Annals of the New York Academy of Sciences

Cover image for Annals of the New York Academy of Sciences

May 1985

Volume 440 Discrete Geometry and Convexity

Pages vii–xii, 1–392

    1. PREFACE (pages vii–xii)

      J. E. Goodman, E. Lutwak, J. Malkevitch and R. Pollack

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14531.x

    2. INTRODUCTION (pages ix–xii)

      J. E. Goodman, E. Lutwak, J. Malkevitch and R. Pollack

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14532.x

  1. Part I. Discrete Problems

    1. Top of page
    2. Part I. Discrete Problems
    3. Part II. Quantitative Convexity
    4. Part III. Qualitative Convexity
    5. Part IV. Polyhedral Geometry
    6. Part V. Tiling, Packing, Covering, and Weaving
    7. Part VI. Computational Aspects
    1. PROBLEMS AND RESULTS IN COMBINATORIAL GEOMETRY (pages 1–11)

      P. Erdös

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14533.x

    2. A COMBINATORIAL VERSION OF THE ISOTOPY CONJECTURE (pages 12–19)

      Jacob E. Goodman and Richard Pollack

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14534.x

    3. OLD AND NEW EUCLIDEAN RAMSEY THEOREMS (pages 20–30)

      R. L. Graham

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14535.x

    4. SOME SIMPLE ARRANGEMENTS OF PSEUDOLINES WITH A MAXIMUM NUMBER OF TRIANGLES (pages 31–33)

      Heiko Harborth

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14536.x

    5. A SURVEY OF THE SLOPE PROBLEM (pages 34–51)

      Robert E. Jamison

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14537.x

    6. PROBLEMS ON EXTREMAL PROPERTIES OF A FINITE SET OF POINTS (pages 52–64)

      W. O. J. Moser

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14538.x

    7. SOME COMBINATORIAL PROBLEMS IN THE PLANE (pages 65–68)

      George B. Purdy

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14539.x

    8. EXTREMAL ARRANGEMENTS OF HYPERPLANES (pages 69–87)

      Thomas Zaslavsky

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14540.x

  2. Part II. Quantitative Convexity

    1. Top of page
    2. Part I. Discrete Problems
    3. Part II. Quantitative Convexity
    4. Part III. Qualitative Convexity
    5. Part IV. Polyhedral Geometry
    6. Part V. Tiling, Packing, Covering, and Weaving
    7. Part VI. Computational Aspects
    1. THE SUM OF DISTANCES DETERMINED BY POINTS ON A SPHERE (pages 88–91)

      G. D. Chakerian and M. A. Ghandehari

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14541.x

    2. THE INTEGRAL-GEOMETRIC DENSITIES OF TANGENT FLATS TO CONVEX BODIES (pages 92–96)

      William J. Firey

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14542.x

    3. VOLUME AND CIRCUMRADIUS OF SIMPLICIAL POLYTOPES (pages 97–105)

      Johann Linhart

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14543.x

    4. ON THE BLASCHKE-SANTALÓ INEQUALITY (pages 106–112)

      Erwin Lutwak

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14544.x

    5. AFFINE ISOPERIMETRIC PROBLEMS (pages 113–127)

      C. M. Petty

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14545.x

    6. ON SOME INVARIANTS UNDER SIMILITUDES FOR CONVEX BODIES (pages 128–131)

      L. A. Santaló

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14546.x

    7. ON THE ALEKSANDROV-FENCHEL INEQUALITY (pages 132–141)

      Rolf Schneider

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14547.x

  3. Part III. Qualitative Convexity

    1. Top of page
    2. Part I. Discrete Problems
    3. Part II. Quantitative Convexity
    4. Part III. Qualitative Convexity
    5. Part IV. Polyhedral Geometry
    6. Part V. Tiling, Packing, Covering, and Weaving
    7. Part VI. Computational Aspects
    1. KRASNOSEL'SKII-TYPE THEOREMS (pages 142–146)

      Marilyn Breen

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14548.x

    2. CHOQUET SIMPLICES IN FINITE DIMENSIONS (pages 147–162)

      René Fourneau

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14549.x

    3. RESULTS OF BAIRE CATEGORY TYPE IN CONVEXITY (pages 163–169)

      Peter M. Gruber

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14550.x

    4. CONCURRENT NORMALS AND CRITICAL POINTS UNDER WEAK SMOOTHNESS ASSUMPTIONS (pages 170–178)

      E. Heil

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14551.x

    5. GENERALIZATIONS OF TIETZE'S THEOREM ON LOCAL CONVEXITY FOR SETS IN Rd (pages 179–191)

      David C. Kay

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14552.x

  4. Part IV. Polyhedral Geometry

    1. Top of page
    2. Part I. Discrete Problems
    3. Part II. Quantitative Convexity
    4. Part III. Qualitative Convexity
    5. Part IV. Polyhedral Geometry
    6. Part V. Tiling, Packing, Covering, and Weaving
    7. Part VI. Computational Aspects
    1. COLORING POLYHEDRAL MANIFOLDS (pages 192–195)

      D. W. Barnette

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14553.x

    2. CONVEX BODIES AND ALGEBRAIC GEOMETRY (pages 196–204)

      Günter Ewald

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14554.x

    3. TRIANGULATING THE d-CUBE (pages 205–211)

      Carl W. Lee

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14555.x

    4. THE NUMBER OF FACES OF SIMPLICIAL POLYTOPES AND SPHERES (pages 212–223)

      Richard P. Stanley

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14556.x

    5. POLYHEDRAL MANIFOLDS WITH PROPERTIES OF THE PLATONIC SOLIDS (pages 224–229)

      J. M. Wills

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14557.x

  5. Part V. Tiling, Packing, Covering, and Weaving

    1. Top of page
    2. Part I. Discrete Problems
    3. Part II. Quantitative Convexity
    4. Part III. Qualitative Convexity
    5. Part IV. Polyhedral Geometry
    6. Part V. Tiling, Packing, Covering, and Weaving
    7. Part VI. Computational Aspects
    1. TILING EUCLIDEAN d-SPACE WITH CONGRUENT SIMPLEXES (pages 230–261)

      Hans E. Debrunner

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14558.x

    2. COVERINGS AND PACKINGS BY SEQUENCES OF CONVEX SETS (pages 262–278)

      H. Groemer

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14559.x

    3. A CATALOGUE OF ISONEMAL FABRICS (pages 279–298)

      Branko Grünbaum and G. C. Shephard

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14560.x

    4. TILING CONVEX POLYGONS WITH EQUILATERAL TRIANGLES AND SQUARES (pages 299–303)

      Joseph Malkevitch

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14561.x

    5. TILING BOUNDED OPEN SETS WITH SQUARES THAT TOUCH THE BOUNDARY (pages 304–322)

      William T. Trotter Jr.

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14562.x

  6. Part VI. Computational Aspects

    1. Top of page
    2. Part I. Discrete Problems
    3. Part II. Quantitative Convexity
    4. Part III. Qualitative Convexity
    5. Part IV. Polyhedral Geometry
    6. Part V. Tiling, Packing, Covering, and Weaving
    7. Part VI. Computational Aspects
    1. REMARKS ON THE SPHERE OF INFLUENCE GRAPH (pages 323–327)

      David Avis and Joe Horton

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14563.x

    2. A NEW BOUND FOR EUCLIDEAN STEINER MINIMAL TREES (pages 328–346)

      F. R. K. Chung and R. L. Graham

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14564.x

    3. GEOMETRIC SORTING THEORY (pages 347–354)

      Jacob E. Goodman and Richard Pollack

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14565.x

    4. LEAST SQUARES FITTING PROCEDURES FOR PROBLEMS INVOLVING MORE THAN ONE HYPERPLANE (pages 355–363)

      A. C. Hayes and D. G. Larman

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14566.x

    5. AN UPDATE ON THE ELLIPSOID ALGORITHM (pages 364–380)

      P. F. Pickel

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14567.x

    1. Index of Contributors (pages 381–382)

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14568.x

    2. Author Index (pages 383–388)

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14569.x

    3. Subject Index (pages 389–392)

      Article first published online: 16 DEC 2006 | DOI: 10.1111/j.1749-6632.1985.tb14570.x

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