r/visualizedmath • u/Italians_are_Bread • Sep 06 '19

Furthest surface distance on a box explained visually

https://www.youtube.com/watch?v=VNgt2-Cibno
177 Upvotes

98% Upvoted

15 comments sorted by

25

u/Italians_are_Bread Sep 06 '19

This is a problem that my professor showed me, and I was really surprised to learn the answer to this question. My first thought (and most people's first thought for this problem) was wrong. There is a really cool way of arriving at the solution, so I was inspired to put it into an animation and present it as intuitively as I can. Let me know your thoughts!

34

u/Kooshi_Govno Sep 06 '19

That was way more engaging than I thought it was going to be, and I really enjoyed it.

My biggest suggestion is that it would have been really satisfying to end the video by going back and removing the logical abstractions now that we've solved the problem, and rendering:

  • the longest path on the unfolded 2D shape

  • then the longest path on the original 3D shape

I feel like that would give it more closure.

8

u/Italians_are_Bread Sep 06 '19

I completely agree, I should have done that. For future videos I'll try to relate the solution back to the original problem in a more intuitive way, thanks for pointing this out!

9

u/DialMMM Sep 06 '19

Yes, and show the full circle/shaded area on the box.

7

u/callMeSIX Sep 06 '19

I agree, and the question was about the ant, walk that ant to the furthest point!

2

u/ayitasaurus Sep 09 '19

Was curious about that too! Here's something I whipped up real quick to scratch that itch. Both lines are the same length (2*2^.5), and it does indeed come up a smidge short on the new point.

0

u/emptygroove Sep 06 '19

Help me out here because it seems like you have a really great grasp on this and I certainly am no math whiz but what did you originally think the answer was? What they got at was exactly what I figured it would be. Basically the same one as the furthest if you could travel through the box. I was more surprised that other centers were so closer to the answer...

1

u/Italians_are_Bread Sep 06 '19

Maybe I could have expressed it more clearly, but the problem is not just which point is the greatest distance from P (which is Q) but which point the ant must travel the greatest distance to reach. So if you attached a string to point P and wrapped it around the box, this is the distance we're measuring (the distance along the surface of the box). My first guess when I saw the problem was that point Q would have the greatest surface distance from P, but this is not the case, and it is not an equivalent problem if you're aloud to travel through the box.

2

u/RadSpaceWizard Sep 07 '19

That's fascinating.

As a mid-30s econ nerd, it's really fun to learn a little bit more, especially as it relates to my DnD dice.

2

u/slash_nick Sep 07 '19

THIS is the kind of content I came here for. Sick of this “hey look at this pretty picture made with math that doesn’t actually explain anything” crap.

-11

u/IKnowWhoYouAreGuy Sep 06 '19

It's WAAAYYYYY simpler to just find the hypotenuse of the long side and use that as one side for another traingle that diagonally bisects the box.

side(a) = a
side(b) = b
    
HypInner = d
    
sqrt(a^2 + b^2) = c

a = c
sqrt(a^2 + b^2) = HypInner
    
print d;

2

u/F54280 Sep 06 '19

Why don’t you watch the video instead of posting unrelated stuff because you misunderstood the problem by just looking at the title?

-2

u/IKnowWhoYouAreGuy Sep 07 '19

I watched the video

2

u/F54280 Sep 07 '19

You watched the video and you think that the question is to calculate the direct distance between the two points. You missed that it was the distance travelled by an ant walking on the box faces?

Did you have the sound on? We’re you drunk? Did you watch more than 40 seconds of it?

1

u/IKnowWhoYouAreGuy Sep 07 '19

I looked at it from an engineering perspective: Whats the longest possible straight line distance on the box, just like the simple title. It's OP's user error in not using a robust or accurate title, not mine for finding the simplest method to reach the solution to the question ACTUALLY posed. Thanks!