Benno Artmann.* ***Euclid. The Creation of Mathematics.**
(New York: Springer-Verlag, 1999). *To
order this book, click
here!*
Reviewed by Kim
Williams
**I**n
spite of our age's growing familiarity with non-Euclidean geometries,
applied geometries in the building trades remain for the most
part firmly Euclidean. As far most builders are concerned, two
parallel lines do not ever intersect, nor should they, and to
this we owe our confidence in buildings with plumb vertical walls
and right angles. Up until the advent of CAD/CAM technology,
almost all architectural projects were visualized in drawings
constructed with compass and straightedge using drafting techniques
that are traceable to Euclid. So for architects and historians
wishing to understand the roots of architectural expression,
perhaps the most important mathematics book of all times is Euclid's*
Elements*. However, in spite of the fact that the geometry
that most of today's architects studied in primary and secondary
school was Euclidean, reading *The Elements* remains a daunting
task. Therein lies the importance of this present book by Benno
Artmann. Long a scholar of Greek mathematics, Dr. Artmann accompanies
the reader of Euclid with a chapter-by-chapter summary and explanation
of key concepts. But the book does more than just illuminate
the books of *The Elements*, necessary as that may be; it
also places its key concepts in their historical context. In
fact, this is two books, one nested inside the other. The
book is prefaced by a note from the author and brief introductions
to *The Elements'* historical context and contents, which
set the stage for the analysis that follows. Interspersed between
chapters analyzing *The Elements* are chapters entitled
"The Origin of Mathematics", in which Artmann tells
us what is happening behind the scenes, as it were. For example,
Chapter 4 deals with Book I of *The Elements*, and follows
the convention adopted by Euclid himself: first definitions,
postulates and common notions are discussed, followed by a discussion
of the theories. But Chapter 5, "Parallels and Axioms"
("The Origin of Mathematics 2") tells us what has been
so important historically about the parallel axiom. This is what
cannot be gleaned by reading *The Elements* alone; this
is what so delighted me about Artmann's book.
Architects and architectural historians reading this book will
be interested to see how many architectural examples Artmann
has included to illustrate Euclid's concepts. A plan of the Tholos
of Delphi decorates the cover; *The Elements* themselves
are illustrated as a map of a castle, the Castrum Euclidis, at
the book's end. In the introduction, Artmann writes, "Knowing
Euclid's *Elements* may be of the same importance for a
mathematician today as knowing Greek architecture is for an architect".
Those who are familiar with Artmann's other work will not be
surprised at his affinity for architecture. Among other publications,
he contributed a paper on the mathematics of Gothic tracery to
the Nexus ‘96 conference on architecture and mathematics,
which appears in the book *Nexus: Architecture and Mathematics*.
I found *Euclid: The Creation of Mathematics *accessible
and well-written. The illustrations are by the author and are
clear and helpful. I doubt if I shall ever turn to Euclid again
without referring to Artmann.
**RELATED SITES
ON THE WORLD WIDE WEB**
A short biography of Euclid Euclid
of Alexandria Euclid:
His Works and Influences Mathematics
and the Liberal Arts: Euclid Introduction
to Euclid's Elements
Copyright ©2000 Kim Williams Books
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