# euclidean

## Definitions

• WordNet 3.6
• adj euclidean relating to geometry as developed by Euclid "Euclidian geometry"
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Century Dictionary and Cyclopedia
• Euclidean Of or pertaining to Euclid, an illustrious Greek mathematician (who lived about 300 b. c.), the author of the “Elements of Geometry,” which has been the chief text-book of this subject down to recent times, and is still much used in England. By fixing the admission of certain propositions as more elementary than others, the work has greatly influenced the mode of presentation of mathematical theories.
• Euclidean Of or pertaining to Euclid, or Eukleides, Arch on Eponymos of Athens for the year 403 b. c. The term specifically notes this date in Greek epigraphy, because under Eukleides the so-called Ionian alphabet, with the letters eta and omega and the upright gamma and lambda, was first brought into official use for public documents, and thereafter became usual, and soon universal, in all inscriptions, etc.; hence it also notes the alphabet commonly used at Athens after the year of Eukleides.
• Euclidean Also spelled Eukleidean.
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Chambers's Twentieth Century Dictionary
• adj Euclidean ū-klid′e-an or ū-kli-dē′an pertaining to Euclid, a mathematician of Alexandria about 300 B.C.
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## Usage

### In literature:

Fourth Dimensional revelations by some Euclidean deity!
"The Metal Monster" by A. Merritt
In their non-Euclidean geometry the part is always greater than the whole.
"The Open Secret of Ireland" by T. M. Kettle
Accordingly the Euclidean property of space arises from the parabolic property of time.
"The Concept of Nature" by Alfred North Whitehead
She could find no hole in Elizabeth's arguments; it was founded as solidly as a Euclidean proposition.
"Miss Mapp" by Edward Frederic Benson
Non-Euclidean geometry, II, 83.
"A Budget of Paradoxes, Volume II (of II)" by Augustus de Morgan
The argument in a Euclidean demonstration would not be made clearer by being cast into formal Syllogisms.
"Logic, Inductive and Deductive" by William Minto
It was developed with rigorous mathematical logic and Euclidean conclusiveness.
"Education: How Old The New" by James J. Walsh
The geometry on such a surface is shown to be Euclidean, limit-lines replacing Euclidean straight lines.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
In elementary geometry, however, the Euclidean idea is still held.
"The Teaching of Geometry" by David Eugene Smith
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### In news:

In Nat Friedman's "Pas de Deux," the perimeter straight-line Euclidean geometry plays the supporting role for the interesting inner fractal geometry.
Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals , and other ideas furnished the mathematical underpinnings.
We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space.
They determine the neighborhood graph using Euclidean distance so that they often fail to nicely deal with sparsely sampled or noise contaminated data.
CEREBELLUM'S FRONT AND BACK can be combined into single flat maps (shown here in Euclidean and hyperbolic views) to reveal details that are normally hidden in the brain's folds.
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### In science:

The total number of such eigenvalues increases with the square root of the Euclidean four-volume.
Random Matrix Theory and Chiral Symmetry in QCD
The QCD partition function can be written as a Euclidean path integral that can be expressed as the expectation value of the fermion determinant, det(D + mf )E .
Random Matrix Theory and Chiral Symmetry in QCD
Here the average is over all gauge ﬁelds weighted by the Euclidean Yang-Mills action, the product is over quark ﬂavors of mass mf , and D is the Dirac operator, which we introduce in great detail in Sec. 2.
Random Matrix Theory and Chiral Symmetry in QCD
For the Euclidean QCD partition function, it is more natural to construct a random matrix model for the Dirac operator.
Random Matrix Theory and Chiral Symmetry in QCD
We now consider QCD in a ﬁnite Euclidean volume V4 = L4 .
Random Matrix Theory and Chiral Symmetry in QCD
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