Archimedes Plutonium wrote:
> Let me tell you how I arrived at this insight. I have a vase, in fact,
> alot of vases near my bed where I sleep and I awoke staring at a
> particular vase that was negative curvature or hyperbolic geometry.
> That is to say it was trumpet shaped at the lip and the the base
> so that as I lay in bed looking at the vase my mind was saying,
> "let me try to squeeze in or fit into that negative curvature one
> of the circles of latitude of a nearby globe."
>
> Then my mind goes to work. It says that every latitude circle of a
> globe would create a vase of negative curvature.
>
> So then the question becomes can I define any given sphere as merely
> a deconstructed set of all the circles from 0 to 1 radius, restricting
> the globe to unit radius.
>
> So in other words, I define a sphere as a set of all circles of radius
> of all the Reals from 0 to 1. So that the North Pole would be a circle
> of 0 radius and the Equator a circle of 1 radius and where there is a
> circle of 0.5000.... radius etc etc. So this sphere is the set of all
> circles from 0 to 1. Correction-- Hemisphere.
>
> Now, what I want to do is construct a Pseudosphere of negative
curvature
> from that same pile or set of circles that were lines of latitude.
>
> Now, here, the mind seems to go puzzled. Puzzled and confused because
> to build the hemisphere from that set of latitudes, it is puzzling how
> those latitudes can thence build a pseudosphere. But it is only a mind
> illusion like an optical illusion. We can build a trumpet shape from
> those same set of latitudes.
>
> What I have described above is a new world definition of a sphere and
> a pseudosphere because we build both from the very same set of circles.
>
> And what I have described above is a way to prove that the Reals are a
> mirror image of the AP-adics.
>
> Now the largest circle in building the sphere is a great-circle of
> radius 1. And the largest circle in building the Pseudosphere is
> 9999...9999radix99
>
> So what I am going to show and prove in the second edition of this
> textbook is that I can tie together Hyperbolic geometry with Elliptic
> geometry in this sphere and pseudosphere building. Building both from
> one set of circles. Building them in one way, I end up with a
> hemisphere, and building them in another way I end up with a 1/2
> Pseudosphere. That tells me the Reals are connected to the AP-adics.
>
> The new definition of a unit-sphere is that of a construction of all
the
> circles whose radii have Real value from 0 to 1 and the new definition
> of pseudosphere is the construction of all the circles from those same
> radii excluding the 0 and 1.
>
> I remember when I studied geometry in the 1970s that there was a
> distinction between analytic geometry and synthetic geometry. The above
> construction is a bit of both for there is analysis and there is
> synthesis in the construction.
>
> The above is a very new definition in mathematics for the sphere
because
> it conjoins the lines of longitude with latitude as never before done.
> In the past, we thought of the lines of latitude as unim****tant or
> nonessential. Our ideas of a sphere relied on great-circles or
> longitudes and latitudes were thought of as garbage-extras. But what my
> new definition brings to light is that lines of latitude are just as
> essential to Elliptic geometry as are lines of longitude. My new
> definition of a sphere tells us that a sphere is dependent on lines
> of latitude.
>
> So I should look forward to the 2nd edition of this textbook.
>
Now it is quite bizarre to the mind, how you can take a set of circles
which includes the latitude circles of the North Pole to the Equator
and form a hemisphere, and yet with that very same set of circles form
a 1/2 Pseudosphere.
What defies our intuition is that if we had a set of hoola-hoops as
latitudes with the largest being the Equator and the smallest close
to the North Pole. What defies our intuition is that we nest those
hoops and gain a hemisphere of a sphere, but the only way we can
gain a Pseudosphere is that if the nesting of the hoops were to be
somewhat submerged or enclosed inside the previous hoop to gain that
negative curvature.
But we all know that circles are not enclosed or submerged to form the
sphere and pseudosphere from the very same set of circles.
So why does this construction defy our intuition and commonsense?
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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