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How to Free Your Inner MathematicianNotes on Mathematics and Life$
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Susan D'Agostino

Print publication date: 2020

Print ISBN-13: 9780198843597

Published to Oxford Scholarship Online: April 2020

DOI: 10.1093/oso/9780198843597.001.0001

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Make an educated guess, like Kepler with his Sphere-Packing Conjecture

Make an educated guess, like Kepler with his Sphere-Packing Conjecture

(p.105) 17 Make an educated guess, like Kepler with his Sphere-Packing Conjecture
How to Free Your Inner Mathematician

Susan D'Agostino

Oxford University Press

“Make an educated guess, like Kepler with his Sphere-Packing Conjecture” provides an accessible discussion of the history and mathematics behind Johannes Kepler’s Sphere-Packing Conjecture—a statement concerning the densest way to pack spheres such as oranges. The discussion is illustrated with numerous hand-drawn sketches. Though Kepler died before proving his conjecture, his legacy demonstrates the power of conjecture in mathematics. Hordes of mathematicians continued work on his claim for four centuries until Thomas Hales provided a proof of Kepler’s conjecture running to over 250 pages. Upon noting real-life sphere-packing applications in internet messaging, satellite broadcasting, and deep-space telecommunications, readers learn that Kepler’s guess changed the world for the better. Mathematics students and enthusiasts are encouraged to let conjecture serve as a catalyst in their mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Keywords:   Kepler, sphere-packing, conjecture, math, Thomas Hales, student, math

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