Zero and Pi : Symbols of Mathematical Spirit

• Autore: Mukhopadhyay Amalkumar
• Pubblicazione: Singapore : , : Springer Singapore Pte. Limited, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (231 pages)
• Disciplina: 510.9
• Altri autori: BhattSiddheshwar Rameshwar
• Nota di contenuto: Intro -- Preface -- Acknowledgements -- Contents -- About the Authors -- Abbreviations -- PART I A JOURNEY IN SEARCH OF THE ORIGIN OF ZERO -- Chapter 1 Zero and Pi: The Symbols of Mathematical Spirit A JOURNEY IN SEARCH OF THE ORIGIN OF ZERO -- 1.1 Probable Foreign Influence on Indian Zero Notation -- 1.2 The Symbol of Zero in India: An Overview -- 1.3 Stages and Chapters -- CHAPTER 2 Evolution of the concept and symbol of Śunya -- 2.1 An Outline of the Chapter -- 2.2 (Stage I) Numerals & -- Void in Non-Indian civilizations -- 2.3 Number-notations in the Indus civilization -- 2.4 Word Numerals among Elites in Vedic India -- 2.5 Concept of a Lack/ Void in Vedic India and Kaṇāda -- 2.6 Word representations of Void in India -- 2.7 Kaṇāda's views on Ākāśa -- 2.8 Metaphysical Origin of the Round symbol of the Void. -- 2.9 Piṅgala's Hint on the Identity of Zero (śūnya) -- CHAPTER 3 3. (Stage II) The Symbol O of Monism to Atheists, a Dot for zero -- 3.1 Transition from Monotheism to Atheism & -- Nāgārjuna -- 3.2 Nāgjuna's Śūnyatā: A New Ontology -- 3.3 The Use of a Dot for Zero, O for an Unknown -- 3.4 Alphabetic Notations of zero in India -- CHAPTER 4 (Stage III) Gupta period: A Turn in the History of Śūnya -- 4.1 Synonyms of Śūnya (following Nāmaliṅgānuśāsana ) -- 4.2 Uniform Numerals in India & -- Brahmagupta -- 4.3 The Round Symbol of Zero in Indian Mathematics -- 4.4 The Symbols O and o in Arabia and China -- 4.5 The Symbols O and 0 in Europe -- 4.6 The Status of Śūnya in Post-Brahmagupta India -- CHAPTER 5 Stage IV Śūnya: Brahmagupta and Bhāskarācārya's thought -- 5.1 Brahmagupta's algebraic thoughts on śūnya -- 5.2 Bhāskara's review of Brahmagupta's śūnya in a frame of history -- 5.3 Bhāskarācārya's new mathematical tool -- 5.4 An application of the concept -- 5.5 Bhāskara's theory on śūnya delayed in the Outer world. ; CHAPTER 6 (Stage V) Ramification of the Indian Concept of Void/Śūnya -- 6.1 Mental void: What is It? -- 6.2 Does a Yoga Entail Mental Void? -- 6.3 Abel's Ramification of Zero - Reminiscent of Indian Thoughts -- Zero and pi: the symbols of Mathematical Spirit PART II A JOURNEY IN SEARCH OF PI -- Zero and pi: the symbols of Mathematical Spirit Part II (A Journey in Search of Pi) -- CHAPTER 7 A JOURNEY IN SEARCH OF Pi Part II -- 7.1 Historical Background of CD⁄ (Pi) in Days of Empirical Geometry -- 7.2 Trade-linked Cultural Exchange between India and Abroad -- 7.3. Greek Geometry, the Classical method, and Its Fate -- 7.4 Scheme of the work: (Chapter Divisions, a Historical approach) -- 7.5 An Appraisement of Part II -- 7.6 Focus on Special Features of Part II: -- 7.7 Conclusion -- CHAPTER 8 THE DESCRIPTIVE GEOMETRICAL STAGES -- 8.2 Division of History into Successive Stages -- 8.3. A General Survey of the Stage I -- 8.4. A Specific Discussion on Stage I -- 8.5 C⁄D in Egypt, China, Babylon, India and the Holy Bible -- 8.6 Rectification of a Circle in India: Approximations of C⁄D -- 8.7 Attempts to Square a Circle in Ancient Greece -- 8.8 C/D=√10 of Sūryaprajñāpti - Its Deduction & -- Status in Later India -- 8.9 Stage II: The Classical Method in Greece, -- 8.10 Classical Method in China, China's Approach to CD= 3927/1250 , -- 8.11 The Approximations 22/7 and 355/113 In India -- 8.12 Stage III: Table of Chords- its Indian and Grecian Origin -- 8.13 Outlines of Grecian Table of Chords: Hipparchus vs. Ptolemy -- 8.14 Āryabhaṭa-I's Relation Between C and D : Bhāskara-II's View -- 8.15 Bhāskara-II's Approximation: Some Views on its Deduction -- 8.16. Bhāskara-I's Key to get C/D≈ 22/7, 355/113 -- 8.17 Stage IV: India's Geometrical Way to Identify C/D -- 8.18 Mādhava's Other Infinite Series: -- 8.19 Mādhava's Arc-chord Relation of a Circle:. ; 8.20 Some Results of Mādhava Rediscovered in Later Europe -- 8.21 Mādhava's Approximation of C⁄D: -- 8.22 Nīlkaṇṭha Somayāji's Confirmation of Bhāskara-I's Conjecture -- 8.23 Other Infinite Series for CD⁄ by Putumanā Somayājī -- 8.24 Historic Background of Stage V -- 8.25 The Dark Period in European Mathematics -- 8.26 Awakening of Latin Europe (11th -15th-century C E): Toledo -- 8.27 Cultivation of the East-West Heritage of Learning in Arabia -- 8.28 The Estimates of CD⁄ in the Muslim world -- 8.29 European Mathematics from 14th-Century to the Renaissance -- 8.30 Stage-V The Classical Method Current in China returns to Europe -- 8.31 Essentiality of the Enowledge of CD⁄ to India -- CHAPTER 9 Identification of π Analytically -- 9.1. Specific Progress in the Age of Mathematical Analysis -- 9.2 Analytical Deduction of Infinite Series or Product for π -- 9.3 The Number 'e 'in a Historical Perspective -- 9.4 Irrationality of π: Lambert-Legendre Episode -- 9.5 Pre 18th ‑Century European Mathematics in China -- 9.6 Japanese Mathematics and Infinite series for π in the Edo period -- 9.7 Transcendental Number: An introduction of Its Concept -- 9.8 The Tanscendence of 'e' and Hermite -- 9.9 Stage VII: Reaching the Target: Identity of π Disclosed -- 9.10 A Note of Reverence for the One Whose Merit went unrecognized -- 9.11 General Discussion and Conclusion -- CHAPTER 10 Contextual Topics on Mathematics (A looking back to the old days) -- 10.1 The Mathematical Idea Relevant to Altars Described in Śulba sūtras -- 10.2 Table of Chords in Ancient India -- 10.3 Āryabhaṭa-I's Influence on Sūryasiddhānta's Table of Chords -- 10.4 Finite Continued Fraction in Ancient India -- 10.5 Identification of e and π- The Two Glamorous Problems -- CHAPTER 11 Historical Retrospect -- 11.1 Indo-West Relation from the 3rd Millennium B C. ; 11.2. The Indo-West Trade-Routes up to the 5th Century B C -- 11.3 Mesopotamia/Babylonia ─ a Land of Ethno-cultural Distinction -- 11.4 Some Basic Information about the land -- 11.5 Indo-Greek Relationship in Hellenistic Period -- 11.6 Alexandria, the Greek Centre of Learning -- 11.7 Baghdad in the Golden Days of Islam -- 11.8 Indo-China Relation in Prehistoric Times -- 11.9 Indo-Chinese Relationship in Early Ages of History -- 11.10 Buddhism in China -- 11.11. Spread of Indian Mathematics and Astronomy in China -- 11.12 Mathematics and Astronomy from Arabia to China -- 11.13 Western Mathematics and Science in Japan (19th-Century) -- Appendices & -- Bibliography Appendix I (Part-I & -- II) -- Appendix II -- Appendix III -- Bibliography -- Books -- Journals -- Electronic Sources -- Wikipedia Free Encyclopedia:.
• Titolo autorizzato: Zero and Pi
• ISBN: 981-9930-72-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910847071903321
• Lo trovi qui: Univ. Federico II