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Pythagorean

Definitions

  • WordNet 3.6
    • adj Pythagorean of or relating to Pythagoras or his geometry "Pythagorean philosophy","Pythagorean theorem"
    • ***
Webster's Revised Unabridged Dictionary
    • n Pythagorean A follower of Pythagoras; one of the school of philosophers founded by Pythagoras.
    • a Pythagorean Of or pertaining to Pythagoras (a Greek philosopher, born about 582 b. c.), or his philosophy. "The central thought of the Pythagorean philosophy is the idea of number, the recognition of the numerical and mathematical relations of things."
    • ***
Century Dictionary and Cyclopedia
    • Pythagorean Of or pertaining to Pythagoras, a Greek philosopher (perhaps 532 b. c.), or the school founded at Crotona (modern Cotrone), in Italy. All testimony concerning this school is of a late date, and the substance of it is rejected by many critics either as improbable, or as probable, and “on that account all the more indemonstrable” (Zeller). The stories are, however, very consistent. The higher grade of the school is represented as a strict monastic community, the doctrine being kept secret, and all betrayals terribly punished, for the purpose of maintaining political ascendancy. Pythagoras is said to have traveled to Egypt and Babylon; and many circumstances are accounted for by supposing that he did so. From those countries he might have brought, as it is said he did, a superior knowledge of mathematics. This knowledge, if kept secret, might have supplied revenues to the school, by calculations and surveys made for citizens. It is difficult to doubt that mathematical science was much advanced within the school. All writers upon ancient mathematics attribute to Pythagoras the Pythagorean proposition and a rule for finding Pythagorean triangles. The importance attached to the pentagram in the school shows that the Pythagoreans were acquainted with its geometrical construction, which is very difficult. They knew the regular or cosmical bodies. They were in possession of many propositions in the theory of numbers, including the doctrine of the arithmetical, geometrical, and harmonical proportions. It is not impossible that they may have had an abacus, little inferior to the Arabic system of arithmetical notation. It is not known how long the society lasted, perhaps for many centuries; as long as it retained any valuable secret it would continue to exist. The Pythagorean philosophy has never been comprehended. The substances of things were held to be abstract numbers; they were in some sense the elements of the universe. Each number, therefore, had its virtue. One was the number of the origin, of reason. Two was the number of matter, of brute force, of evil. Three was the number of mediation, four of justice, five of reproduction, etc. Ten governed the world. In the Pythagorean oath, Pythagoras is called the revealer of the quaternary number — that is, ten — as if something decimal were what he chiefly taught. Something fundamental was also found in odd and even, in square numbers, and the like. Harmony, or music, consists in number. The soul is the harmony, or number, of the body. The universe has also a soul. The remainder of the prominent Pythagorean teachings with which we are acquainted are apparently religious. Pythagoras taught the transmigration of souls. Spirits, both ghosts and demigods, were an object of Pythagorean belief. The brotherhood celebrated certain mysterious rites connected with a view of life as a process of purification. About the time of Augustus, perhaps earlier, Pythagoreanism became mixed with Platonism.
    • n Pythagorean A follower of Pythagoras, the founder of the Italic sect of philosophers.
    • ***
Chambers's Twentieth Century Dictionary
    • adj Pythagorean pi-thag-ō-rē′an pertaining to Pythagoras (c. 532 B.C.), a celebrated Greek philosopher, or to his philosophy
    • n Pythagorean a follower of Pythagoras
    • ***

Etymology

Webster's Revised Unabridged Dictionary
L. Pythagoreus, Gr.

Usage

In literature:

Number and harmony, as in the Pythagorean system, are everywhere dominant in this under-world.
"Scientific American Supplement, No. 365, December 30, 1882" by Various
The Pythagoreans founded their philosophy, religious associations, and political institutions at one and the same time.
"The Atlantic Monthly, Volume 20, No. 117, July, 1867." by Various
In this way Pericles was impressed by the Pythagorean philosophy, and very often quotes it in his speeches.
"Little Journeys To The Homes Of Great Teachers" by Elbert Hubbard
Its doctrine is Pythagorean.
"A Popular History of the Art of Music" by W. S. B. Mathews
Crotona, Italy, home of the Pythagorean School, x, 84.
"Little Journeys to the Homes of the Great - Volume 14" by Elbert Hubbard
The dispersal of the Pythagoreans led to the settlement of many of them, and of their imitators, in Rome and various parts of Italy.
"Outlines of Greek and Roman Medicine" by James Sands Elliott
Pythagoreans, fish reverenced by, why, 54.
"The Biglow Papers" by James Russell Lowell
Apollonius of Tyana, a modern Pythagorean, is the most famous magician of antiquity.
"The Superstitions of Witchcraft" by Howard Williams
Strange attempt to propagate Pythagoreanism; this also dealt with by the government.
"The Religious Experience of the Roman People" by W. Warde Fowler
The Pythagoreans chose the letter Y as their symbol for a good and evil life.
"St. Winifred's" by Frederic W. Farrar
One fact became important to the thought-life of the Pythagoreans.
"Christianity As A Mystical Fact" by Rudolf Steiner
Not that the Pythagorean hypothesis was totally forgotten.
"Great Men and Famous Women. Vol. 3 of 8" by Various
It is well known that the Pythagoreans found all the modes of space in the relations of numbers.
"Notes and Queries, Number 77, April 19, 1851" by Various
It's what you call Pythagoreanism, isn't it?
"The Works of Robert Louis Stevenson - Swanston Edition Vol. 13 (of 25)" by Robert Louis Stevenson
The organization attempted by the Pythagoreans is an exception to the general policy of the Greeks.
"History of the Intellectual Development of Europe, Volume I (of 2)" by John William Draper
Colebrooke saw a striking similarity between the Buddhist philosophy and that of the Pythagoreans.
"Bible Myths and their Parallels in other Religions" by T. W. Doane
We must christen our new art of gardening the Pythagorean.
"Villa Eden:" by Berthold Auerbach
Pythagorean Marquis Valadi, inflamed with "violent motions all night at the Palais Royal"?
"Library of the World's Best Literature, Ancient and Modern, Vol. VIII" by Various
There he founded the Pythagorean Society and lived for many years at the head of it.
"A Critical History of Greek Philosophy" by W. T. Stace
It existed among the Pythagoreans and Druids.
"Religion In The Heavens" by Logan Mitchell
***

In poetry:

Shall a mere shepherd provide the cure of kings?
Heaven itself delights in ironies such
As this, in which a boy's fingers would touch
…….Pythagorean strings
"Saul And David" by Anthony Hecht

In news:

The Pythagoreans of ancient Greece were fascinated by whole numbers.
So, while the Rays' record is sparkly, and even their Pythagorean Expected Record is impressive, there are chinks in the armor.
Pythagorean Fearem (Live at Rock the Garden, 2012).
He is packing up his many books, including those on Euclid, the Greek mathematician, and the Pythagorean Theorem, subjects he has taught for 34 years.
"You mean like the Pythagorean Theorem.".
Indeed, the diagram implies the existence of a right triangle with sides 12, 12, and 17, and that's not quite a Pythagorean triple: 122 + 122 = 288 and 172 = 289.
Nick Begich Interview, live on The Pythagorean Flux (This Weds.
Sept 12th, at 1:00 PM Dr Nick Begich will join " Pythagorean Flux" host David Hovey for a discussion of government "mind-control" programs.
Fred Bell on Pythagorean Flux.
Tune in for Dr Fred Bell on the Pythagorean Flux: Wed, July 25 at 1:30PM.
Pondering an Artist's Perplexing Tribute to the Pythagorean Theorem .
Proving (a Theorem ) and Disproving (a Theory) Applying the Pythagorean Theorem to Real Life.
The Egyptians knew that a 3,4,5 triangle for which the Pythagorean theorem holds was a right triangle, but theorems, the proof of the relationship, are Hellenic.
Fred Bell on Pythagorean Flux .
Tune in for Dr Fred Bell on the Pythagorean Flux : Wed, July 25 at 1:30PM.
***

In science:

On the other hand, a Pythagorean theorem is a consequence of rotational symmetry, and the latter can be obtained through the commutation of Lorentz transformations.
Causal set as a discretized phase spacetime
In light of this, one might argue that if we ”don’t know” Lorentz transformations, we shouldn’t ”know” Pythagorean theorem either.
Causal set as a discretized phase spacetime
On the one hand, postulating Pythagorean theorem requires less axioms and less small constants, so it is more natural from the formal point of view.
Causal set as a discretized phase spacetime
In light of this controversy, I leave it to the reader to choose between sec 3.3 where Pythagorean theorem is postulated by hand and sec 3.4 through sec 3.6 where other axioms are postulated in order to derive it.
Causal set as a discretized phase spacetime
In fact, we are yet to see whether simple things like Pythagorean theorem or Lorentzian geometry hold.
Causal set as a discretized phase spacetime
The reason they are viewed as completely independent of each other is that we are not allowed to use Pythagorean theorem, which means we don’t have means of doing the usual derivations that are used to prove the dependence of γ on v .
Causal set as a discretized phase spacetime
However, there is a geometric way of making this independence compatible with what one would expect of scattering when Pythagorean theorem does hold.
Causal set as a discretized phase spacetime
Rather than using the Pythagorean length of each edge of P, it is more convenient to use a combinatorial metric for the length, which for simplicity we also call length.
Regular Polyhedra of Index Two, I
We can find the shortest distance between two points by using the Pythagorean Theorem, assuming, of course, that we superimpose a grid on the plane the two points lie in. A triangle is simply defined to be three points in space which are joined by three line segments.
Volumes in Hyperbolic Space
Note that the linear sum S is quite distinct from the pythagorean sum variable Q.
Pion interferometry with higher-order cumulants
Br(cid:127)ocker: \Characterization of fans and hereditarily pythagorean (cid:12)elds", Math. Z.  ( )  {. [Br] L.
Separation of Semialgebraic Sets
If F is formal ly real, then statements (1)-(6) hold if and only if F is not a Pythagorean field.
Galois Groups Over Nonrigid Fields
If F is formal ly real, then G1 occurs as a Galois group over F if and only if F is uniquely ordered, which in this case is equivalent to F not being Pythagorean.
Galois Groups Over Nonrigid Fields
Eckert, Primitive Pythagorean Triples, The College Math.
Pythagorean Triples and a New Pythagorean Theorem
Hall, Genealogy of Pythagorean Triads, Math.
Pythagorean Triples and a New Pythagorean Theorem
***