Symmetry

Hans Walser

96 pages, parution le 25/10/2001

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Résumé

We meet symmetry everywhere: in the cycle of the seasons, in the two-sided symmetry of the humam face, but just as much in the 4-stroke motor, in the decimal expansion of the fraction 1/7, and in carpet patterns, ornaments, poems, and songs. Science, art, and modern production methods are based, in a far-reaching way, on symmetric forms and structures.

In this book numerous examples of symmetry arc presented in accessible form. The author, who has also written in the same series, the book The Golden Section,, contributes here to “shyarpening” to -sharpening the eye" of the reader for recognizing symmetry all around us and for appreciating its essential role as a Methodological tool. This English edition has been prepared, with the author's cooperation, to make it available to English-speaking students of mathematics. The treatment is informal and the text is enriched by the presence of very illuminating diagrams. Question, are posed at fairly, frequent intervals and the answers to these questions appear at the end of each chapter.

Contents

1	Little Mirror, Little Mirror	1
1.1	Ever Further Inwards	1
1.1.1	The Mirror in a Mirror in a Mirror	1
1.1.2	An Avenue of Poplars	4
1.1.3	The Monitor in the Monitor	5
1.2	Seen from the Side	7
	Answers to Questions	9
2	Inside and Outside	11
2.1	Reflecting In a Circle	11
2.2	Composition of Two Circle-Reflections	14
2.3	Direct Construction of the Image Point	15
2.4	Circle-Reflection Invariants	15
2.5	Image of a Straight Line	19
2.6	Representation in Cartesian Coordinates	21
2.7	Image of a Circle	22
2.8	Square-Reflection	25
2.9	Other Reflections	26
	Answers to Questions	27
3	Symmetric Procedure	31
3.1	Center of Gravity in the Triangle	31
3.2	Center of Gravity in the Quadrilateral	32
	Answers to Questions	35
4	Parquet Floors, Lattices and Pythagoras	39
4.1	Parquet Floors	39
4.2	Parquets and Pythagoras	43
4.3	Construction of a Proof-Diagram	45
4.4	Other Cathetus-Figures	48
4.5	Covering of Lattice Points	49
4.6	Pythagorean Triangles	54
4.7	Parametrizing the Primitive Triangles	55
4.8	In a Regular Triangular Lattice	57
	Answers to Questions	59
5	The Problem of the Center	69
5.1	Where is the Center of the World?	69
5.2	Mean Values	71
5.2.1	Half is Eaten	71
5.2.2	Average Speed	72
5.2.3	Correcting Systematic Errors	73
5.2.4	Minimal Supply Channels	75
	Answers to Questions	76
6	Symmetry in Word, Script and Number	81
6.1	Palindromes	81
6.2	Palindromic Numbers	82
6.3	Rhyming Schemes	82
	Answers to Questions	84
	References	87
	Index	93

L'auteur - Hans Walser

Hans, Walser is a teacher at the State College of Thurgau in Switzerland and lecturer at the ETH Zürich (Swiss Federal Institute of Technology) and the University of Basel. He received his Ph.D from the ETH Zürich in 1975. His primary research interest is in geometry. He is currently involved in the instruction and education of future high school teachers. He was a visiting guest and lecturer at Santa Clara University in 1996 and 1998. The Mathematical Association of America has also published the English translation of "Symmetry," by Hans Walser.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Hans Walser
Parution	25/10/2001
Nb. de pages	96
Format	15,2 x 22,8
Couverture	Broché
Poids	159g
Intérieur	Noir et Blanc
EAN13	9780883855324
ISBN13	978-0-88385-532-4