#How would I find the blue section's area?
winter marlin
for help, use #1015578016606343218 or #1020426321261756536
spark stump
have you heard of inclusion exclusion principle
next gale
have you heard of inclusion exclusion principle
No
shell orchidBOT
Coffeλ
spark stump
$\abs{A} +\abs{B} - \abs{A\cap B}$
shell orchidBOT
Coffeλ
orchid depot
But then you still need to calculate area of diskcaps, don't you
Do you know how to calculate the area of a disksegment? (A piece of pie)
spark stump
Do you know how to calculate the area of a disksegment? (A piece of pie)
yeah why not
orchid depot
I meant OP
spark stump
hey I have an idea!
@orchid depot rotation conserves area right
tilt the picture 45 degrees
then we can find them easily.
spark stump
Why does that make it easier in any way
well he didn't give us an area nor distance between centres lol
I'd demonstrate
orchid depot
I guess the distance between the centers is sqrt(2) for closest and 2 for furthest
spark stump
let's assume radius = r and distance of each centre from origin = d
orchid depot
I think you only need radius chosen, the distance between the circles gets fixed by putting the centers on other circles
spark stump
when it's spun 45deg(wlog, let's say clockwise)
the centre of bottom left circle is moved to (-d/sqrt(2),-d/sqrt(2)) = let, (-k, - k)
now we can make the equation of this circle :
(x+k)^2 + (y+k)^2 = r^2
now we just have to calculate the area this covers in the ++ quadrant
and the blue area is 4x that
what does translating a circle from (0,0) to (-k, - k) do to the area on the positive x quadrant?
something like this might help too
orchid depot
Why do you want to translate a circle
next gale
Do you know how to calculate the area of a disksegment? (A piece of pie)
Uh no, I can subtract a regular polygon from the circle and divide by the number of sides at best
next gale
well he didn't give us an area nor distance between centres lol
I feel like it's fairly clear
orchid depot
It's a fraction of the disk's area
You can prove it by approximating the disk with triangles
next gale
You can prove it by approximating the disk with triangles
Bes5 I have been able to do is 2 right triangles per cap (or one isosceles)
next gale
I feel like it's fairly clear
That the radius is sqrt(2)
next gale
OH!
waitaminute
that should have been somewhat obvious how did i not think of that
im an idiot
next gale
0.732^2 + 4(area of segment of circle - area of triangle) = blue area
witha little bit of trig i think i can solve it
thx
next gale
next gale
A ≈ 4{(2π×(2sin⁻¹(0.366/√2)/360)) - ((√[2-0.366²])(0.366)(0.5))} + 0.732²
Is that abt right?
next gale
:D
next gale
?
ebon river
hybrid scrollBOT
-2×sqrt(3) - 4×sqrt(-5 + 3×sqrt(3)) + 2×π/3 + 4 = 0.858729555779608