Southern Hospitality:


Southern Hospitality wrote:

Odysseus wrote:

[clip]
Were you perhaps thinking of Kepler, who (beside his more famous
astronomical work) did some research into polyhedra, IIANM
discovering a number of stellated forms?


I did some research on this and I don't think it's Kepler but more like
Archimedes or Euclid (or any of the other hundred or so geometers of the
past).

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From what you say you did no research on that. No rational and factual
research would result in thew conclusion that, "I (you) don't think its
Kepler". There is no evidence for that.

And, you say, "more like"...? That is the puniest attempt at lying about
the facts of science that I have heard yet. "More like"? Is that some sort
of Platonic approximation that "Archimedes or Euclid" created the theory
concerning the stellated geometric solids? Really, now....is it the one, or
is it the other....just to pin down your claim with a little anti-Platonic
precision of thought.

If you knew the facts you would have said, for example, that the theory of
the primary closest packing solids, and the discussions of their properties
and proofs, was first set forth by Pythagoras.

Plato, some two hundred years later, plagiarized that theory and claimed to
have originated the 'Platonic solids' and 'closest packing solids' (a
modern term). Plato's claim of authorship was false.

Aristotle made many comments on not so much the content of Pythagoras's
geometrical discoveries, rather upon the methods used to construct his
system of geometry. Aristotle forever change the course of geometric and
scientific inquiry as well as defining correct thinking and validation of
concepts.

In the time of Euclid or before, "the other hundred or so geometers of the
past" had little to do with the proofs of the concepts or definitions of
polyhedra. They were more concerned with the fundamental concepts of
geometry and also the methods of the discovery, formulation, and
identification of concepts, as well as the proof and validation of
concepts. Methods of presentation of scientific matters and argumentation
were also developed and refined. The several of them created the basic
methods that are still in use today.

Another one hundred or so years after Plato, Euclid did work in defining
the geometry of solids, and he cataloged the appropriate works of
Pythagoras in "The Elements". Euclid did further developmental work, and he
furnished proofs of many of the basic stellated solid forms. (That is the
Aristotelian concept of form [meaning functioning causal scientific
principle], and not Plato's [meaning ideal unknowable idea] ).

Many modern scientists lie about the works of Euclid with their claims that
Euclid's works are invalid for modern science because they are supposed to
have dealt only with plane geometry. Two of the books of the "Elements"
deal exclusively with proofs of solid entities. Actually, all of the
"Elements" dealt with solid geometry, and only some of the geometric
principles of the "Elements" (a majority) had proofs that were reduced for
simplicity's sake to planar elements.

Or course, since that time numerous stellated forms have been discovered
and cataloged by geometers, and their properties have been proved. Geodesic
solids are one class of stellated solids that are more recent. Actually,
the stellated solids would be a subclass of the geodesic solids. The
'closest packing' solids, in a selected context would also be a subclass,
and all are a subclass of geometric solids.

Ralph Hertle