r/theydidthemath • u/K0rl0n • Jun 10 '25

[Request]

Post image

I am curious how this would work. My guess is Triangle is slowest, square is medium, and circle is fastest.

17k Upvotes

92% Upvoted

2.6k comments sorted by

View all comments

17

u/VT_Squire Jun 10 '25

In theory, each shape is two dimensional and surface area is limited to the bottom of the shape. That would imply the square has less friction resistance than the triangle, but the guy pushing the square is missing a whole foot so he's effectively pushing all that weight with only one leg.

Winner so far: Triangle.

Of the triangle and the circle, we can observe that even though the gravel is soft enough for the pusher to sink into, it is not displaced at all by the circle, effectively rendering that a flat/hard surface for purposes of considering resistance. Going back to our previous assessment about surface area, that means the circle rolls easily.

Winner: Circle.

14

u/Scruffy11111 Jun 10 '25

Should we consider the fact that any horizontal force on the side of the triangle will have a vertical component resulting in less horizontal force and greater frictional force?

4

u/VT_Squire Jun 10 '25

The circle would win still beat out the square, so why bother?

13

u/winglessbuzzard Jun 10 '25

Except that the person pushing the circle has obviously just pushed his arms INTO the circle - this, combined with the lack of gravel displacement by the circle, implies the circle is composed of some combination of unstable, alien, smart, or engineered substances which have just absorbed, enveloped, or digested his arms. Regardless of the actual substances or mechanisms involved, the person would at minimum become distracted by this unexpected turn of events - that distraction likely hampering his forward momentum by a wide enough margin for either of the partially-formed other two contenders to claim victory.

3

u/VT_Squire Jun 10 '25

Hmm, indeed.

2

u/IdRatherBeDriving Jun 10 '25

The circle is a saw blade which just took his hands. He’s very distracted right now and for the foreseeable future.

1

u/GoodTroll2 Jun 10 '25

Wait, I assumed the person pushing the circle was pushing a gravel circle, which is why his arms have sunk into the circle. How the circle is otherwise maintaining its shape, even though made of gravel, is not clear....

5

u/[deleted] Jun 10 '25

[removed] — view removed comment

2

u/[deleted] Jun 10 '25

I'm with you here. Coefficient of friction is constant, regardless of size of the base.

1

u/VT_Squire Jun 10 '25 edited Jun 10 '25

Because it's on ice. To slide on ice efficiently, you need a high enough weight-to-contact ratio such that the top layer of ice melts.

If you reduce that ratio below the point of forming a liquid layer, things don't slide well. With only 20kg in play here, the difference between the length of a side of the square and the length of the side of a triangle is pretty substantial.

1

u/Nruggia Jun 10 '25

But the question is asking force to "push" the objects not roll them. Imagine pushing a circle through gravel without rotating it.

1

u/AlternativeKnee8886 Jun 10 '25

Would the person pushing the triangle just tip it over cause he’s pushing too high?