Re: Discrete with fast method...

On 30 mar, 19:25, "mina_world" <mina_wo...@xxxxxxxxxxx> wrote:
Hello teacher ~

http://board-2.blueweb.co.kr/user/math565/data/math/fast001.jpg

Without drawing...

Find the value of ?  (Let ? = (15, 7))

Of course, I can find...
I can make a sequence with
a_1=(1,1), a_2=(3,1), a_3=(5,1), a_4=(7,1), ....

so, a_1=1, a_2=4, a_3=11, a_4=22, ....
so, a_n - a_(n-1) = a_(n-1) - a_(n-2) + 4
... ... ...
so, a_n = 2n^2 - 3n +2

I need the value of (21, 1).
Since a_11=(21, 1),
a_11 = 2.(11)^2 - 3.11 + 2 = 211.

so, (15, 7) = (21, 1) + 6 = 217

Do you know more good method ?
(more fast method..)

Dear Mina,

we may start with one way fillings ,
left/right(A) and right/left (B).
Points have a given parity :
for P(xp,yp) (xp+yp mod.2)
And accordingly belong to A or to B ...

Alain
.

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