Views : 581,745
Genre: Science & Technology
Date of upload: Feb 23, 2020 ^^
Rating : 4.957 (234/21,322 LTDR)
RYD date created : 2022-04-04T10:47:49.199415Z
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Top Comments of this video!! :3
6:18 This mod 10 design was brought to you by, brilliant
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Hi. I discovered these exact patterns a few years back and it feels strangely validating to have someone else discover them too. I would like to be the first to have discovered these things but that's highly unlikely since there's nothing new under the sun. Let me recommend that you stop limiting the periods to bouncing within a circle and give them the angles of a triangle or a pentagon or a hexagon. Whatever polygon you like. You will see some very beautiful and awesome line designs, there's one that even looks like a profile of a brain. It's fascinating. Also, I used a different kind of modulo that does not allow zeroes to be produced, I guess you could say it is an 'inclusive modulo' since it produces the dividend if the divisor fits exactly. Be careful though, you may lose many many hours watching the designs produced:D
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5:30 When you just want to do mathematics but accidentally start summoning a demon.
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9:42 It contains 1, 3, 7, and 9 because the chosen mod is 10. Except for two and five, all of these numbers are coprime with tenābecause primes are necessarily coprime with every number that isn't a multiple of themselves. Two and five are the only exceptions because they are the factors of ten.
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Hi Jacob. I found some interesting ones.
Just woow:
For mod = 675
and every [fib+fib] * 947
with a fib start position of 6,7
Butt/Mushroom:
For mod = 2529
and every [fib+fib] * 2
with a fib start position of 0,1
eye:
For mod = 2529
and every [fib+fib] * 2
with a fib start position of 2:2
Infinity mandala:
For mod = 376
and every [fib+fib] * 2
with a fib start position of 2:2
Regular mandana:
For mod = 688
and every [fib+fib] * 662
with a fib start position of 2:8
I also made an online demo where everyone can experiment with values I tried linking it before but it didn't work, will now try in the reactions of this comment.
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10:14 I actually used this framework a couple years ago to solve an interesting puzzle I came across at a conference: āarrange the digits 1 through 16 so that every pair of digits sums to a perfect square.ā I used this visitation method to find other sequences of digits, 1 to n, for which this is possible, and their respective solutions. Turns out theyāre connected to Pythagorean triples, and the visitation of all possible sequence of digits makes nice parallel lines.
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@jacobyatsko
1 year ago
Some notes and responses to common questions: - The video was made using Adobe Illustrator and After Effects. I would not recommend doing a similar video this way, as it requires laying out every shot perfectly beforehand and animating every line more or less individually, rather than relying on a coding background (I have basically none) and a program that could simply generate the animations instead. A drawback of the way I did it is stuff like the missing line in the decagon that people have pointed out at 0:50. - Despite looking similar, I assure you there's no connection between the 10 graph and the Brilliant logo :D. (Also, what do we call these images? Designs? Graphs? Patterns? Symbols? Let me know what you think) - Could this be done in 3D? I'm not exactly sure. You could pick a point on the sphere to start, but how do you go about distributing the rest of the points on the sphere, in a regular pattern? It's easy to do it with a circle because you just go around the circle. But with a sphere, you have to choose between two axes of movement. - Thanks to everyone who reassured me that the mod operation can apply to fractions as well as integers!
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