-
holden just spammed my youtube subscriptions
by
A_Humanoid_Figure, Apr 30, 2025, 8:33 PM
-
where are the monthly blog posts
by
wu2481632, Apr 17, 2025, 4:39 AM
-
holden so orz bro how
by
Yiyj1, Apr 3, 2025, 4:20 AM
-
nsml problem reveal when?
by
ethanzhang1001, Mar 7, 2025, 8:08 PM
-
holden is so
by
Clew28, Jul 30, 2024, 5:54 PM
-
hi would you mind if i stole an old asy from this blog?
by
YaoAOPS, Jul 23, 2024, 8:06 AM
-
hi brother
by
The_Elephant, Feb 3, 2024, 5:23 AM
-
oh hey that's just like last night except "rachmaninoff" was actually "me", and "stravinsky" was actually "your mom", and the "giant jar of honey" did not contain "honey"
by
chickenugget, Jan 20, 2024, 5:32 AM
-
did you know that one time rachmaninoff showed up to stravinsky's house with a giant jar of honey, because stravinsky once mentioned he liked honey
by
rjiangbz, Dec 3, 2023, 3:56 PM
-
omg what the shout box is a turtle :exploding_mind:
by
Luraibird49, Nov 25, 2023, 3:51 PM
-
you seem like a super cool person. contrib?
by
LJCoder619, Nov 7, 2023, 5:04 PM
-
@below it’s my favorite too : )
by
wu2481632, Sep 4, 2023, 10:57 PM
-
woah how so orz? also my favorite composition of yours is Scherzo!
by
agoel2010, Aug 28, 2023, 10:07 PM
-
Is this blog name a reference to a specific piece lol
by
ihatemath123, Aug 28, 2023, 4:02 AM
-
turtle so orz
by
akpi, Aug 4, 2023, 1:49 AM
-
wait, how do you use the encyclopedia of triangle points/centers?
by
WireCat, Oct 13, 2018, 8:51 PM
-
woah, im shouting!
by
jlamslam, Aug 8, 2018, 3:24 AM
-
by
yrnsmurf, Jul 21, 2018, 5:37 PM
-
hi turtle <3
also can i have contrib 
by
MathStudent2002, Jul 20, 2018, 11:22 PM
-
hiiiiiiiiii turtttttttle geeeeeniusssss <3
by
thepiercingarrow, Jul 14, 2018, 8:18 PM
-
blog is very genius
by
pyaops, Jul 14, 2018, 7:50 PM
-
contribubby plz
by
fatant, Jul 10, 2018, 4:40 PM
-
didn't know u had a blog
request contrib
by
mathisawesome2169, Jul 10, 2018, 12:17 AM
-
hey you should make me contrib too
by
yrnsmurf, Jul 8, 2018, 1:37 AM
-
contrib? :0
by
pyaops, Jul 6, 2018, 2:37 PM
-
nice blog
contrib?
by
WireCat, Jul 6, 2018, 5:14 AM
-
nice blog
by
pyaops, Jul 5, 2018, 1:27 AM
-
Oi when did you make a blog
Contrib plz
by
franchester, Jul 4, 2018, 4:21 AM
-
first shout >
by
math101010, Jun 30, 2018, 2:42 AM
by The_Turtle, Dec 5, 2023, 1:38 AM 
and call a lattice triangle 
marine if ![$[ABO]=[BCO]=[CAO]=\frac{1}{2}$](http://latex.artofproblemsolving.com/a/8/c/a8c32d5f95cae4222c76f62d5c24dac5327c65f5.png)
. Find all points in 
that don't lie in the interior of any marine triangle.
February 2025
January 2025
.
of any lattice triangle 
must intersect the ray starting at 
pointing away from 
.
to contain ![\[[ABO] \geq \min\bigg(\underbrace{1 + \frac{1}{2} \cdot 3 - 1}_{\text{in interior}}, \: \underbrace{0 + \frac{1}{2} \cdot 4 - 1}_{\text{on perimeter}}\bigg) > \frac{1}{2}.\]](http://latex.artofproblemsolving.com/c/f/4/cf421248e82cdc6f0970ab9e57155b282e19737f.png)
Hence 
cannot be marine.![\[\sim\]](http://latex.artofproblemsolving.com/c/d/1/cd1143692f2d3443a2baccf54c53881c3a1ef47c.png)
![\[(x, y) \mapsto (x-y, y) \quad \text{and} \quad (x, y) \mapsto (x, y-x)\]](http://latex.artofproblemsolving.com/9/3/c/93c50974ffbf98c97f758dadd05904f5a39c3ed8.png)
preserve the marine-ness of triangles since shear transformations preserve area. Therefore 
lies in a marine triangle if its image under one of the above transformations lies in a marine triangle.
if 
for some 
.
then the point lies inside the marine triangle with vertices 
as desired.