Відео

I thought it was obvious that the choice of hurdle height and distance between hurdles affects the build of the best hurdlers. Was this a surprise?

Love your videos, man!!! Cheers from brazil 🎉

The first answer is intuitive since a single square contributes less of the roll's volume when the roll is bigger

8 kids?! And you're smart? Singlehandedly counteracting Idiocracy!!

The math overkill overkill would be to solve for a generalised base radius and height (or base:height ratio) and plot the optimal theta for the ratio. I wonder how that graph looks like.

I think the real question is why use a sheet of tree pulp to wipe your bottom, sometimes not getting everything out, instead of using good old water to get every nook and cranny cleaned

it depends how much time you spend accelerating again (as you mention at the end, due to falling off the track, hitting things, braking, etc)

Surface tension

I am currently studying to be a teacher and these are the types of problems we teach in high school. Using trig functions for simple problems such as these always hurts since student don't keep track of what increases and decreases plus we do not allow calculators or any other tech. Instead you could use h to be a varable and find r simply by Pythagoras theorem. Then once you find the maximum just solve for theta. Way easier.

What if.. Hear me out.. you stop moving or walk back.

6:37 ah, that name brings back some trauma. A professor cursed me by requiring LaTeX, and now I can never leave its infinite frustrations behind.

I have thought of this so many times but never gotten to the answer

You know, you could have calculated the volume of the frustum very easily a third way: calculate the cross-section area of the top, the bottom, and the middle, and then use Simpson's rule.

Easy Fix. Set hurdle height and separation as a ratio of each runner's height. So each runner is running a race proportionally challenging to their height.

Small rollers rise up

The problem should give an angle that the sauce piles at, not a height. The viscosity will affect how it can pile and it won't be a cone, but it would be better to approximate it as such than to not.

I find the choices you made a bit confusing. You use the area of length•thickness which is the area of the EDGE of paper. But whenever normal people talk about area of toilet paper, they typically imagine the SURFACE area of the paper, i.e. the functional side of the paper. This will certainly lead to a lot of confusion from the viewers. It might be a good idea to make this point more explicit, so that people don’t get lost. Alternatively, it might have been better to talk about the volume of paper, which is more natural for some.

As a former nerd who just want to live a life without much work, but still needs the answers, This was my method. If it's a circular cup, obviously just worry about that cross section diagram, more the area, more the volume. To maximize the area of that shape, we need the triangles on side to be bigger. But that also reduces the area of the middle rectangle. The average guy would just guess 45°, but I actually thought a little bit, area of triangle is ½bh so to maximize that, b=h should be true. That means it's a triangle with 90°, 45°,45° as the angles.🤷🏻‍♀️ Now obviously the rectangle got smaller, So not quite 45° then. Let's settle at 40°

People who use water

In the metric world your math would be a lot easier.

For those who pee standing up, where should we be aiming to minimize splatter? Might be out of the scope of what math can solve for without physics, but thought I could ask anyway.

what sociopath is a big chooser??? you're manually sliding the thing because you wanna take from the bigger roll????!

I love videos like this, where it's just "here"s the mathematical answer to a weird problem".

I was also beaten as a child. With calculus.

What else that would be interesting is how much toilet paper is on a regular roll compared to the large commercial rolls in the public restrooms, taking into account the core radius and the entire radius?

Hang on. I actually HAVE heard this problem before, years ago. Couldn't tell you where, but I'm sure I've heard it!

I shared this with my cat, and now she walks around like she owns the place.

Tall elite ILCA sailors?

Cool video!

wait wtf 70% of the world doesn't have regular access to toilet paper?!?!?!

Very useful video, thganks! I'll do the exact opposite so I can leave someone without anything

At 6:00, it might help to set R to be the initial radius (a fixed value), then for r=1/2×R or r=1/3×R, we see the roll decreasing twice or three times as fast, since dr/dt is inversely proportional to r. It looks like you have r as the variable for current radius, but also use 1/2r and 1/3r as the current radius.

How about what is the optimal way to hold the max amount of water in your hands?

I was actually going to make this same video! You beat me to it!

did not ask

What is math?

You want us to adjust the hurdles for every racer? ... your failure is assuming Simone Biles doesn't kick our collective tooshes in every ... single ... Olympic ... event ... shot-put, swimming, equestrian, sailing; you name it ... Simone Biles wins ... she's a trained athlete and we sit all day watching UA-cam videos ... what next, grown men on the girl's volleyball team? ... saddest day of my life was listening to Tom Hanks make Simone Biles cry on National Public Radio ... what a mean person ... everybody loves Simone...

Tons of Math...in game.... definitely Path of Exile.

I've thought about this before lol Yes, I'm a math nerd

What about 400m Hurdles?

I'm 6'2" with long legs, looks like I made a mistake

i absolutely hate how every youtuber insists on jamming in clips from movies we've never seen to ruin the flow of their videos

I have no idea why i watched this, we don't have arby's or self sauce stations in my country lol. Still enjoyed the video though!

Surely to be inclusive the hurdles need to go, the gender discrimination needs to go, the age discrimination needs to go, and mechanical, powered aids permitted, offered free to all, to allow those with limited mobility to compete, along with the unfit and poor, then replace the stopwatches with a raffle of entrants, to create an elite inclusive, diverse event. I suspect the viewing figures may suffer, as the world is a biased place. 😛

Just when you think the video is done, he includes new variables to solve for

If I may propose a variant of the problem... Sauce sticks to things. Like food. We like it for that. But sauce also sticks to the edges of its container. Lets say that all sauce within one millimeter of the container's physical edge is unusable. (For sake of argument, say that using it would require dipping the food up against the edge of the paper cup, which scrapes off tiny bits of paper that ruin the sauced-food.) What's the optimal angle under this condition? How much of the sauce (as a proportion of the total amount in the container) is still usable?

You tricked me into listening to a calculus lesson

So you’re saying there’s a high barrier to entry? (I’ve been making this joke for years oops)

who cares about hurdles, noone watches that shit, everyone is just there to watch the 100m

There is another sport where arbitrary height based decision changes the sport - american baseball. In layman understanding - there is legal zone you have to throw the ball, that is defined not by the person throwing the ball, but by the batter from the opposing team, more specifically by their limb/torso etc. position and size. Because of that, the leagues ban dwarfs from participating, as it creates throws that are impossible or at least bad for throwers, making a team of dwarfs potentially a world champion winning team, due to impossible throws for the opposing team. To hear less botched explanation you can view "Why MLB Banned Dwarfs From Baseball" here on youtube.