/sci/ - Science & Math

>>11156244
>And here I thought you would give a creative or insightful proof of the result...
hahaha of course not, it's just autism

>>11156146
well I'm not going to write it all out for you
but you can find the intersections of all of the black lines by typing stuff like "intersection of -2x+1 and x+1/2" into wolfram alpha
once you have all those intersection points, you can find the equations for the red lines by typing "line through (1/3,5/6) and (3/5,1/5)" etc.
after that you can find the intersections of the red lines in the same way
these intersections are (143/345,221/345), (53/128,41/64) and (75/181,116/181)
then you can find the area of the triangle by typing "area of triangle (143/345,221/345), (53/128,41/64), (75/181,116/181)"
and it will tell you it's 1/15985920, which is about 6.2555E-8, which is the same result geogebra gives me (see pic)

you can do all these steps by hand of course, but it's just a lot of work

nobody?

ok it's 1/15985920

>>11153312
ok I awake now
where is answer

ok I go sleep now
somebody better have the answer when I wake up

>>11153156
I know it's obvious that it's a fraction, but I didn't really expect a unit fraction

>>11153135
yeah that's what I used
the solution is pretty nice, it's a unit fraction

>>11153114
you good?

>>11153080
here is a zoomed in version
triangle is in the bottom right
black line is there for scale

I made a geometry problem for you.

Pic related is the unit square.
What is the area of the triangle inside the red lines?

>b-but the red lines all intersect in a single point
no, they don't

>>10602769
ooh right, I think I see it

>>10602717
>>10602722
Yes, I know what those angles are
That obviously doesn't answer my question

>>10602727
don't impersonate me pls

>>10602706
OP

>>10602693
because I hate it when someone is acting retarded and then because of the context people think it's me
has happened to me multiple times

>>10602645
I have only checked for 10 additional triangles, and for those it stays consistent, yes.

I created this spiral by continously adding a perpendicular line to the previous spoke.
The line ends when it hits an integer point.

I marked the triangles that have a 1:1 side ratio with red and the triangles that have a 2:1 side ratio with blue.

My question is why does it create this repeating red-red-blue pattern?

>>10596252
[eqn] \lfloor (\varphi + \pi)^e \rfloor [/eqn]

>>10596252
[eqn] \lfloor (\phi + \pi)^e \rfloor [/eqn]

Which of these triangles has a bigger perimeter?

You should be able to solve this.

>>10594902
oh yeah I need such a big brain to input the circles into wolfram alpha

>>10594524
sorry I didn't mean to post the answer, but that dude was really annoying me

>>10594529
nice, there we go

>>10594486
I think you mean diameter
You are right about the second one, but I think you made a calculating error on the first one

I already posted the answer >>10594470

>>10594470
oh yeah and here is the geogebra file:
https://www.geogebra.org/graphing/dxrqzt3t