Figurate numbers /:
Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs. This book is the first of this topic written in unifi...
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs. This book is the first of this topic written in unified systematic way. It also contains many exercises with solutions. |
| Beschreibung: | 1 online resource (xviii, 456 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 443-447) and index. |
| ISBN: | 9789814355490 9814355496 1280669543 9781280669545 9786613646477 6613646474 |
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| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 443-447) and index. | ||
| 505 | 0 | |a 1. Plane figurate numbers. 1.1. Definitions and formulas. 1.2. Main properties of polygonal numbers. 1.3. Square triangular numbers. 1.4. Other highly polygonal numbers. 1.5. Amount of a given number in all polygonal numbers. 1.6. Centered polygonal numbers. 1.7. Other plane figurate numbers. 1.8. Generalized plane figurate numbers -- 2. Space figurate numbers. 2.1. Pyramidal numbers. 2.2. Cubic numbers. 2.3. Octahedral numbers. 2.4. Other regular polyhedral numbers. 2.5. Some semiregular and star polyhedral numbers. 2.6. Centered space figurate numbers. 2.7. Other space figurate numbers. 2.8. Generalized space figurate numbers -- 3. Multidimensional figurate numbers. 3.1. Pentatope numbers and their multidimensional analogues. 3.2. Biquadratic numbers and their multidimensional analogues. 3.3. Other regular polytope numbers. 3.4. Nexus numbers. 3.5. Pyramidal numbers of the second order and their multidimensional analogues. 3.6. Centered multidimensional figurate numbers. 3.7. Generalized multidimensional figurate numbers -- 4. Areas of number theory including figurate numbers. 4.1. Addition and multiplication tables. 4.2. Pascal's triangle and binomial theorem. 4.3. Pythagorean triples and other Diophantine equations. 4.4. Perfect numbers. 4.5. Mersenne and Fermat numbers. 4.6. Fibonacci and Lucas numbers. 4.7. Palindromic numbers. 4.8. Other special numbers. 4.9. Prime numbers. 4.10. Magic constructions. 4.11. Unrestricted partitions. 4.12. Waring's problem -- 5. Fermat's polygonal number theorem. 5.1. History of the problem. 5.2. Lagrange's four-square theorem. 5.3. Gauss's three-triangular-number theorem; elementary considerations. 5.4. Proof of the Gauss's three-triangular-number theorem. 5.5. Sums of squares and Minkowski's convex body theorem. 5.6. Cauchy's proof of the polygonal number theorem. 5.7. Pepin's proof of the polygonal number theorem. 5.8. Other results related to the problem -- 6. Zoo of figurate-related numbers -- 7. Exercises. | |
| 520 | |a Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs. This book is the first of this topic written in unified systematic way. It also contains many exercises with solutions. | ||
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| 776 | 0 | 8 | |i Print version: |a Deza, Elena. |t Figurate numbers. |d Singapore : World Scientific, ©2012 |z 9789814355483 |w (OCoLC)711045395 |
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| DE-BY-FWS_katkey | ZDB-4-EBA-ocn793804649 |
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| _version_ | 1816881795049717761 |
| adam_text | |
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| author | Deza, Elena |
| author2 | Deza, M., 1939- |
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| author_GND | http://id.loc.gov/authorities/names/no2009165732 http://id.loc.gov/authorities/names/n85202710 |
| author_facet | Deza, Elena Deza, M., 1939- |
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| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA241 |
| callnumber-raw | QA241 .D49 2012 |
| callnumber-search | QA241 .D49 2012 |
| callnumber-sort | QA 3241 D49 42012 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 1. Plane figurate numbers. 1.1. Definitions and formulas. 1.2. Main properties of polygonal numbers. 1.3. Square triangular numbers. 1.4. Other highly polygonal numbers. 1.5. Amount of a given number in all polygonal numbers. 1.6. Centered polygonal numbers. 1.7. Other plane figurate numbers. 1.8. Generalized plane figurate numbers -- 2. Space figurate numbers. 2.1. Pyramidal numbers. 2.2. Cubic numbers. 2.3. Octahedral numbers. 2.4. Other regular polyhedral numbers. 2.5. Some semiregular and star polyhedral numbers. 2.6. Centered space figurate numbers. 2.7. Other space figurate numbers. 2.8. Generalized space figurate numbers -- 3. Multidimensional figurate numbers. 3.1. Pentatope numbers and their multidimensional analogues. 3.2. Biquadratic numbers and their multidimensional analogues. 3.3. Other regular polytope numbers. 3.4. Nexus numbers. 3.5. Pyramidal numbers of the second order and their multidimensional analogues. 3.6. Centered multidimensional figurate numbers. 3.7. Generalized multidimensional figurate numbers -- 4. Areas of number theory including figurate numbers. 4.1. Addition and multiplication tables. 4.2. Pascal's triangle and binomial theorem. 4.3. Pythagorean triples and other Diophantine equations. 4.4. Perfect numbers. 4.5. Mersenne and Fermat numbers. 4.6. Fibonacci and Lucas numbers. 4.7. Palindromic numbers. 4.8. Other special numbers. 4.9. Prime numbers. 4.10. Magic constructions. 4.11. Unrestricted partitions. 4.12. Waring's problem -- 5. Fermat's polygonal number theorem. 5.1. History of the problem. 5.2. Lagrange's four-square theorem. 5.3. Gauss's three-triangular-number theorem; elementary considerations. 5.4. Proof of the Gauss's three-triangular-number theorem. 5.5. Sums of squares and Minkowski's convex body theorem. 5.6. Cauchy's proof of the polygonal number theorem. 5.7. Pepin's proof of the polygonal number theorem. 5.8. Other results related to the problem -- 6. Zoo of figurate-related numbers -- 7. Exercises. |
| ctrlnum | (OCoLC)793804649 |
| dewey-full | 512.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.72 |
| dewey-search | 512.72 |
| dewey-sort | 3512.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Plane figurate numbers. 1.1. Definitions and formulas. 1.2. Main properties of polygonal numbers. 1.3. Square triangular numbers. 1.4. Other highly polygonal numbers. 1.5. Amount of a given number in all polygonal numbers. 1.6. Centered polygonal numbers. 1.7. Other plane figurate numbers. 1.8. Generalized plane figurate numbers -- 2. Space figurate numbers. 2.1. Pyramidal numbers. 2.2. Cubic numbers. 2.3. Octahedral numbers. 2.4. Other regular polyhedral numbers. 2.5. Some semiregular and star polyhedral numbers. 2.6. Centered space figurate numbers. 2.7. Other space figurate numbers. 2.8. Generalized space figurate numbers -- 3. Multidimensional figurate numbers. 3.1. Pentatope numbers and their multidimensional analogues. 3.2. Biquadratic numbers and their multidimensional analogues. 3.3. Other regular polytope numbers. 3.4. Nexus numbers. 3.5. Pyramidal numbers of the second order and their multidimensional analogues. 3.6. Centered multidimensional figurate numbers. 3.7. Generalized multidimensional figurate numbers -- 4. Areas of number theory including figurate numbers. 4.1. Addition and multiplication tables. 4.2. Pascal's triangle and binomial theorem. 4.3. Pythagorean triples and other Diophantine equations. 4.4. Perfect numbers. 4.5. Mersenne and Fermat numbers. 4.6. Fibonacci and Lucas numbers. 4.7. Palindromic numbers. 4.8. Other special numbers. 4.9. Prime numbers. 4.10. Magic constructions. 4.11. Unrestricted partitions. 4.12. Waring's problem -- 5. Fermat's polygonal number theorem. 5.1. History of the problem. 5.2. Lagrange's four-square theorem. 5.3. Gauss's three-triangular-number theorem; elementary considerations. 5.4. Proof of the Gauss's three-triangular-number theorem. 5.5. Sums of squares and Minkowski's convex body theorem. 5.6. Cauchy's proof of the polygonal number theorem. 5.7. Pepin's proof of the polygonal number theorem. 5.8. Other results related to the problem -- 6. Zoo of figurate-related numbers -- 7. 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| id | ZDB-4-EBA-ocn793804649 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:23Z |
| institution | BVB |
| isbn | 9789814355490 9814355496 1280669543 9781280669545 9786613646477 6613646474 |
| language | English |
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| physical | 1 online resource (xviii, 456 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific. |
| record_format | marc |
| spelling | Deza, Elena. http://id.loc.gov/authorities/names/no2009165732 Figurate numbers / Elena Deza, Michel Marie Deza. Singapore ; Hackensack, NJ : World Scientific. 1 online resource (xviii, 456 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Print version record. Includes bibliographical references (pages 443-447) and index. 1. Plane figurate numbers. 1.1. Definitions and formulas. 1.2. Main properties of polygonal numbers. 1.3. Square triangular numbers. 1.4. Other highly polygonal numbers. 1.5. Amount of a given number in all polygonal numbers. 1.6. Centered polygonal numbers. 1.7. Other plane figurate numbers. 1.8. Generalized plane figurate numbers -- 2. Space figurate numbers. 2.1. Pyramidal numbers. 2.2. Cubic numbers. 2.3. Octahedral numbers. 2.4. Other regular polyhedral numbers. 2.5. Some semiregular and star polyhedral numbers. 2.6. Centered space figurate numbers. 2.7. Other space figurate numbers. 2.8. Generalized space figurate numbers -- 3. Multidimensional figurate numbers. 3.1. Pentatope numbers and their multidimensional analogues. 3.2. Biquadratic numbers and their multidimensional analogues. 3.3. Other regular polytope numbers. 3.4. Nexus numbers. 3.5. Pyramidal numbers of the second order and their multidimensional analogues. 3.6. Centered multidimensional figurate numbers. 3.7. Generalized multidimensional figurate numbers -- 4. Areas of number theory including figurate numbers. 4.1. Addition and multiplication tables. 4.2. Pascal's triangle and binomial theorem. 4.3. Pythagorean triples and other Diophantine equations. 4.4. Perfect numbers. 4.5. Mersenne and Fermat numbers. 4.6. Fibonacci and Lucas numbers. 4.7. Palindromic numbers. 4.8. Other special numbers. 4.9. Prime numbers. 4.10. Magic constructions. 4.11. Unrestricted partitions. 4.12. Waring's problem -- 5. Fermat's polygonal number theorem. 5.1. History of the problem. 5.2. Lagrange's four-square theorem. 5.3. Gauss's three-triangular-number theorem; elementary considerations. 5.4. Proof of the Gauss's three-triangular-number theorem. 5.5. Sums of squares and Minkowski's convex body theorem. 5.6. Cauchy's proof of the polygonal number theorem. 5.7. Pepin's proof of the polygonal number theorem. 5.8. Other results related to the problem -- 6. Zoo of figurate-related numbers -- 7. Exercises. Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs. This book is the first of this topic written in unified systematic way. It also contains many exercises with solutions. English. Numbers, Natural. http://id.loc.gov/authorities/subjects/sh85093214 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Nombres naturels. Théorie des nombres. MATHEMATICS Number Theory. bisacsh Number theory fast Numbers, Natural fast Deza, M., 1939- http://id.loc.gov/authorities/names/n85202710 Print version: Deza, Elena. Figurate numbers. Singapore : World Scientific, ©2012 9789814355483 (OCoLC)711045395 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=457171 Volltext |
| spellingShingle | Deza, Elena Figurate numbers / 1. Plane figurate numbers. 1.1. Definitions and formulas. 1.2. Main properties of polygonal numbers. 1.3. Square triangular numbers. 1.4. Other highly polygonal numbers. 1.5. Amount of a given number in all polygonal numbers. 1.6. Centered polygonal numbers. 1.7. Other plane figurate numbers. 1.8. Generalized plane figurate numbers -- 2. Space figurate numbers. 2.1. Pyramidal numbers. 2.2. Cubic numbers. 2.3. Octahedral numbers. 2.4. Other regular polyhedral numbers. 2.5. Some semiregular and star polyhedral numbers. 2.6. Centered space figurate numbers. 2.7. Other space figurate numbers. 2.8. Generalized space figurate numbers -- 3. Multidimensional figurate numbers. 3.1. Pentatope numbers and their multidimensional analogues. 3.2. Biquadratic numbers and their multidimensional analogues. 3.3. Other regular polytope numbers. 3.4. Nexus numbers. 3.5. Pyramidal numbers of the second order and their multidimensional analogues. 3.6. Centered multidimensional figurate numbers. 3.7. Generalized multidimensional figurate numbers -- 4. Areas of number theory including figurate numbers. 4.1. Addition and multiplication tables. 4.2. Pascal's triangle and binomial theorem. 4.3. Pythagorean triples and other Diophantine equations. 4.4. Perfect numbers. 4.5. Mersenne and Fermat numbers. 4.6. Fibonacci and Lucas numbers. 4.7. Palindromic numbers. 4.8. Other special numbers. 4.9. Prime numbers. 4.10. Magic constructions. 4.11. Unrestricted partitions. 4.12. Waring's problem -- 5. Fermat's polygonal number theorem. 5.1. History of the problem. 5.2. Lagrange's four-square theorem. 5.3. Gauss's three-triangular-number theorem; elementary considerations. 5.4. Proof of the Gauss's three-triangular-number theorem. 5.5. Sums of squares and Minkowski's convex body theorem. 5.6. Cauchy's proof of the polygonal number theorem. 5.7. Pepin's proof of the polygonal number theorem. 5.8. Other results related to the problem -- 6. Zoo of figurate-related numbers -- 7. Exercises. Numbers, Natural. http://id.loc.gov/authorities/subjects/sh85093214 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Nombres naturels. Théorie des nombres. MATHEMATICS Number Theory. bisacsh Number theory fast Numbers, Natural fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85093214 http://id.loc.gov/authorities/subjects/sh85093222 |
| title | Figurate numbers / |
| title_auth | Figurate numbers / |
| title_exact_search | Figurate numbers / |
| title_full | Figurate numbers / Elena Deza, Michel Marie Deza. |
| title_fullStr | Figurate numbers / Elena Deza, Michel Marie Deza. |
| title_full_unstemmed | Figurate numbers / Elena Deza, Michel Marie Deza. |
| title_short | Figurate numbers / |
| title_sort | figurate numbers |
| topic | Numbers, Natural. http://id.loc.gov/authorities/subjects/sh85093214 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Nombres naturels. Théorie des nombres. MATHEMATICS Number Theory. bisacsh Number theory fast Numbers, Natural fast |
| topic_facet | Numbers, Natural. Number theory. Nombres naturels. Théorie des nombres. MATHEMATICS Number Theory. Number theory Numbers, Natural |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=457171 |
| work_keys_str_mv | AT dezaelena figuratenumbers AT dezam figuratenumbers |