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NNTP-Posting-Date: Sun, 11 Aug 2024 02:40:21 +0000
Subject: Re: Infested Spiral Infinity...
Newsgroups: sci.math
References: <v994je$149dh$1@dont-email.me>
 <opKdneW65pc-gSX7nZ2dnZfqnPidnZ2d@giganews.com>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 10 Aug 2024 19:40:56 -0700
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On 08/10/2024 07:06 PM, Ross Finlayson wrote:
> On 08/10/2024 06:36 PM, Chris M. Thomasson wrote:
>> Spirals in spirals forever...
>>
>> https://paulbourke.org/fractals/septagon
>>
>> Paul was kind enough to write about my formula.
>
> The spiral's the oldest symbol for "mathematics"
> in the world, since before recorded history.
> Anantha, Thoth, and so on.
>
> The, "spiral space-filling curve", is as simple as
> drawing a line from zero to one, which it is,
> in all the dimensions at once. Of course it's,
> "non-standard", but anybody who puts pencil to
> paper does it each time. It's really about the
> first sort of "standard extra-ordinary super-standard",
> function, being that it has real analytical character and all.
>
> DesCartes of course has a theory where vortices
> are ubiquitous in the space. Einstein has what's
> called his bridge into the centrally symmetric.
>
>
> When we were in junior me and my lab partner
> made Turbo Pascal draw evolving spirals all
> over the screen, but somehow nobody ever had
> an epileptic fit, that our goal was a sort of
> optical overload, all based on some simple formulas
> and the power of the computer.
>
> We got a good grade for it, ....
>
> Anyways "infested" isn't the right word,
> more like "infectious".
>
>

It seems the idea that "there are no, _non-trivial_,
solutions singularity-free to the field equations",
makes for a particular, _non-trivial_, sort of approach
what's otherwise the trivial, or vanishing, while,
this is already a most usual sort of approach when
there are simply interacting terms, as of what the
linear or non-linear predominate, the idea is to make
a sort of super-standard least-non-trivial to help explain
what all gets involved making a right angle, of a straight line.

Here that's being called "Zeno's swath".

 From a spiral-space-filling-curve, for example of a disc,
lines are pretty simple as going out and establishing
what's called "shortest distance is a straight line",
and vice-versa, then simply orthogonal lines are
the most of those, shells, in the least of those, dimensions.


If you've never heard of the Archimedean spiral,
it's more a usual thing that basically is a spiral,
that, increases distance one in each revolution.
Anyways, it's not constructible with edge and compass.
However, given an Archimedean spiral to accompany
edge and compass, makes for solving angle-trisection,
circle-squaring, and, cube-doubling.

In case you never heard of it, they already have one.

So, if you can only bring one more tool after edge and compass,
an Archimedean spiral might be a nice thing to have.


Less baggage.