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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Chasles and the Projective Geometry: The Birth of a Global Foundational Programme for Mathematics, Mechanics and Philosophy

Chasles and the Projective Geometry: The Birth of a Global Foundational Programme for Mathematics, Mechanics and Philosophy

Bussotti, Paolo

Hardcover

General MathematicsGeometry

ISBN10: 3031542657
ISBN13: 9783031542657
Publisher: Birkhauser
Published: Jul 18 2024
Pages: 572
Weight: 2.19
Height: 1.25 Width: 6.14 Depth: 9.21
Language: English

This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles' extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed parabolic, to the graphic context, so expressing the metric properties by means of this specific polarity--a foundational argument. Beyond the celebrated Chasles theorem, he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles' philosophy of duality is explained. It is grounded on theduality principles of projective geometry. Finally, the author presents Chasles' synthetic solution for the intricate problem of ellipsoid attraction--the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions.

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