I'm looking for symbolic geometry software that can find and show things
with a strict construction without necessarily using the Pythagorean
theorem or the infinite plane because of the following quote.

Synergetics:http://www.rwgrayprojects.com/synergetics/synergetics.html

825.26 Pythagorean Proof
825.261 All of these steps were eventually taken and proven in a complex
of other proofs. In the meantime, they were diverted by the
Pythagoreans' construction proof of "the square of the hypotenuse of a
right triangle's equatability with the sum of the squares of the other
two sides," and the construction proof that any non-right triangle's
dimensional values could be obtained by dropping a perpendicular upon
one of its sides from one of its vertexes and thus converting it into
two right triangles each of which could be solved arithmetically by the
Pythagoreans' "squares" without having to labor further with empirical
constructs. This arithmetical facility induced a detouring of strictly
constructional explorations, hypotheses, and proofs thereof.
825.27 Due to their misassumed necessity to commence their local
scientific exploration of geometry only in a supposed plane that
extended forever without definable perimeter, that is, to infinity, the
Ionians began using their right-triangle exploration before they were
able to prove that six equilateral triangles lie in a circle around
point D. They could divide the arithmetical 360 degrees of circular
unity agreed upon into six 60-degree increments. And, as we have already
noted, if this had been proven by their early constructions with their
three tools, they might then have gone on to divide all planar space
with equilateral triangles, which models would have been very convenient
in connection with the economically satisfactory point-locating
capability of triangulation and trigonometry.
-- End of Quote --
[...]
Cliff Nelson
[...]

On Apr 23, 5:19 pm, Clifford Nelson <cjnels...@verizon.net> wrote:
I'm looking for symbolic geometry software that can find and show things
with a strict construction without necessarily using the Pythagorean
theorem or the infinite plane because of the following quote.

Synergetics:http://www.rwgrayprojects.com/synergetics/synergetics.html

825.26 Pythagorean Proof
825.261 All of these steps were eventually taken and proven in a complex
of other proofs. In the meantime, they were diverted by the
Pythagoreans' construction proof of "the square of the hypotenuse of a
right triangle's equatability with the sum of the squares of the other
two sides," and the construction proof that any non-right triangle's
dimensional values could be obtained by dropping a perpendicular upon
one of its sides from one of its vertexes and thus converting it into
two right triangles each of which could be solved arithmetically by the
Pythagoreans' "squares" without having to labor further with empirical
constructs. This arithmetical facility induced a detouring of strictly
constructional explorations, hypotheses, and proofs thereof.
825.27 Due to their misassumed necessity to commence their local
scientific exploration of geometry only in a supposed plane that
extended forever without definable perimeter, that is, to infinity, the
Ionians began using their right-triangle exploration before they were
able to prove that six equilateral triangles lie in a circle around
point D. They could divide the arithmetical 360 degrees of circular
unity agreed upon into six 60-degree increments. And, as we have already
noted, if this had been proven by their early constructions with their
three tools, they might then have gone on to divide all planar space
with equilateral triangles, which models would have been very convenient
in connection with the economically satisfactory point-locating
capability of triangulation and trigonometry.
-- End of Quote --
[...]
Cliff Nelson
[...]

This is quit hard to parse. Does it have content? I don't know. What
non-finite plane do you have in mind? I don't know. Is "vertexes" a
word? I don't know.

How about four finite planes, and multiplication (of the number of

Are you looking for proof/construction software that does Euclidean
geometry? If so, I suspect it is a stretch to require that it do the
software equivalent of tying a hand behind its back. If you seek
software to do some flavor of non-Euclidean geometry, that might be
another matter. But it would be useful to have some clarity here:
you'll get better advice if you say specifically what sort of geometry
you wish to pursue.

One thing that occurs to me is you might want "geometry proof/
construction software" that avoids algebra. If so, sci.math.symbolic

is probably not the best forum to come to for advice.

Daniel Lichtblau
Wolfram Research

[...]
How about four finite planes, and multiplication (of the number of
locations) accomplished by subdivision.
[...]

One thing that occurs to me is you might want "geometry proof/
construction software" that avoids algebra. If so, sci.math.symbolic

I thought that was called "strict construction" in Euclidean geometry.
Every symbolic geometry program I can find seems to just apply the
Pythagorean theorem and almost nothing more.

Cliff Nelson
[...]

This is quit hard to parse. Does it have content? I don't know.

On Apr 24, 1:51 am, Clifford Nelson <cjnels...@verizon.net> wrote:
[...]
How about four finite planes, and multiplication (of the number of
locations) accomplished by subdivision.
[...]

I'm not sure what you mean by "finite planes", or doing multiplication
as subdivision. Taking a wild guess, maybe you have in mind geometric
constructions that make use of cross ratios?

One thing that occurs to me is you might want "geometry proof/
construction software" that avoids algebra. If so, sci.math.symbolic

I thought that was called "strict construction" in Euclidean geometry.
Every symbolic geometry program I can find seems to just apply the
Pythagorean theorem and almost nothing more.

Cliff Nelson
[...]

I am not familiar with geometrical strict construction (though I
gather that "strict constructionism" is a style of interpretation of
US Constitutional law). I'll venture to guess what you have in mind is
a way to do geometry that is independent of the parallel line
postulate, and hence applicable to non-Euclidean geometries as well?

As for existing programs, I am somewhat at a loss. I believe those
that do either geometry theorem proving, or constructions, use
algebraic methods. If you want to avoid Euclidean distance (hence
Pythagorean formula), a place to look might be in work by Hongbo Li
and coauthors. They've done things with Clifford algebra methods,
applicable to non-Euclidean gemoetry. I believe this work involves
existing software and not just purely theoretical papers.

Daniel Lichtblau
Wolfram Research

I don't want to avoid Euclidean distance, just the Pythagorean formula
in proofs.

Clifford Nelson wrote:


I don't want to avoid Euclidean distance, just the Pythagorean formula
in proofs.



Given the level of double-talk in Buckminster Fuller's writings, I think
that all you have to do to avoid the Pythagorean formula is to rename it
and write it in some obscure fashion.

For example use the HoloClifford formula, b=sqrt(c-a)*sqrt(c+a) which
relates the 3 values of the HoloEssences of the three Holoburbles of a
triple-connected geomevertor.

Rewriting the double-talk we would have,
use the Pythagorean formula [square it...] with relates the lengths of
the sides of a right triangle.

You can't play the game unless you are willing to make up the name.

If this message sounds unsympathetic, you've got it.

Regards
RJF