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Thursday, May 21, 2020 | History

2 edition of twenty-seven lines upon the cubic surface found in the catalog.

twenty-seven lines upon the cubic surface

Henderson, Archibald

twenty-seven lines upon the cubic surface

by Henderson, Archibald

  • 172 Want to read
  • 10 Currently reading

Published by University Press in Cambridge .
Written in English

    Subjects:
  • Surfaces, Cubic

  • Edition Notes

    Bibliography: p. [96]-100.

    Statementby Archibald Henderson.
    SeriesCambridge tracts in mathematics and mathematical physics,, no. 13
    Classifications
    LC ClassificationsQA603 .H5
    The Physical Object
    Pagination100 p.
    Number of Pages100
    ID Numbers
    Open LibraryOL6539537M
    LC Control Number12001206
    OCLC/WorldCa2135085

    It is hypothetized that the algebra of the configuration of twenty-seven lines lying on a general cubic surface underlines the dimensional hierarchy of. Around the History of the Twenty-seven Lines upon Cubic 2 From the diagonal surface to geometrical equations The Nachrichten der Königlichen Gesellschaft der Wissenschaften und der G.A. Univer-sität zu Göttingen of contains a account (p. ) of when Clebsch presented two.

    Other Works: Book: "The Twenty-Seven Lines Upon the Cubic Surface". See more»Occupation: Writer. THE TWENTY-SEVEN LINES ON THE SMOOTH CUBIC X ˆ P3 C 3 X= Pn and L= O Pn(1) and s= x 0 2(X;L), we would visualize sas the hyperplane H= fx 0 = 0g. This explains why the dimension is dimV 1, because if two sections agree up to scalar, then they give rise to the same zero section.

    Website dedicated to cubic surfaces, by Oliver Labs: Knörrer and Miller: Topologische Typen reeller kubischer Flächen, Mathematische Zeitschrift volume ; pp. 51 - 91 A. henderson, the 27 lines upon the cubic surface, Hafner, N. Y., B. Segre, the non-singular cubic surfaces, Oxford, The Twenty-Seven Lines Upon the Cubic Surface: 2: The Conquest of the Old Southwest; the romantic story of the early pioneers into Virginia, the Carolinas, Tennessee, and Kentucky, George Bernard Shaw: man of the century: 7: Mark Twain: European Dramatists: 2: Campus of the First State University. 4.


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Twenty-seven lines upon the cubic surface by Henderson, Archibald Download PDF EPUB FB2

Buy The Twenty-Seven Lines upon the Cubic Surface (Cambridge Tracts in Mathematics) on FREE SHIPPING on qualified orders The Twenty-Seven Lines upon the Cubic Surface (Cambridge Tracts in Mathematics): Henderson, Archibald: : BooksCited by:   Buy Twenty-Seven Lines Upon the Cubic Surface on FREE SHIPPING on qualified orders Twenty-Seven Lines Upon the Cubic Surface: Henderson, Archibald: : Books Skip to main contentPrice: $ Ludwig Schläfli An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface, Quarterly J.

Math. 2 55–56; Gesammelte Mathematische Abhandlungen, 2 – (Birkhäuser, Basel, ).Cited by: 3. The twenty-seven lines upon the cubic surface by Archibald Henderson. Henderson, Archibald, Chicago: ,  Abstract Citations References Co-Reads Similar Papers Metrics Export Citation NASA/ADS.

The Twenty-Seven Lines upon the Cubic Surface Abstract. Publication: Nature. Pub Date: January DOI: /a0 Bibcode: Natur Buy The Twenty-Seven Lines upon the Cubic Surface by Archibald Henderson from Waterstones today. Click and Collect from your local Waterstones or get FREE UK delivery on orders over £ The discovery of 27 lines on a general cubic surface can be considered as the first non-trivial result on algebraic surfaces of order higher than 2.

In fact, it can be considered as the beginning of modern algebraic geometry. This animation by Greg Egan shows 27 lines on a surface defined by cubic equations: the Clebsch surface.

It illustrates a remarkable fact: any smooth cubic surface contains 27 lines. In its most symmetrical presentation, the Clebsch surface is defined by the equations $$ \begin{array}{c} x_0+x_1+x_2+x_3+x_4 = 0 \\.

cubic surface contains a finite number of lines. Salmon proves that the number of lines must be equal to Salmon’s proof is presented in Cayley’s paper [Cay].

In the same paper Cayley shows that a general cubic surface admits 45 tritangent planes, i.e. planes planes which intersect the surface along the union of three lines.

About this Book Catalog Record Details. The twenty-seven lines upon the cubic surface / by Archibald Henderson, Archibald, View full catalog record. Rights: Public Domain. Genre/Form: Academic theses: Additional Physical Format: Online version: Henderson, Archibald, Twenty-seven lines upon the cubic surface.

Twenty-seven Lines on a cubic surface: encounters between groups, equations, and geometry in the second half of the 19th century Article June with 6 Reads How we measure 'reads'.

A brief history In Archibald Henderson wrote in his book [Hen] “While it is doubteless true that the classification of cubic surfaces is complete, the number of papers dealing with these surfaces which continue to appear from year to year furnish abundant proof of the fact that they still possess much the same fascination as they did in the days of their discovery of the twenty-seven lines upon the cubic surface.”.

The twenty-seven lines upon the cubic surface / By Archibald Henderson. Abstract. Reprint. Originally published. Chicago: University of Chicago, "A dissertation submitted to the faculty of the graduate school of Arts and Literature in candidacy for the degree of Doctor of Philosophy."Includes bibliographical references (p.

[96 Author: Archibald Henderson. Cubic surface Twenty-seven lines: Additional Physical Format: Online version: Henderson, Archibald, Twenty-seven lines upon the cubic surface. New York, Hafner Pub. [?] (OCoLC) Document Type: Book: All Authors / Contributors: Archibald Henderson.

An Attempt to Determine the Twenty-Seven Lines upon a Surface of the Third Order, and to Divide such Surfaces into Species in Reference to the Reality of the Lines upon the Surface.

Quarterly Journal for Pure and Applied Mathematics, II–66, –, Cited by: 3. The set of 27 lines on a cubic surface. It is a well-known fact that on a generic cubic surface, K 3, there is a configuration of 27 lines.

Although this configuration is geometrically perfectly symmetric as it stands, it exhibits a remarkable non-trivial structure when intersection/incidence relations between the individual lines are taken Cited by: 5. Henderson, Archibald (), [Expression error: Missing operand for > The twenty-seven lines upon the cubic surface], Reprinting of Cambridge Tracts in Mathematics and Mathematical Physics, No.

13, Merchant books, MRISBN Henderson, Archibald, The twenty-seven lines upon the cubic surface, (Cambridge, University Press, ) (page images at HathiTrust; US access only) Henderson, Archibald, The twenty-seven lines upon the cubic surface / ([Ann Arbor, MI]: University of Michigan University Library, [?]) (page images at HathiTrust; US.

The Twenty-Seven Lines Upon the Cubic Surface by Archibald Henderson avg rating — 0 ratings — published — 3 editions. In the previous post, we introduced the Fano scheme of a subscheme of projective space, as the Hilbert scheme of planes of a certain dimension on that subscheme.

In this post, I’d like to work out an explicit example, of the 27 lines on a smooth cubic surface in ; as we’ll see, the Fano scheme is 27 reduced points, and the count can be made with a little calculation on the Grassmannian.Abstract. Abstract. We discuss the contribution of Luigi Cremona to the early development of the theory of cubic surfaces.

1. A brief history In Archibald Henderson wrote in his book [Hen] “While it is doubteless true that the classification of cubic surfaces is complete, the number of papers dealing with these surfaces which continue to appear from year to year furnish abundant proof Author: Igor V.

Dolgachev.The problem of the twenty-seven lines upon a cubic surface is of such scope and extent and is allied to so many other problems of importance that,to give a resume of all that has i Extrait d'une lettre addressee a M.

O. Jordan, Journal de Liouville.