/sci/ - Science & Math

>>15640609
My balls work together.

>>15629229
hover peace on earth

Place the circle in a polar coordinate system with center at origin. Let t be the map (bijection) from the circle to the group R/2pi associating to a point its angle in this coordinate system. Four points A,B,C,D define a trapezoid with parallel sides AB and CD iff t(A)+t(B) = t(C)+t(D) (proof left to (You)). Rephrase the problem as follows:

- Given a 2022-coloring of R/2pi find distinct elements a,b,c,d \in R/2pi such that a+b=c+d

For any integer N>0 there is a finite subgroup of R/2pi of order N. Partition this subgroup by colors and let S be a subset with maximal size in this partition, so that |S| >= N/2022. Let

T = S + S = {s+s' | s,s' \in S, s != s'}.

If every sum s+s' is distinct then

|T| = |S| (|S|-1) >= N/2022 * (N/2022-1),

but for large enough N this is > N, contradiction. So there are values s+s' = s''+s''' as needed.

Place the circle in a polar coordinate system with center at origin. Let t be the map (bijection) from the circle to the group R/2pi associating to a point its angle in this coordinate system. Four points A,B,C,D define a trapezoid with parallel sides AB and CD iff t(A)+t(B) = t(C)+t(D) (proof left to (You)). We rephrase the problem as follows:

- Given a 2022-coloring of R/2pi find distinct elements a,b,c,d \in R/2pi such that a+b=c+d

For any integer N>0 there is a finite subgroup of R/2pi of order N. Partition this subgroup by colors and let S be a subset with maximal size in this partition, so that |S| >= N/2022. Let

T = S + S = {s+s' | s,s' \in S, s != s'}.

Then

|T| = |S| (|S|-1) >= N/2022 * (N/2022-1).

For large enough N this is > N so there are two values s+s' = s''+s''' as needed.

https://www.youtube.com/watch?v=VtJFb_P2j48

>puts a giant mirror in front of it

Cya losers

>>12169719
Its a dumb question anyway. A lot of cheap misdirection and a fairly simplistic deduction

>>12072457
>anywhere between 14-18

Sorry, I'm not an American.

>>12072163