any N.
9:36 we all know what this "sort of star shape" is actually called... Right?
I think that that would looks modern Einstein
With all physical effort just for us to learn about Modular Arithmetic and Primes! ❤
Tip watch this at 1.75x speed
No comment
This lesson has some interesting music theory applications. Western music can be understood as a mod 12 system. And the intervals between pitch classes can cycle through all 12 pitch classes in only two ways: by half step, or through the circle of fifths--or their inversions. The other intervals make augmented triads, diminished seventh chords, whole tone scales and tritones, all of which are cycles that include only 3, 4, 6 and 2 pitch classes, respectively. Hearing these relationships might be helpful for some learners with musical inclinations.
Yeah I love music theory and will be making some episodes about it in the future. I need to turn one of my clocks into a giant circle of fifths haha
@@ComboClass I'm excited to see that clock! There is also the tangential issue of factors of 2 and factors of 3 being coprime. Since intervals based in 5ths rely on vibrations of lengths based on 2/3 and octaves based on vibrations/string lengths of 1/2, the history of how to finagle this to something that SOUNDS good is pretty interesting. In other words if you cycle through 2/3 intervals you will only approximate an octave after 12 cycles...but we've tweaked this so no one actually is able to notice this discrepancy in practice.
@@jasmint6703 If you aren't already familiar with ViHart's videos then you definitely should check them out, I think you would find them fascinating. The one titled "Twelve Tones" in particular.
This man is an absolut legend.
Almost brole his leg for our entertainment
*for our enlightenment :D
I struggled with arithmetics before but since I discovered your channel I feel so much enlighted ! Thank you so much for sharing you passion for primes numbers, mods, and all the rest !
Professor Domotro getting himself injured in the pursuit of teaching knowledge. What a legend.
Absolutely loving this backyard mathematics professor. So glad I found this channel.
Hell yeah, new Combo Class video! :D
Just watched, RIP your leg LMAO
Rip leg 1201-2022
You have one of the coolest channels I have ever seen… you really point out some of my favorite aspects of math!! I am very grateful I found your channel
If you went through the process multiple times and set the base to various highly composite numbers, could the ratio get any lower than 1/3? Because 6 and 12 had the best ratio and they are highly composite, would the trend continue or is 1/3 the lowest.
There are some mods/bases later with even smaller ratios (although if you were using them as numerical bases they might be less practical). For example, the only numbers coprime to 30 and smaller than it are 1, 7, 11, 13, 17, 19, 23, and 29, which is just 8 out of 30 numbers
Man this is such a good channel, you're so unique!! Are you a teacher professionally lol?
Currently I’m a private teacher/tutor for some students. I’m also going to start offering online group classes in math and stuff which will be available on the patreon I’ll be launching at the beginning of December
If every class is like a Combo Class, then the whole class would get an A,
I came here cause I was bored, came out amazed and excited for more
Thank you! This gave me some new perspective on a problem Im solving!
Interesting how numbers that are coprime to n, that aren't 1 or n-1 make spiky intersecting shapes that touch every node.
It’s always a good day when Combo Class uploads a new video! 😄
Love your class man! I made a poster looking at the 1st 144 numbers like this. I call it the 12x Spiral.
Which one had the lowest proportion of coprimes?
To check if number is prime I was divising it by numbers up to this number root, for obvious reasons. I believe that by making the mod checks, like in this video I could improve my prime checker alghorithm. It would be more code and memory complicated, but I believe it would be faster. 🤔
second comment on your video but I love your physical comedy bits, they help the math bit so much by making math fun in any way shape or form; you're one of the only people I know who makes me feel like that, god work.
I’m going to be starting grad school in math soon and it’s so nice to have such high level concepts explained in these easily digestible videos! Thank you!!
It’s amazing to find a channel that covers topics that are my niche interests!
Like the animations, good touch.
God i want to like the video but it has 456 likes
A post! Good day lol
hey i know you!!
@@MayorVideo My channel, or do you know me from the comments on these videos?
@@Asterism_Desmos He has your IP address. 🫢
… 🤨🤨
@@unclegardener and family somewhere underground
every time i take a deeper look at the classroom i see something new and obscure i love it
happy 16:16 video
god bless combo class the funniest math youtube channel out there
Be careful out there with that desk dude! We need more combo class!🤣🤣 great vid as usual guys!!
Very interesting to see these as visual representations of cyclic groups and their generators. I am coincidentally self studying abstract algebra at the moment, so this is great!
Dude, you're a gem on youtube.
What's special about 12 that we use it for clock faces anyhow?
My suggestion in a word: tides. Starting with low tide, a clock divided into 12ths could tell you successively what proportion of the tidal range had been reached at a given time until 6 at high tide, and while it recedes until 12 again. 1 o'clock tells you that 1/12 of the range has been reached, 2 o'clock that another 2/12 has been added (so increase in height and water flow is speeding up), at 3 o'clock that another 3/12 has been reached and we're now at maximum flow speed. By 4 another 3/12 has been added. The speed would be diminishing but the height would still be increasing till 6 when the tide starts to recede again. This change in flow speed is represented by the sequence 1 2 3 3 2 1, which of course sums to exactly 12. If the clock face were divided into 16 say, then the sequence would be 1 2 3 4 4 3 2 1 which sums to more than 16, and if 10 the sequence would be 12321 which sums to less than 10. The high tide to high tide cycle seems to roughly match the midday to midday cycle at 2:1, so 2 lots of 12 covers the latter. Tide, both high water and flow speed, must have been of immediate practical importance to early shore based and many riverine civilizations, enough to decide the number of time division units you were going to use over the tidal cycle.
The artistic idea of this performance is 11 out of 10. For me it does in some sense represent how we try get focused on a problem inside our brain which is full of valuable throwaway thoughts. We can not clean it up completely but just grab the part we need and work with that. An then for a moment all the noise gets into background for the time you are in the thinking process.
voted "professor most likely to contract tetanus while delivering a lecture," by 23k students currently enrolled
love ya, bro!
Do you know if there is a more efficient algorithm for searching for primes using other bases, such as 6 or 12?
Injury type: occupational
Occupation: mathematics
So, this proves that infinity is prime and that a circle with infinitely many points would have all of those points hit by any and every prime number of skips.
really glad the algorithm gods blessed us this time. love the quirkinesss of your vids!
His videos are perfect representation of my life, total mess but there's value if you wish to see ❤️
you are simple amazing. Keep doing videos please, your content is unique :)
You're like one of those Berlin crackheads. love it
I am not going to stay safe. I am going to do drugs tomorrow.
make your new shows with this stylee.....
Show us on the chart: where did the coprime touch the mod?
You could represent it as ≡|X|
Wounded in the line of duty 😭 but his pain is our gain!
dude is just a maths lover like me lol
Great video as always
Circle of 5ths
You need a stunt double!
Great topic ...
Domotro: gets hurt
Also Domotro: stay safe
😂
Isn't there any number high enough to be used as a base for numbering big numbers but having few enough coprime numbers to help us hunt primes? 97 sounds like a good start!
Great stuff, also someone was pissed in a car :D So much honking going on!