Video

16:07 2^Aleph0

1:16 the sum from n = 0 to ∞ of 1/2^n

You good man? I noticed that little "I hate this channel" in the corner around the 1:55 mark. I hope you're alright

Cool, so "real gears" are floating point numbers, and "nonslipping rolling wheels" are integer numbers??? THAT IS SO COOL!!! Instead of a clock with continuous motion, I can have a clock with lag!!!!!!!! Bro.... Computers do that!!!!!!!! 5 5 5 timer bro!!!!!!! Yay😁

I have no clue what I'm listening to but it's super interesting

Thoroughly enjoyed this one ❤❤

15:35 D.I method: am I a joke to you?

now find out how to make a rack and pinion

As an engineer, most of the time it is just using square teeth or triangular teeth, giving the gears the right number of teeth to get the ratio we want, and adding lube. The wear on gears will basically do what your algorithm does, but to both of them. That and that paint brush thing.

Math X Engineering. My favorite ship

Those who like Taylor’s because they are Swifties | | V

I love the sponsored segment "people should learn to think critically, but that misinformation should be buried and filtered by politicians, after all, everyone knows politicians are non-biased and never make decisions based on their own personal misconceptions." If this guy cared about the truth and people learning to think critically he wouldn't then follow that up with "but we do need censorship." Honestly, I will never understand how people can have full faith and confidence in their own opinion while also fearing conflicting ideas out of fear that they will supplant their own when forced under comparison.

once you said 1/x was close but (0,infinity) doesnt count, i just thought adding 0.1 or 0.3. 1/(x-0.1) was an easy solution

the cardioid makes an onion. the ❤️ makes an 🧅. is this the mathematical connection between love and Shrek we've been looking for for the past 23 years?

Mechanical Engineer here: Your negative space to determine the shape has a problem in that the "peaks" and "troughs" of gears don't touch. Making them touch causes problems in their function. If I recall correctly the problem is the gears will bind. Gear contact is a more complex interaction then you seem to realize. Gears can drive in both direction, your clover gear can't drive the square gear without perfect friction. Gears work better with lower friction not higher friction, those are not gears. Without friction the clover will rotate the square so the close side is perpendicular to the line between the axels and then spin freely wit the square staying stationary. The contact point on gears jump, they don't trace out the shape of the gears in one continuous motion. In fact if your gears don't rotate both ways you only need about half of each tooth! Less the half of the perimeter would be a contact surface! I think you designed noncircular friction rollers. Which are not actually gears. Some people list them as a type of gear but they just are not; although they are a direct competitor for the same applications. Edit: you comment on the similarity to the wheel for a square is your "gear" is allowing some slippage to adjust for constant angular speed by allowing specific amount of slippage without actually supplying a mechanism to control the amount of slippage. In a gear the slippage is controlled by the geometry of the teeth, that is why teat have their peculiar shape.

"Tell me that's not cool" Me: That's not cool

conected because it exists and is connected just infinitly much

i would think that we could observe that if the wheel moved to the center then was moved a bit over it would there on the line and that would be a simple observation

isnt it just 3*sqare(2.5)x^2.5

My feet don’t have zero width unfortunately

Epic!!!! ❤❤❤

“ShIfT gEaRs” 🤓👆

That was amazingly put. Congrats, I really learned from it.

It's cosine not sine wave!

This should be a 3b1b SOME submission...

Math and engineering majors are on a whole different level dude. You lost me like 9 minutes in

My favorite function is $$f(x)=\begin{cases}x&x\in\mathbb Q\\x+1&x otin\mathbb Q\end{cases}$$ Changing to complex numbers does not help here.

i'll only save it for later lol i am only at 3rd year college for bsmath... i can't take this kind of math yet lol

26:20 You've created an anti-cam. I hate it. 😂👏👏👏👏👏

hi, can you tell me wich software?

I love the visuals But if you were to ask me about the math I’d go Uuummm… ummmm mmmmmm Idk

I'm sure this wouldn't actually be practical, but if all you need is constant rotation at the input and the output and not necessarily at every intermediate step, you could use wheels as gears, right? It seems like it should be possible to cancel out all the jerkiness so that the input and output rotate together smoothly, with only internal gears moving at non-constant rates.

great video but I will say it would have been nice to see the gear partners spinning like gears once the problem was solved, instead of rolling around each other. still great stuff though keep it up

I hate it when my gears slip but in the wrong way.

It's pronounced 'envolope'.

Hey, it's the Rubix Cube!

18:49 I've yalling "bezier curve" all the time lol

Isn't the rotation property of complex numbers more a result of multiplying any number pairs by coordinates on the unit circle, rather than the fact of one of the coordinates being imaginary?

when youre so fed up with scrolling thru tt that youre watching how a gear is made for any shape 😭 (its interesting tho)

What if R is not constant and is a tensioned spring instead?

The slippage is more perpendicular to the axel-line for the gears than expected considering the hook the video claims in the beginning, but also the gears in the example seem to break contact before they would drag against eachother by dezign Also, misinformation should be determined by the listener and not governed by a central body or even someone else, that’s how fascizm begins, hence The First Amendment

another rotation to get dialup

When it got to the envelope I stopped understanding but that was probably my fault cause I spaced out when he was talking

cannot be asked to watch half an hour of yipyap someone tell me where he answers the question that is the title, which is the only reason i clicked on this video, to find out what gear shape meshes with a square, i click and i'm greeted with a half hour long video, it doesn't require 30 whole minutes to tell me what gear shape meshes with a square.

This was too difficult for me, i don't have the mathematical backing to understand some of the concepts. Sad because i really wanted to get it.

Imaginary numbers looks like x,y coordinates. Why its written as a+bi when its just vector (a,b)? Its main feature is rotation by multiplying on i, which can be done with usual vector with similar rotation rule.

great work/presentation! you got a new fan ;)

Beep boop beep boop beep

one of the best videos I've seen for some time

I would argue that the curve with the line along the y-axis is still connected with the path definition (Disclaimer: I am not a mathematician, so feel free to correct me if I'm misusing terminology; more notes at bottom). There are only two possible scenarios for the "endpoints" of the separated curves without the vertical line (these "endpoints" reflect the y-value of the function immediately to the left and immediately to the right of x=0). The endpoints are either located at effectively the same point to create what would normally be a removable discontinuity or located at different y-values to create what would normally be a jump discontinuity. These types of discontinuity usually refer to functions where the limits at the x-value are known. In this case, the limits from the left and right are undefined due to the oscillating pattern. However, the function is bounded between two y-values, so we know that the "endpoints" of both sides will each have a y-value between -1 and 1. This would mean that adding a line at x=0 that ranges from y=-1 to y=1 should attach to both disconnected "endpoints" regardless of where they are positioned relative to the y-axis. Although we cannot determine the precise values of the path function as it meets the y-axis, similar to the way that we cannot determine a finite limit at x=0, an indefinite path function must exist that traces the vertical line to connect the two segments. Note: This is the result of a bunch of concepts and theorems back from Calculus 1 that have been scrambled together from memory to try to make something that resembles a decent explanation. The main inspiring concepts aside from discontinuity were the Intermediate Value Theorem and the Squeeze Theorem. It's also 2:30am as I'm finishing this (I got hyperfixated on number stuff again), so please let me know if there's something that doesn't make sense, and I'll try my best to clarify later