Isometrica A geometrical introduction to planar crystallographic groups 1st Edition by George Baloglou 0979207606 9780979207600

A product of the author’s teaching of “Symmetries” (SUNY Oswego, 1995-2007), “Isometrica” is a student-oriented book, written in fact in the second person. The subject is one of humanity’s first mathematical creations, predominant in ancient art of many cultures, namely the repeating, symmetrical subsets of the plane known as border patterns and wallpaper patterns (planar crystallographic groups). The book’s ultimate goal is to prove that there exist precisely seventeen wallpaper patterns (chapter 8). This classical result is not reached via the standard algebraic machinery of Group Theory, but through the geometrical study of isometries (distance-preserving transformations) in chapters 1, 3, 7. Border patterns and wallpaper patterns are introduced in chapters 2 and 4, whereas their two-colored versions are discussed in chapters 5 and 6, in aesthetically appealing and geometrically intriguing fashion. Intuition is emphasized over rigor, and the only prerequisite is some high school Geometry.

“… Baloglou demonstrates how he masters the challenging problem of giving a “General education course devoted entirely to symmetry”. He succeeds presenting the material in a smooth conversational style, avoiding technical discussions and definitions. Each pattern is discussed extensively so that its characteristics become familiar to the student. After comparing many patterns, stressing similarities and differences, the students will have learned to find the place of every given pattern in the lists at the ends of the chapters. …” — Erich Ellers, Zentralblatt (November 2008)

“It’s a beautiful book; thanks for your tremendous work!” — Janos Pach, New York University (August 30, 2007)

“… It is like being able to enjoy music without learning the notation.” — Dani Novak, Ithaca College (May 20, 2007)