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Space-filling curves / Hans Sagan
Space-filling curves / Hans Sagan
Autore Sagan, Hans
Pubbl/distr/stampa New York : Berlin, c1994
Descrizione fisica xv, 193 p. : ill. ; 24 cm
Disciplina 513.3
Collana Universitext
Soggetto non controllato Curve su superfici
Topologia
ISBN 0-387-94265-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-990001496010403321
Sagan, Hans  
New York : Berlin, c1994
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Space-Filling Curves [[electronic resource] /] / by Hans Sagan
Space-Filling Curves [[electronic resource] /] / by Hans Sagan
Autore Sagan Hans
Edizione [1st ed. 1994.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
Descrizione fisica 1 online resource (XV, 194 p.)
Disciplina 516.3/62
Collana Universitext
Soggetto topico Geometry
ISBN 1-4612-0871-8
Classificazione 54F50
28A75
54-03
01A55
01A60
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 1.1. A Brief History of Space-Filling Curves -- 1.2. Notation -- 1.3. Definitions and Netto’s Theorem -- 1.4. Problems -- 2. Hilbert’s Space-Filling Curve -- 2.1. Generation of Hilbert’s Space-Filling Curve -- 2.2. Nowhere Differentiability of the Hilbert Curve -- 2.3. A Complex Representation of the Hilbert Curve -- 2.4. Arithmetization of the Hilbert Curve -- 2.5. An Analytic Proof of the Nowhere Differentiability of the Hilbert Curve -- 2.6. Approximating Polygons for the Hilbert Curve -- 2.7. Moore’s Version of the Hilbert Curve -- 2.8. A Three-Dimensional Hilbert Curve -- 2.9. Problems -- 3. Peano’s Space-Filling Curve -- 3.1. Definition of Peano’s Space-Filling Curve -- 3.2. Nowhere Differentiability of the Peano Curve -- 3.3. Geometric Generation of the Peano Curve -- 3.4. Proof that the Peano Curve and the Geometric Peano Curve are the Same -- 3.5. Cesaro’s Representation of the Peano Curve -- 3.6. Approximating Polygons for the Peano Curve -- 3.7. Wunderlich’s Versions of the Peano Curve -- 3.8. A Three-Dimensional Peano Curve -- 3.9. Problems -- 4. Sierpi?ski’s Space-Filling Curve -- 4.1. Sierpi?ski’s Original Definition -- 4.2. Geometric Generation and Knopp’s Representation of the Sierpi?ski Curve -- 4.3. Representation of the Sierphiski-Knopp Curve in Terms of Quaternaries -- 4.4. Nowhere Differentiability of the Sierpi?ski-Knopp Curve -- 4.5. Approximating Polygons for the Sierpi?ski-Knopp Curve -- 4.6. Pólya’s Generalization of the Sierpi?ski-Knopp Curve -- 4.7. Problems -- 5. Lebesgue’s Space-Filling Curve -- 5.1. The Cantor Set -- 5.2. Properties of the Cantor Set -- 5.3. The Cantor Function and the Devil’s Staircase -- 5.4. Lebesgue’s Definition of a Space-Filling Curve -- 5.5. Approximating Polygons for the Lebesgue Curve -- 5.6. Problems -- 6. Continuous Images of a Line Segment -- 6.1. Preliminary Remarks and a Global Characterization of Continuity -- 6.2. Compact Sets -- 6.3. Connected Sets -- 6.4. Proof of Netto’s Theorem -- 6.5. Locally Connected Sets -- 6.6. A Theorem by Hausdorff -- 6.7. Pathwise Connectedness -- 6.8. The Hahn-Mazurkiewicz Theorem -- 6.9. Generation of Space-Filling Curves by Stochastically Independent Functions -- 6.10. Representation of a Space-Filling Curve by an Analytic Function -- 6.11. Problems -- 7. Schoenberg’s Space-Filling Curve -- 7.1. Definition and Basic Properties -- 7.2. The Nowhere Differentiability of the Schoenberg Curve -- 7.3. Approximating Polygons -- 7.4. A Three-Dimensional Schoenberg Curve -- 7.5. An No-Dimensional Schoenberg Curve -- 7.6. Problems -- 8. Jordan Curves of Positive Lebesgue Measure -- 8.1. Jordan Curves -- 8.2. Osgood’s Jordan Curves of Positive Measure -- 8.3. The Osgood Curves of Sierpi?ski and Knopp -- 8.4. Other Osgood Curves -- 8.5. Problems -- 9. Fractals -- 9.1. Examples -- 9.2. The Space where Fractals are Made -- 9.3. The Invariant Attractor Set -- 9.4. Similarity Dimension -- 9.5. Cantor Curves -- 9.6. The Heighway-Dragon -- 9.7. Problems -- A.1. Computer Programs 169 A.1.1. Computation of the Nodal Points of the Hilbert Curve -- A.1.2. Computation of the Nodal Points of the Peano Curve -- A.1.3. Computation of the Nodal Points of the Sierpi?ski-Knopp Curve -- A.1.4. Plotting Program for the Approximating Polygons of the Schoenberg Curve -- A.2. Theorems from Analysis -- A.2.1. Binary and Other Representations -- A.2.2. Condition for Non-Differentiability -- A.2.3. Completeness of the Euclidean Space -- A.2.4. Uniform Convergence -- A.2.5. Measure of the Intersection of a Decreasing Sequence of Sets -- A.2.6. Cantor’s Intersection Theorem -- A.2.7. Infinite Products -- References.
Record Nr. UNINA-9910480138103321
Sagan Hans  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Space-Filling Curves [[electronic resource] /] / by Hans Sagan
Space-Filling Curves [[electronic resource] /] / by Hans Sagan
Autore Sagan Hans
Edizione [1st ed. 1994.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
Descrizione fisica 1 online resource (XV, 194 p.)
Disciplina 516.3/62
Collana Universitext
Soggetto topico Geometry
ISBN 1-4612-0871-8
Classificazione 54F50
28A75
54-03
01A55
01A60
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 1.1. A Brief History of Space-Filling Curves -- 1.2. Notation -- 1.3. Definitions and Netto’s Theorem -- 1.4. Problems -- 2. Hilbert’s Space-Filling Curve -- 2.1. Generation of Hilbert’s Space-Filling Curve -- 2.2. Nowhere Differentiability of the Hilbert Curve -- 2.3. A Complex Representation of the Hilbert Curve -- 2.4. Arithmetization of the Hilbert Curve -- 2.5. An Analytic Proof of the Nowhere Differentiability of the Hilbert Curve -- 2.6. Approximating Polygons for the Hilbert Curve -- 2.7. Moore’s Version of the Hilbert Curve -- 2.8. A Three-Dimensional Hilbert Curve -- 2.9. Problems -- 3. Peano’s Space-Filling Curve -- 3.1. Definition of Peano’s Space-Filling Curve -- 3.2. Nowhere Differentiability of the Peano Curve -- 3.3. Geometric Generation of the Peano Curve -- 3.4. Proof that the Peano Curve and the Geometric Peano Curve are the Same -- 3.5. Cesaro’s Representation of the Peano Curve -- 3.6. Approximating Polygons for the Peano Curve -- 3.7. Wunderlich’s Versions of the Peano Curve -- 3.8. A Three-Dimensional Peano Curve -- 3.9. Problems -- 4. Sierpi?ski’s Space-Filling Curve -- 4.1. Sierpi?ski’s Original Definition -- 4.2. Geometric Generation and Knopp’s Representation of the Sierpi?ski Curve -- 4.3. Representation of the Sierphiski-Knopp Curve in Terms of Quaternaries -- 4.4. Nowhere Differentiability of the Sierpi?ski-Knopp Curve -- 4.5. Approximating Polygons for the Sierpi?ski-Knopp Curve -- 4.6. Pólya’s Generalization of the Sierpi?ski-Knopp Curve -- 4.7. Problems -- 5. Lebesgue’s Space-Filling Curve -- 5.1. The Cantor Set -- 5.2. Properties of the Cantor Set -- 5.3. The Cantor Function and the Devil’s Staircase -- 5.4. Lebesgue’s Definition of a Space-Filling Curve -- 5.5. Approximating Polygons for the Lebesgue Curve -- 5.6. Problems -- 6. Continuous Images of a Line Segment -- 6.1. Preliminary Remarks and a Global Characterization of Continuity -- 6.2. Compact Sets -- 6.3. Connected Sets -- 6.4. Proof of Netto’s Theorem -- 6.5. Locally Connected Sets -- 6.6. A Theorem by Hausdorff -- 6.7. Pathwise Connectedness -- 6.8. The Hahn-Mazurkiewicz Theorem -- 6.9. Generation of Space-Filling Curves by Stochastically Independent Functions -- 6.10. Representation of a Space-Filling Curve by an Analytic Function -- 6.11. Problems -- 7. Schoenberg’s Space-Filling Curve -- 7.1. Definition and Basic Properties -- 7.2. The Nowhere Differentiability of the Schoenberg Curve -- 7.3. Approximating Polygons -- 7.4. A Three-Dimensional Schoenberg Curve -- 7.5. An No-Dimensional Schoenberg Curve -- 7.6. Problems -- 8. Jordan Curves of Positive Lebesgue Measure -- 8.1. Jordan Curves -- 8.2. Osgood’s Jordan Curves of Positive Measure -- 8.3. The Osgood Curves of Sierpi?ski and Knopp -- 8.4. Other Osgood Curves -- 8.5. Problems -- 9. Fractals -- 9.1. Examples -- 9.2. The Space where Fractals are Made -- 9.3. The Invariant Attractor Set -- 9.4. Similarity Dimension -- 9.5. Cantor Curves -- 9.6. The Heighway-Dragon -- 9.7. Problems -- A.1. Computer Programs 169 A.1.1. Computation of the Nodal Points of the Hilbert Curve -- A.1.2. Computation of the Nodal Points of the Peano Curve -- A.1.3. Computation of the Nodal Points of the Sierpi?ski-Knopp Curve -- A.1.4. Plotting Program for the Approximating Polygons of the Schoenberg Curve -- A.2. Theorems from Analysis -- A.2.1. Binary and Other Representations -- A.2.2. Condition for Non-Differentiability -- A.2.3. Completeness of the Euclidean Space -- A.2.4. Uniform Convergence -- A.2.5. Measure of the Intersection of a Decreasing Sequence of Sets -- A.2.6. Cantor’s Intersection Theorem -- A.2.7. Infinite Products -- References.
Record Nr. UNINA-9910789341503321
Sagan Hans  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Space-Filling Curves [[electronic resource] /] / by Hans Sagan
Space-Filling Curves [[electronic resource] /] / by Hans Sagan
Autore Sagan Hans
Edizione [1st ed. 1994.]
Pubbl/distr/stampa New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
Descrizione fisica 1 online resource (XV, 194 p.)
Disciplina 516.3/62
Collana Universitext
Soggetto topico Geometry
ISBN 1-4612-0871-8
Classificazione 54F50
28A75
54-03
01A55
01A60
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. Introduction -- 1.1. A Brief History of Space-Filling Curves -- 1.2. Notation -- 1.3. Definitions and Netto’s Theorem -- 1.4. Problems -- 2. Hilbert’s Space-Filling Curve -- 2.1. Generation of Hilbert’s Space-Filling Curve -- 2.2. Nowhere Differentiability of the Hilbert Curve -- 2.3. A Complex Representation of the Hilbert Curve -- 2.4. Arithmetization of the Hilbert Curve -- 2.5. An Analytic Proof of the Nowhere Differentiability of the Hilbert Curve -- 2.6. Approximating Polygons for the Hilbert Curve -- 2.7. Moore’s Version of the Hilbert Curve -- 2.8. A Three-Dimensional Hilbert Curve -- 2.9. Problems -- 3. Peano’s Space-Filling Curve -- 3.1. Definition of Peano’s Space-Filling Curve -- 3.2. Nowhere Differentiability of the Peano Curve -- 3.3. Geometric Generation of the Peano Curve -- 3.4. Proof that the Peano Curve and the Geometric Peano Curve are the Same -- 3.5. Cesaro’s Representation of the Peano Curve -- 3.6. Approximating Polygons for the Peano Curve -- 3.7. Wunderlich’s Versions of the Peano Curve -- 3.8. A Three-Dimensional Peano Curve -- 3.9. Problems -- 4. Sierpi?ski’s Space-Filling Curve -- 4.1. Sierpi?ski’s Original Definition -- 4.2. Geometric Generation and Knopp’s Representation of the Sierpi?ski Curve -- 4.3. Representation of the Sierphiski-Knopp Curve in Terms of Quaternaries -- 4.4. Nowhere Differentiability of the Sierpi?ski-Knopp Curve -- 4.5. Approximating Polygons for the Sierpi?ski-Knopp Curve -- 4.6. Pólya’s Generalization of the Sierpi?ski-Knopp Curve -- 4.7. Problems -- 5. Lebesgue’s Space-Filling Curve -- 5.1. The Cantor Set -- 5.2. Properties of the Cantor Set -- 5.3. The Cantor Function and the Devil’s Staircase -- 5.4. Lebesgue’s Definition of a Space-Filling Curve -- 5.5. Approximating Polygons for the Lebesgue Curve -- 5.6. Problems -- 6. Continuous Images of a Line Segment -- 6.1. Preliminary Remarks and a Global Characterization of Continuity -- 6.2. Compact Sets -- 6.3. Connected Sets -- 6.4. Proof of Netto’s Theorem -- 6.5. Locally Connected Sets -- 6.6. A Theorem by Hausdorff -- 6.7. Pathwise Connectedness -- 6.8. The Hahn-Mazurkiewicz Theorem -- 6.9. Generation of Space-Filling Curves by Stochastically Independent Functions -- 6.10. Representation of a Space-Filling Curve by an Analytic Function -- 6.11. Problems -- 7. Schoenberg’s Space-Filling Curve -- 7.1. Definition and Basic Properties -- 7.2. The Nowhere Differentiability of the Schoenberg Curve -- 7.3. Approximating Polygons -- 7.4. A Three-Dimensional Schoenberg Curve -- 7.5. An No-Dimensional Schoenberg Curve -- 7.6. Problems -- 8. Jordan Curves of Positive Lebesgue Measure -- 8.1. Jordan Curves -- 8.2. Osgood’s Jordan Curves of Positive Measure -- 8.3. The Osgood Curves of Sierpi?ski and Knopp -- 8.4. Other Osgood Curves -- 8.5. Problems -- 9. Fractals -- 9.1. Examples -- 9.2. The Space where Fractals are Made -- 9.3. The Invariant Attractor Set -- 9.4. Similarity Dimension -- 9.5. Cantor Curves -- 9.6. The Heighway-Dragon -- 9.7. Problems -- A.1. Computer Programs 169 A.1.1. Computation of the Nodal Points of the Hilbert Curve -- A.1.2. Computation of the Nodal Points of the Peano Curve -- A.1.3. Computation of the Nodal Points of the Sierpi?ski-Knopp Curve -- A.1.4. Plotting Program for the Approximating Polygons of the Schoenberg Curve -- A.2. Theorems from Analysis -- A.2.1. Binary and Other Representations -- A.2.2. Condition for Non-Differentiability -- A.2.3. Completeness of the Euclidean Space -- A.2.4. Uniform Convergence -- A.2.5. Measure of the Intersection of a Decreasing Sequence of Sets -- A.2.6. Cantor’s Intersection Theorem -- A.2.7. Infinite Products -- References.
Record Nr. UNINA-9910811737603321
Sagan Hans  
New York, NY : , : Springer New York : , : Imprint : Springer, , 1994
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Space-filling curves / Hans Sagan
Space-filling curves / Hans Sagan
Autore Sagan, Hans
Pubbl/distr/stampa New York : Springer-Verlag, c1994
Descrizione fisica xv, 193 p. : ill. ; 24 cm.
Disciplina 516.362
Collana Universitext
Soggetto topico Curves on surfaces
Topology
ISBN 0387942653
Classificazione AMS 26A99
AMS 54F50
QA643.S12
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991001359139707536
Sagan, Hans  
New York : Springer-Verlag, c1994
Materiale a stampa
Lo trovi qui: Univ. del Salento
Opac: Controlla la disponibilità qui