Hello CA! Good to see you.
LOL! Thanks for this Topol :D
Hey AA! Yeah, the diagram is just arbitrary, to show the big picture. I'll be making some that are accurate soon! The key to this is that 8 triangles of u and u+1 make 4 rectangles that fit perfectly around the center square.
Diagram time? I need a set of colored tiles so I can play blocks with these ideas.
>This will REALLY help if you visualise the smaller (x+n) squares and throw in a few much larger (x+n) squares.
>Focus on the patterns in the way f is distributed in each of the 8 triangles. Look at symmetries and how to construct the triangles when you know you need the two different portion sizes of f. This affects the values of 2d(n-1)
Lads, VQC said we are really close at this point. He basically said we can do it from here.
Let's expand our minds, and feel the emotion of success!
Visualize.
Conceptualize.
Realize.
Our minds are our own Personal VQC's.
Space Jesus Says "You will know the Truth, and the Truth will set you free."
Hey CA! I'm following you well. This is a solid and interesting idea. Can you post your output to show and explain?
In row one, (x+n)^2 is always equal to f.
You're also saying that (b-a)/2 = x+n for all (e,n)?
Can you clarify Pls?
>
Good points, CA! I'm examining them closely to make sure I understand your ideas. Here we go.
>We can solve (x+n) from f if f is a square number.
>If f is square, then (x+n) is the root of f.
>this leads me to believe that in order to factor c we need to factor f (recursive solution). This is because for our first step if we had a case where e = 0 then we'd have a solution. For this if we (for our f) have e=0, then we have a solution.
>I think we need to do this because the correct (x+n) often seems to be a multiple of a factor of f.
(often a multiple of the gcd of the original (x+n) and f).
>If f is prime, not sure what to do.
>Still a lot to think about.
Now we're talking. (e,1) is supposed to be our big clue. We still haven't figured that out. After 6-7 months. How does (e,1) play into factoring and given c or x+n value?
Hey Lads, bear in mind: My diagrams are an exploration of three things.
Using f to fill the square
Using f to find an iterative match.
Using the polite triangle numbers to understand f.
Just trying to work out the ideas!
New tab didn't work, but downloading it and opening it did. Thx!