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Topic: Elliptic geom proving lines in Euclidean & 1-1 Correspondence of
sphere with plane #1297 Correcting Math 3rd ed

Replies: 2   Last Post: Nov 17, 2012 3:03 AM

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 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
Elliptic geom proving lines in Euclidean & 1-1 Correspondence of
sphere with plane #1297 Correcting Math 3rd ed

Posted: Nov 17, 2012 1:26 AM

Let the geometry prove it. Or, let Elliptic geometry prove the
Euclidean problem.

With Euclidean plane geometry just a vast grid of points with empty
space in between, there being 10^2412 points in the first quadrant
with empty space of 10^-603 between successive Real points.

Now if we pick up a globe of Earth and take the grid system of
longitude lines and latitudes we see that the empty space between
intersection points is small near the poles but huge near the
equator.

So in the Euclidean plane the empty spaces form perfect squares of
10^-603 sides but in the globe the empty spaces are spherical
quadrilaterals that are small in area at the poles and get
progressively larger towards the equator.

Now I bet mathematicians have figured out this size increase of those
quadrilaterals at the poles as they grow larger towards to the
equator. And I bet it is a factor of pi increase.

Now here is the thing to make the points of the grid of Euclidean
geometry correspond directly to the points of the globe, a sphere of
Elliptic Geometry. We have the same number of points in each, but we
increase the size of the points as we approach the x-axis. Now we
probably need all 4 quadrants. So if we did that in each of the 4
quadrants, that we are in fact transforming the Euclidean plane to be
the surface of a sphere in Elliptic geometry.

So, now we see how a plane in flat Euclidean Geometry is transformed
directly into a surface of Elliptic geometry, the sphere. And we can
likely define Euclidean geometry as the geometry that has a uniform
spacing of the empty space between successive Real points. Whereas
Elliptic geometry has a variable size spacing depending on direction
of a line (great circle).

Now as for the conjecture that the lines of Euclidean geometry given a
single point and given all the angles possible that the line ray of an
angle intersects with another point to be truly a line (two points
determine a line)? Well, if Euclidean geometry is a 1-1 Correspondence
and transformation of one to the other by varying the size of the
empty space to form a sphere. We know the sphere lines (great circles)
have a antipode to each podal point. And so each angle starting at the
pole and encompassing all of the 360 degrees of angle possible, that
each line has at least two points of intersection.

Quite simply, we let the geometry do the proof for us. And that is how
it should be for most of mathematics, for if it is really true, then a
proof is like a pleasure walk, not some arduous struggling workout
with all sorts of questionable references.

Google's New-Newsgroups censors AP posts but Drexel's Math Forum does
not and my posts in archive form is seen here:

http://mathforum.org/kb/profile.jspa?userID=499986

Archimedes Plutonium
http://www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies