# Expressing depth in nonlinear space

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1. +y coordinate as a, +x as b, C is the found by pythagorean, we need to make C a curve so we have in quadrant 1 three x coordinates and 3 y coordinates, x1 = 2C/pi, y1=C/pi, x2 & y2 = (x1+y1)/2, x3=y1, y3=x1. Of course quadrant 3 is all negatives, quadrant 2 x are positive and y are negative, quadrant 4 y is pos x is neg

(Did the math on that it works to make a perfect circle)

2. a 45 degree angle or C can be found by starting at the top corner of quadrant 4 and bottom corner of quadrant 2 and having C be crossing (0,0), so a and b are doubled. Then you can get the other diagonal through 3 and 1 quadrants using the same formula for a curve, now you have 3 dimensions and 2 angled slices of a sphere that cross at 4 points

3. We need them to cross at 8 points because we want to put 8 more spheres around the first one, we want 8 more spheres because of the fact that the dividend between the formula for the volume of sphere over the same formula only with r halved will always yield 8 meaning 8 spheres can surround one sphere in twice the volume without any of the radii crossing but only a maximum of 8

4. So you need 4 more diagonals at 4 45/2 degree angles between the two 45 degree diagonals, these 6 3D slices of the sphere that are angled will intersect at 8 points: these points can be changed by changing the viewing angle of the whole sphere longitudinally using (x-x/2, y) for quandrant 1. These points can be calculated where two slices have the same value using the lateral transformations (x-x/n, y+y/n) for quadrant 1.

5. These 8 new spheres are either closer to you than the original or further away, depth, we express this using y2=y1-y1/r over x2=x1-x1/r where r=C/2 all for quadrant 1.

The instructions I gave for the coordinates of those spheres don't become connected to "various physical phenomena and equations" until gravitons are introduced. Which were tricky to put in there, because they are created by the collapse of the spheres into each other and therefore produce a net drag on them and each other much like particles. A system like the universe can naturally comes into form.

Actually doing the math for gravitons in that way however was tricky. When we said that the x and y parameters of an outside sphere was x2=x1-x1/r (for the spheres touching the inner one at it's back half as opposed to it's front half) where r=C(pythagorean for quadrant 1 of the first sphere)/2 we were saying the radii of the outer sphere and inner sphere were touching. Keep in mind we are always starting at the centeral sphere which is why when we put spheres around a single outer layer of 9 we only need the two diagonal discs to create for points where there are 32 more spheres in front and 32 more in back relative to the original central sphere we started with.

When we take the form y2=y1-2y1/r we are placing the center of an outer sphere at the radial surface of the inner sphere. When this happens one of the discs of an outer sphere & one in the inner sphere are the same x & y values at 2 points (found using lateral transformations), top & bottom.

Saying top is x2, y2 and bottom is x1,y1 if where stacking in the quadrant 1 direction the center for your graviton is found with (y2+y1)/2 and (x2+x1)/2 and the length of your x and y coordinates in it's first quadrant is also found by finding the average of the height and width of quad 1 for the two spheres that are crossing through one another.

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