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John Stillwell
Springer

The Four Pillars of Geometry

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AuthorJohn Stillwell
PublisherSpringer
PublishedMay 30 2022
Book FormatHardcover
ISBN-139780387255309
Dimensions9.4 X 6.4 X 0.9 inches
Weight 1.15 pounds
BISAC
CategoriesMathematics > Geometry - General
LanguageEnglish

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Book Description

Many people think there is only one right way to teach geometry. For two millennia, the right way was Euclid's way, and it is still good in many respects. But in the 1950s the cry Down with triangles! was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new right way, or was the right way something else again, perhaps transformation groups? In this book, I wish to show that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Euclid-style construction and axiomatics seem the best way to start, but linear algebra smooths the later stages by replacing some tortuous arguments by simple calculations. And how can one avoid projective geometry? It not only explains why objects look the way they do; it also explains why geometry is entangled with algebra. Finally, one needs to know that there is not one geometry, but many, and transformation groups are the best way to distinguish between them. Two chapters are devoted to each approach: The ?rst is concrete and introductory, whereas the second is more abstract. Thus, the ?rst chapter on Euclid is about straightedge and compass constructions; the second is about axioms and theorems. The ?rst chapter on linear algebra is about coordinates; the second is about vector spaces and the inner product.

Author Bio

John Stillwell was born in Melbourne, Australia, and taught at Monash University from 1970 until 2001, before moving to USF in 2002.

He was an invited speaker at the International Congress of Mathematicians in 1994, and his mathematical writing has been honored with the Chauvenet Prize of the Mathematical Association of America in 2005 and the book award of the Association of Jesuit Colleges and Universities in 2009.

Among his best-known books are Mathematics and Its History (3rd edition, 2010) and Yearning for the Impossible (winner of the AJCU book award in 2009).

His interests are history of mathematics in the 19th and 20th centuries, number theory, geometry, algebra, topology, foundations of mathematics.

In Australia during spring and summer.

Source: University of San Francisco

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The Four Pillars of Geometry

Mathematics

Geometry - General

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