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Video summary of the Sylvester�Gallai theorem.
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The premise is a little ambiguous... do you mean a line that contains ONLY, i.e. exactly, two points? no more no less? I guess I'm confused because I would have thought the definition of a line is that it has at least two points, so the premise of multiple points and the ability to line implies a priori that there's 2-point-lines. The whole exercise seemed circular and weird. Am I missing something?
@rizzwan-42069 Says:
where can i do the puzzle
@nicolasturek7563 Says:
solution is simple, n points on the line and than remove the line and... you have no line with less than n points
@mayochupenjoyer Says:
i’m trying not to get a big head about it but i saw one solution around 1:10
@beirirangu Says:
I went about the solution in a different way, and ended up with a fractal: imagine three non-linear points, now imagine joining every point with a line, then imagine putting a point on every line segment such that every line has at least 3 points, then join the new points with the other points with new lines and repeat trying to put points and lines with the assumption that it's possible to make every line have at least 3 points... that and a different way is a grid-like pattern and fractional angles
@canbastemir2122 Says:
I think this is called Slvester problem. Nice problem and elegant solution.
@nqppqn Says:
no
@septicwahab4312 Says:
Me: *tries this problem, solves it in 1 min 21 secs, hmm yes*
Zach: This problem was not solved for 50 years.
Me:| Ohh
@plutonicattic7995 Says:
i found it almost immediately
@astropig_3212 Says:
Me: draws a line with a bend
@AlwaysOnForever Says:
This looks simple but the problem is i didn't learn math with english and if i see someone explaining math with english, it got me headache
@swattofficer6624 Says:
Sir, this is a Wendy’s.
@Tocaraca Says:
This is too high level for me lmao
@MetroAndroid Says:
Are you Glink's brother?
@peterhofer8998 Says:
Thank you so much. It's highly inspirating and fascinating.
@ajreukgjdi94 Says:
Sooooo, I missed something, because it sounds like you just proved L1 must always have only 2 points. in fact, at 6:08, you said "give me any line on our finite list. If it contains 3 or more points, then I can find another line, higher up on our list." So, I give you L1, either it has 2 points, or you can find another line higher up on the list right? Why go through all the rigmarole of constructing new lines when you could just find L1 and quit? Well, unless picking any arbitrary line and cascading through this process is computationally faster I guess.
@okboing Says:
immediately I thought of the bounding polygon for the points, hardly 30 seconds in. Any line through two of the outer points will only pass through two points...
unless there is a point straight between every outermost point. then, I can't be sure.
@PunnamarajVinayakTejas Says:
Fuck, what a beautiful proof
@fromfareast3070 Says:
but does this algorithm stuck in a loop?
@regarrzo Says:
I think you need the limitation that one spot may not contain two points. Else two pairs of two points lying on top of each other and a fifth point to break collinearity is a counterexample.
@ruisen2000 Says:
What if the line had 3 points, and the third point was exactly at P? Then starting at P, there would be no direction where you would find 2 or more points.
@whengaming9999 Says:
Idk why but I thought the top dot to the one besides the backwards L would only go through two points.
Only to remember that it’s impossible for someone with the intelligence of a loaf of bread to solve mathematically.
@cones914 Says:
Yes there is. I can just go around some points.
@leach_ Says:
What about just a bunch of points in a straight line. If that is allowed.
@gigaprofisi Says:
0:41
What about the top one and the one furthest between the two points directly below it?
@bobbysanchez6308 Says:
What influences the number of lines which intersect exactly two points? What is the maximum number/proportion of such lines?
@felpy2881 Says:
Have a plane with 3 dots in a row
@Nathouuuutheone Says:
I don't get how that's a proof.
@vladimirfokow6420 Says:
Beautiful!
@chrissekely Says:
Could someone here prove the spherical geometry equivalent of this theorem to be either true or not true? In which important ways would that geometry be different? I'm guessing this thinking could be extended to infinite curved spaces such as theoretical versions of our universe (of course this is also graduating from surfaces to volumes).
@ahoj7720 Says:
What I find most puzzling is that it is true on the Euclidian (R^2) plane only. You can find configurations of 9 points in the complex plane (that is C^2) with the property that all lines contain exactly 3 points (find one !) And also, more exotic, the projective plane of order 2 (the Fano configuration) has the same property. So a proof of that theorem cannot avoid the use of some metric property.
@Tadesan Says:
Gradient ascent!
@Ny0s Says:
Really cool
@ryanbrown4902 Says:
wait but the point that's across from L5 and the middle point on the bottom, connect those, wouldn't it just be a line with only 2 points and also not L1? Or is that just irrelevant, and the goal was to prove that L1 would always be a line with only 2 points?
@shaun6342 Says:
Disculpa
@shaun6342 Says:
Astronomy last class chapter 2
@ZachTheHuman Says:
Haven’t finished the video, my thought right now is that you can bend the paper with the dots on it so that a straight line along the Z-axis hits two. Gonna see how close I got.
@boat13042 Says:
Zach: "If you really understand that..."
Yeah, I think I understand it well.
Zach: "...then you should also see that we basically answered our question."
Seem I understand nothing.
@HansLemurson Says:
So...the line with the shortest distance to its nearest neighboring point will always have 2 points? That's an unintuitive prediction.
@Catman_321 Says:
What if there is an infinite number of points placed randomly
Does this still apply
*the dots cannot be placed in a grid formation or anything like that
@sage3626 Says:
Question can higher dimensional beings see the future for us?
@raspberryjam Says:
I've got a question: What if I've got an equilateral triangle, with three overlapping points at each vertex?
@mohammodzubair1137 Says:
can you make videos on what universities teach if you take a masters in engineering
@casaroli Says:
This is beautiful.
@l0k048 Says:
duuuude... what
@Smona Says:
Maybe the real treasure is the lines containing only two points we found along the way
@suyashverma15 Says:
Simply awesome. 👍☺
@vixguy Says:
Just make a tiny line. :bigbrain:
@calebos04 Says:
Question: Is there always a line that passes through two points?
Me: ...
*draws one dot*
@8316WC Says:
in addition, if you randomly place points at non-incremental places (so not a finite graph at the intersections) it is statistically impossible for any 3 points to form a straight line.
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