A Study Of Various Bases For Prognosis In Plane Geometry

Author : David Hilbert
Publisher : Prabhat Prakashan
ISBN 13 :
Total Pages : 94 pages
Book Rating : 4./5 ( download)

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Download or read book The Foundations of Geometry written by David Hilbert and published by Prabhat Prakashan. This book was released on 2023-10-01 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Foundations of Geometry by David Hilbert: The Foundations of Geometry is a groundbreaking work by mathematician David Hilbert that explores the fundamental principles and axioms of geometry. Hilbert presents a rigorous and comprehensive framework for understanding the logical foundations of geometry, laying the groundwork for further advancements in mathematical thinking. Key Aspects of the Book “The Foundations of Geometry”: Axiomatic Approach: Hilbert's work introduces an axiomatic approach to geometry, emphasizing the importance of precise definitions, logical deductions, and the systematic development of geometric concepts. He establishes a set of axioms and explores their implications, providing a solid foundation for the study of geometry and mathematical reasoning. Geometric Systems: The book delves into different geometric systems, such as Euclidean geometry, non-Euclidean geometries (like hyperbolic and elliptic geometries), and projective geometry. Hilbert explores the relationships between these systems, elucidating their distinctive properties, postulates, and implications for mathematical understanding. Logical Consistency: Hilbert's emphasis on logical consistency and rigor makes The Foundations of Geometry a seminal work in the field. He demonstrates the power of logical reasoning, the importance of clear definitions, and the significance of axiomatic systems in establishing a coherent and reliable mathematical framework. David Hilbert, a German mathematician, is widely regarded as one of the most influential mathematicians of the 20th century. Born in 1862, Hilbert made significant contributions to various branches of mathematics, including number theory, algebra, and mathematical logic. His groundbreaking work on the foundations of mathematics, known as Hilbert's program, had a profound impact on the field and set the stage for advancements in mathematical logic and computer science. Hilbert's rigorous approach to mathematical reasoning and his emphasis on precision and clarity continue to shape the discipline to this day.