Logo

Combigeo - Shared screen with speaker view
espen slettnes
04:55
https://espen.slett.net/BMC_lectures/Combigeo_Problem_Solving/2020-10-28.pdf
espen slettnes
08:23
https://espen.slett.net/BMC_lectures/Combigeo_Problem_Solving/2020-10-28.pdf
espen slettnes
10:30
https://espen.slett.net/BMC_lectures/Combigeo_Problem_Solving/2020-10-28.pdf
Nathan Barnes
11:57
Anything less than 2
Sebastian Weinberger
15:07
As the number of triangles —> infinity the areas have to go to 0, so at least one of a, b, and c goes to 0
Nathan Barnes
15:49
Otherwise we run out of space and they have to overlap
Corinne Young
17:36
diameter
Samuel Sha
17:38
2
espen slettnes
22:59
https://espen.slett.net/BMC_lectures/Combigeo_Problem_Solving/2020-10-28.pdf
Jason Hallsten
23:30
0
Jason Hallsten
23:54
theta
Jayanth Sadhasivan
23:54
2sin(theta/2)
Sebastian Weinberger
24:20
So… theta?
Sebastian Weinberger
25:16
It approaches two?
Sebastian Weinberger
26:14
Symmetry
Jayanth Sadhasivan
26:45
even
Jayanth Sadhasivan
26:55
0
Sebastian Weinberger
28:20
For small enough theta O(theta^2) is negligible compared to theta
Jayanth Sadhasivan
31:25
2
espen slettnes
31:46
https://espen.slett.net/BMC_lectures/Combigeo_Problem_Solving/2020-10-28.pdf
Nathan Barnes
32:09
6
Samuel Sha
32:42
1
Paikea Melcher
32:43
1
Jayanth Sadhasivan
33:32
yes
Samuel Sha
35:11
yes
Nathan Barnes
35:32
It stays the same
Nathan Barnes
37:49
No
Nathan Barnes
37:54
Because you can reverse the course of the line
Nathan Barnes
39:36
It has to be the green line
Nathan Barnes
43:24
Since no 3 points are collinear, T can only increase by 1 at a time
Nathan Barnes
44:58
Any value?
Nathan Barnes
45:44
n/2
Nathan Barnes
52:16
You can do odd n with a regular n-gon
Nathan Barnes
57:14
Another triangle
Nathan Barnes
59:41
Just add another equilateral triangle with one of the vertices being the center
Sebastian Weinberger
01:02:35
Can we use a bunch of disjoint regular n-gons?
Nathan Barnes
01:02:46
No
Nathan Barnes
01:02:59
Because of the bisectors between points in different n-gons
Sebastian Weinberger
01:03:30
Oh right
Sebastian Weinberger
01:03:56
I totally forgot
Emma Lynch
01:06:11
n(n-1)/2 ?
Nathan Barnes
01:06:12
n-2 (assuming n is even)
Nathan Barnes
01:08:42
≤n*floor(n-1/2)
Nathan Barnes
01:09:12
≥n
Nathan Barnes
01:09:48
n(n-1)/2?
Nathan Barnes
01:10:53
n is odd
Nathan Barnes
01:20:20
Each side of a rectangle can contain at most 1 point
Nathan Barnes
01:22:17
We can think of adding the sides one by one
Nathan Barnes
01:22:24
(starting with the ones on the outside)
Nathan Barnes
01:22:38
Oh
Nathan Barnes
01:23:54
The right angles it makes with the other side
Nathan Barnes
01:24:15
The ones at its ends
Nathan Barnes
01:26:39
The ones of the original rectangle
Nathan Barnes
01:30:13
3
Nathan Barnes
01:30:59
5
Emma Lynch
01:32:13
yes
Emma Lynch
01:33:04
6
Nathan Barnes
01:34:18
6?
Emma Lynch
01:34:22
7
Nathan Barnes
01:35:00
The largest odd number less than n?
Jayanth Sadhasivan
01:35:24
n-2
Sebastian Weinberger
01:35:34
Not quite
Emma Lynch
01:35:58
2n/3 + 1 (maybe?)
Nathan Barnes
01:37:22
We can bend one of the sides
Sebastian Weinberger
01:38:05
That’s not for n = 5, right?
Zihongbo Wang
01:38:13
(n-2)*180
Nathan Barnes
01:38:48
360
Nathan Barnes
01:46:18
The center of mass?
Jason Hallsten
01:47:30
its on the line
Jayanth Sadhasivan
01:48:54
midpoint
Nathan Barnes
01:48:59
The circumcenter
Nathan Barnes
01:50:54
The perpendicular bisector of AC has to pass through B
Sebastian Weinberger
01:53:50
Platonic solids?
Jason Hallsten
01:55:59
cube
Nathan Barnes
01:56:08
Tetrahedron, cube, octahedron, dodecahedron, icosahedron
Jason Hallsten
01:56:08
tetrahedron
Andrew Sylvester
01:56:17
tetrahedron, cube, octahedron, dodecahedron, icosahedron
Nathan Barnes
01:58:40
2 opposite vertices
Nathan Barnes
02:00:17
Take the convex hull
Nathan Barnes
02:01:51
They're all regular
Jason Hallsten
02:03:59
circle
Nathan Barnes
02:04:59
They're regular
Corinne Young
02:05:38
Congruent
Samuel Sha
02:08:29
thank you!