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Zach I would love to have the Desmos link that you used to create the circles.
@bundamole2658 Says:
What I first thought was to create a regular poligon with the number of sides being the number of fountains and then going on the midpoint of every one of the sides and putting a fountain there. Could someone please explain to me why this work or why this doesn't work?
@hennie3663 Says:
Wasted 7 min, saw the answer immediately
@hssaugat1589 Says:
I didn't solve it mathematically, but still got a similar solution, a star made of two triangles but touching the circumference would be dumb so at around 75% closer to circumference from centre and obv 1 in centre
@wydadiyoun Says:
Just when I wanted to comment "prove it" you gave the proof! thanks!
@Jiyoon02 Says:
My guess before watching the video: 0.5km
But I can't prove it soundly on the fly. Hopefully will find it in the video
Now Ill go back to watching it.
@TwilitbeingReboot Says:
"Shopping mall" seems like a much worse analogy than "public park".
@cocozer833 Says:
wouldn't taking 1km times 3.14 divided by however many fountains you have give you about the right answer?
@musicmaker368 Says:
Here me out ... put them all in the middle. Constant 1km at most from anywhere
@jamesthomas6984 Says:
Prevideo guesstimate:
place one in the center then set the rest equidistant from eachother in a circle at 0.5r from the center?
Postvideo:
Oh mother of god.
@Woodside235 Says:
Thinking about how you could make an approximation using a simulation where the fountains can move around and are repelled by one another.
@louf7178 Says:
Cool application. Things like this could also be applied to fire hose or extinguisher locations.
@hisheighnessthesupremebeing Says:
Is this another case of Americans not familiar with the metric system or do you guys have Malls with a 1.24 Mile diameter?
@agranero6 Says:
ohhh departing from any point!
@niconeedsanap8130 Says:
Heres the problem, malls don’t have water fountains to tempt you to buy it
@Derkeller7773 Says:
I started watching the video and seemed interesting then I realized I don’t care for maths or geometry or malls
@dumnor Says:
What if count people? Each area has different density of people so putting water fountain in the middle of storage would make no sense.
@jackrain0461 Says:
I wonder how this can relate to the traveling salesman problem
@Tadesan Says:
Furthest away from the black people.
@Madtrack Says:
Man this is so simple yet still so hard. Surely a predicted population density map as well as a layout of walls would make it more realistic and applicable. And of course as a classic engineer I will solve it via computationally brute force.
@jasonpatterson8091 Says:
Tried 7 evenly spaced fountains, got around 0.555km walking distance max. Tried 1 in the center with 6 evenly spread, 0.5km max walking distance (with centers placed at sqrt(3)/2 from the center, for extra fun.) No idea how to prove that that is optimal though.
@abstragic4216 Says:
I arrived at the same solution from a different direction, with 6 abutting equilateral triangles surrounding the centre of the mall. The size of the triangles was determined by looking at one of them, and constructing a line from mall centre through the centroid of the triangle and extending beyond the outer side an equal distance from triangle centroid to outer side, to reach the mall boundary. Some simple Pythagorean geometry gave a triangle side length of √3/2km, so the 7 fountains would be arranged with a central one and 6 at a distance of approximately 866m from it and spaced at 60° intervals.
@fatalheart7382 Says:
The shortest distance between an infinite amount of points is the circumference of a circle. If you take any amount of randomly distributed points and try to adjust their position around the center of a circle, you'll find the shortest distance in the polygon's sides.
@Thardoc Says:
Great example where the math is hard but most people can intuit the answer in seconds
@danielbbg6199 Says:
hexagon with one in the middle
@mondrider994 Says:
How many colours does it take to taste math? Square
@Tasarran Says:
I instinctively knew this was going to be the maximal solution. Hexagons are the bestagons.
@SpringoFlamingo Says:
I’ve watched so many of his sketches that everything he says sounds like a joke now…💀
@TheJohtunnBandit Says:
If you've ever put 7 oranges in a round bowl you likely already knew the answer, or at least if you -like me- strongly prefer symmetry.
@Rising_Pho3nix_23 Says:
I would create distance from center half of radius. angled at 360* / number_of_fountains. Simple.
In this specific example, I would have the first fountain 0.5km from center at true north, then id have another fountain 0.5km from center at 51.23* east, and so on.
@AutismPrimeFrance Says:
Hexagons are the best
@dontich Says:
I came up with separating them equally on 7 symmetrical rays such that the max distance to the top of the ray is equal to how far out on the ray they are placed. That gives from the law of sins:
sin(2*pi/17)/c = sin(13*pi/17) / 1
solving for c
c = sin(2*pi/17)/sin(13*pi/17)
or 0.53620899822
This method would be easily scalable to N fountains -- the issue is the damn center one -- that makes it more complicated for sure. You would need to do your approach for that then find out which solution returns the lower result.
Looks like 0.5 is better when one is in the center!
@kayleighlehrman9566 Says:
It would be a more practical scenario if the circular area represented a park, since most buildings aren't circular but outdoor park areas can be
@NickdeVera Says:
i'm a math noob but i've watched enough educational stuff to recognize that 2d packing problems = honeycomb, "bees figured out optimum beehives"
@jksupergamer Says:
This problem wouldnt occur if we just had 10298283930022 water fountains
@fanOfMinecraft-UAs_channel Says:
Easiest solution: just sell water bottles, and don't put the drink fountains at all! Like in my country drink fountains are really unpopular and because of that we don't fricking care
@BodywiseMustard Says:
Fucking hell, you explain so slowly
@polydipsiac Says:
Oh darn. I guessed a spiral 🌀
@ChristianoMDSilva Says:
Somehow I got the right answer just by looking at the thumbnail. Must have been a mix of knowledge and luck 😅
@BrianHurry Says:
Just recently space the damn thing what a dumb question. Unless you're in grade 3i guess
@leooram1959 Says:
Solution: no water fountines, people buy bottled water. #engineeringRules
@adusgaming2546 Says:
Long story short, hexagons = bestagons
@ZealanTanner Says:
I paused at the beginning to try it myself. I came up with ⅟√3. Let’s see if I’m right
Edit: I was close but misunderstood the question. Totally my fault. Not a bad question
@sunnycideup4725 Says:
Is…..is the answer not obvious? i feel like im missing something here
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