3 edition of **Double elliptic geometry in terms of point and order alone.** found in the catalog.

Double elliptic geometry in terms of point and order alone.

John Robert Kline

- 389 Want to read
- 19 Currently reading

Published
in [n.p
.

Written in English

**Edition Notes**

[Reprinted from Annals of Mathematics, Second Series, Vol. 18, No. 1, September, 1916]

Series | University of Pennsylvania |

The Physical Object | |
---|---|

Pagination | 31-44 p. |

Number of Pages | 44 |

ID Numbers | |

Open Library | OL15383048M |

The first non-Desarguesian plane was noted by David Hilbert in his Foundations of Geometry. [16] The Moulton plane is a standard illustration. In order to provide a context for such geometry as well as those where Desargues theorem is valid, the concept of a ternary ring has been developed.. Rudimentary affine planes are constructed from ordered pairs taken from a ternary ring. Introductory Non-Euclidean Geometry - Ebook written by Henry Parker Manning. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Introductory Non-Euclidean Geometry.

This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. The Elements of Non-Euclidean Geometry - Ebook written by D. M.Y. Sommerville. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read The Elements of Non-Euclidean Geometry.

Dissertation: "Double Elliptic Geometry in Terms of Point and Order Alone." His advisor: R. L. Moore. R. L. Moore, full name Robert Lee Moore [14 Nov ] received his Ph.D. from the University of Chicago in Dissertation: "Metrical Hypotheses for Geometry.". The simplest model of elliptic geometry is that of spherical geometry, where points are points on the sphere, and lines are great circles through those points. On the sphere, such as the surface of the Earth, it is easy to give an example of a triangle that requires more than °: For two of the sides, take lines of longitude that differ by 90°.

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Double elliptic geometry in terms of point and order alone. [Lancaster, Pa., ] (OCoLC) Material Type: Thesis/dissertation: Document Type: Book: All Authors / Contributors: John Robert Kline. Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must r, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two).

"Double Elliptic Geometry in Terms of Point and Order" is an article from The Annals of Mathematics, Volume View more articles from The. Double elliptic geometry in terms of point and order alone / By John Robert Kline. Abstract "Reprinted from Annals of mathematics, second series, vol.

xviii, no. 1, September, ".Thesis (PH. D.)--University of Pennsylvania, Mode of access: InternetAuthor: John Robert Kline. John R. Kline: Double elliptic geometry in terms of point and order alone University of Pennsylvania, Ph.D. George Hallet, Jr.: Linear order in three dimensional Euclidean and double elliptic spaces University of Texas, Austin, Ph.D.

Anna Mullikin: Certain theorems relating to plane connected point sets University of Texas, Austin, Ph.D. Raymond L. Wilder: Concerning. Dissertation: Double Elliptic Geometry in Terms of Point and Order Alone Mathematics Subject Classification: 54—General topology Advisor: R.

(Robert Lee) Moore. Often an elliptic geometry that satisfies this axiom is called a single elliptic geometry. Note that with this model, a line no longer separates the plane into distinct half-planes, due to the association of antipodal points as a single point. Klein formulated another model for elliptic geometry through the use of.

DOUBLE ELLIPTIC GEOMETRY IN TERMS OF POINT AND ORDER ALONE.* BY J. KLINE. Introduction. In his Rational Geometry,t Halsted built up two-dimensional double elliptic geometry, in terms of the undefined symbols point, order, asso-ciation and congruence. In the present paper I propose a categorical set of ten mutually independent axioms for.

sections towill hold in Elliptic Geometry. The material on system will follow that of H.S.M. Coxeter in his book Non-Euclidean Geometry[6] role for elliptic geometry that four-point betweenness served in Chap.

Some properties of Euclidean, hyperbolic, and elliptic geometries. Euclidean Hyperbolic Elliptic Two distinct lines intersect in one point. Two distinct lines intersect in one point. (single) Two distinct lines intersect in one point.

(double) Two distinct lines intersect in two points. The sum of the measures of the angles of a triangle is J. Kline, "Double Elliptic Geometry in Terms of Point and Order Alone," Annals of Mathematics, vol. 18 (), pp.

tI have not completely proved that -my Double Elliptic sets satisfy Condition 3. footnote below concerning 7B. I need something not so technical for a junior graduate student but at the same time I would wish to get a book with authority on elliptic curves.

Thanks. aic-geometry elliptic-curves Also I am taking the guess that you are reading algebraic geometry from the standard book of Hartshorne.

Both points of view have a measure of. Double elliptic geometry in terms of point order and congruence: Caris, Perry Aquila: A solution of the quadratic congruence, modulo p, p = 8n+1, n odd: Gehman, Harry Merrill: (J.

Kline) Concerning the subsets of a plane continuous curve: Hartley, Robert William: (H. Mitchell). VII Double Elliptic Geometry 1. Introduction 2.

Riemann 3. The Elliptic Geometries 4. Geometry on a Sphere 5. A Description of Double Elliptic Geometry 6. Double Elliptic Geometry and the Physical World 7. An Axiomatic Presentation of Double Elliptic Geometry VIII Single Elliptic Geometry 1. Intoduction 2.

Geometry on a Modified Hemisphere 3. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share.

The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section on the author's useful concept of inversive distance. Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence.

If we call a straight line of the bundle a s. polnt" in elliptic space and a plane of the bundle a "line", we can easily see how the following well-known theorems from Euclidean geometry can be modified to represent something in the elliptic geometry.

3 El, Two lines. Foundations of geometry is the study of geometries as axiomatic are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint.

The query for equilateral point sets in elliptic geometry leads to the search for matrices B of order n and elements whose smallest eigenvalue has a high multiplicity.

For n elliptic points A 1, A 2,A n, carried by the unit vectors a 1,a n and spanning elliptic space E r−1, the Gram matrix is symmetric, semipositive definite, and. Double elliptic geometry in terms of point and order alone / ([Lancaster, Pa.

Princeton, N.J., ]), by John Robert Kline (page images at HathiTrust; US access only) Non-Euclidean geometry: a critical and historical study of its development / (Chicago: Open Court Publishing Company, ), by Roberto Bonola, trans.

by H. Carslaw (page. Yes, the example in the Veblen's paper gives a model of ordered geometry (only axioms of incidence and order) with the elliptic parallel property. If I understood his example correctly, he just takes the projective plane $\mathbb{P}^2(\mathbb{Q})$ and defines the ordering of points there.bian elliptic functions.

These elliptic integrals and functions ﬁnd many applications in the theory of numbers, algebra, geometry, linear and non-linear ordinary and partial diﬀerential equations, dynamics, mechanics, electrostatics, conduction and ﬁeld theory.

An elliptic integral is any integral of the general form f(x)= A(x)+B(x) C(x.APPENDIX A Euclid's Definitions, Postulates, and the First 30 Propositions of Book I* Definitions 1. A point is that which has no part. 2. A line is breadthless length. 3. The extremities of a line are points.

4. A straight line is a line which lies evenly with the points on itself. 5. A .