## Ancient Indian Leaps into MathematicsThis book presents contributions of mathematicians covering topics from ancient India, placing them in the broader context of the history of mathematics. Although the translations of some Sanskrit mathematical texts are available in the literature, Indian contributions are rarely presented in major Western historical works. Yet some of the well-known and universally-accepted discoveries from India, including the concept of zero and the decimal representation of numbers, have made lasting contributions to the foundation of modern mathematics. Through a systematic approach, this book examines these ancient mathematical ideas that were spread throughout India, China, the Islamic world, and Western Europe. |

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### Contents

1 | |

Indias Contributions to Chinese Mathematics Through the Eighth Century CE | 32 |

The Influence of Indian Trigonometry on Chinese CalendarCalculations in the Tang Dynasty | 45 |

His Book on Number Theory and Indian References | 55 |

On the Application of Areas in the Sulbasutras | 63 |

Divisions of Time and Measuring Instruments of Varahmihira | 74 |

The Golden Mean and the Physics of Aesthetics | 111 |

Pingala Binary Numbers | 121 |

The Reception of Ancient Indian Mathematics by Western Historians | 135 |

Methodology and Motivation | 153 |

The Algorithm of Extraction in Greek and SinoIndian Mathematical Traditions | 171 |

The Ancient Indian Mathematician | 185 |

Mainland Southeast Asia as a Crossroads of Chinese Astronomy and Indian Astronomy | 193 |

Mathematical Literature in the Regional Languages of India | 201 |

212 | |

### Common terms and phrases

19-year cycle algebra algorithm of extraction Ancient Indian Leaps ancient Indian mathematics Arabic arithmetic Aryabhat.¯iya Aryabhat.a Aryabhata average-month-length average-year-length B.S. Yadav Bh¯askara Brahmagupta calculation century c.e. Chap China Chinese Chinese calendar Chinese mathematics Chiuchi circumference commentary Computer Dayanli defun Delhi delta-month delta-year difference Dynasty Epanthema equation example formula geometrical given Hindu history of mathematics Iamblichus Indian astronomy Indian mathematics Indian trigonometry kalas kastha Kerala Leaps into Mathematics length Liu Hui lunar lunisolar calendar math mean-month-length measure meter method modern Mohan eds months-per-year moon Mount Meru muhurtas nadi nadika Pi˙ngala binary number problem Pythagorean quantities realistic falcon rectangle rule s-date S¯urya-Siddh¯anta S¯utra Sanskrit Sarma scholars Science Singh single-cycle-epoch solar calendar solution Springer Science+Business Media square root Sulbas¯utras syllables Tang Dynasty texts Thymaridas tradition translated Treatise triangle University Varahmihira Ved¯a˙nga Jyotis.a verse writes Yi Xing yuga