Views : 2,057,104
Genre: Education
Date of upload: Aug 27, 2019 ^^
Rating : 4.906 (1,237/51,199 LTDR)
RYD date created : 2022-04-09T19:53:36.008848Z
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Top Comments of this video!! :3
I was a machine designer for a few years number theory is geat for gear train design. Thanks for the video.
I designed a concentric speed reducer once. The ratio was 6.0025 to 1.
My boss said why not 6 to 1? I said because the square root of 6 is an irrational number. He asked why and i said because the number of teeth in the 1st gear is 20 the second is 49 thats on the same shaft as the 3rd gear that has 20 that drives the 4th gear with 49 teeth. Fun and interesting.
Prime numbers with gears are cool too.
If you have 2 gears with number of teeth 12 and 60
This means every tooth in the gear with 12 will match every 5th tooth and only that tooth per revelotion and not engage any others this increases ware on the teeth. But in the above 49 is divisable by 9 and 20 divisable by 2 and 5. There is no common prime between 20 and 49. Because 20=2Ă2Ă5 & 49=7Ă7. This means that each tooth of one gear will eventualy mesh with every tooth of the second gear. Therefore spreading ware over all the grear teeth.
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The 12 spoke wheel reminds me of music theory and the circle of fifths, a model that visually represents harmony and dissonance between different tones of sound(music notes). The circle of fifths, comprised of the 12 notes of the chromatic scale, visualizes intervals that would fully revolve a musician around the chromatic scale. These intervals, despite whatever root note you start off with, are constant in all musical harmony and dissonance.
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A professor once made us write out our work on graph paper. One character per cell. If the character drifted out of the cell, the grade was a zero. He specified every single minute detail. It was quite controlling.
However. He didnât specify what number system. I wrote the entire problem, and solution in Roman numerals because he didnât specify Arabic numerals.
He returned my paper with:
âTouchĂ© 100â
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at the beginning of this school year i discovered modular arithmetics in the notebook of an older student, the first thing i did with the power i was just given was make an unbreakable code to send messages to my friends, for those interested what i first did was converting text to morse so - and . then changing it to binary 0 and 1, and then attirbute any number wit a rest of a when divided by an integer x to , same for 1 with any number congruent to b mod x, and then the only thing you need is the key looking like this [x,a,b] to crypt or decrypt the message, it was stupid, it was not useful at all, it was not optimized either, But oh my god it was fun
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@zachstar
4 years ago
2:50 should be "For any composite number x one of its prime factors must be less than OR EQUAL TO its own square root." (the 'or equal to' part only would apply to primes squared but still needed to be included). I was so focused on my specific example and wasn't thinking lol. Thanks to those who caught it and hope you guys enjoy the video!
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