The Crocheter's Treasure Chest: 80 Classic Patterns for Tablecloths, Bedspreads, Doilies and Edgings (Dover Knitting, Crochet, Tatting, Lace)

Superb introduction for readers with limited formal mathematical training. Topics include Euclidean algorithm and its consequences, congruences, powers of an integer modulo m, continued fractions, Gaussian integers, Diophantine equations, more. Carefully selected problems included throughout, with answers. Only high school math needed. Bibliography.;Cover; Title Page; Copyright Page; Preface; Contents; Chapter 1. Introduction; 1-1 What is number theory?; 1-2 Foundations; 1-3 Proofs by induction; 1-4 Indirect proofs; 1-5 Radix representation; Chapter 2. The Euclidean Algorithm and its Consequences; 2-1 Divisibility; 2-2 The Euclidean algorithm and greatest common divisor; 2-3 The unique factorization theorem; 2-4 The linear Diophantine equation; 2-5 The least common multiple; Chapter 3. Congruences; 3-1 Introduction; 3-2 Elementary properties of congruences; 3-3 Residue classes and arithmetic (mod m). Cover Title Page Copyright Page Preface Contents Chapter 1. Introduction 1-1 What is number theory? 1-2 Foundations 1-3 Proofs by induction 1-4 Indirect proofs 1-5 Radix representation Chapter 2. The Euclidean Algorithm and its Consequences 2-1 Divisibility 2-2 The Euclidean algorithm and greatest common divisor 2-3 The unique factorization theorem 2-4 The linear Diophantine equation 2-5 The least common multiple Chapter 3. Congruences 3-1 Introduction 3-2 Elementary properties of congruences 3-3 Residue classes and arithmetic (mod m). 3-4 Reduced residue systems and Euler's < U+007a> -function3-5 Linear congruences 3-6 Polynomial congruences 3-7 Quadratic congruences with prime modulus Chapter 4. The Powers of an Integer Modulo m 4-1 The order of an integer (mod m) 4-2 Integers belonging to a given exponent (mod p) 4-3 Indices Chapter 5. Continued Fractions 5-1 Introduction 5-2 The basic identities 5-3 The simple continued fraction expansion of a rational number 5-4 The expansion of an irrational number 5-5 The expansion of quadratic irrationalities 5-6 Approximation theorems Chapter 6. The Gaussian Integers. 6-1 Introduction6-2 Divisibility, units, and primes 6-3 The greatest common divisor 6-4 The unique factorization theorem in Z[i] 6-5 The primes in Z[i] 6-6 Another quadratic domain Chapter 7. Diophantine Equations 7-1 Introduction 7-2 The equation x2 + y2 = z2 7-3 The equation x4 + y4 = z4 7-4 The equation x2 − dy2 = 1 7-5 The equation x2 − dy2 = −1 7-6 Pell's equation and continued fractions Appendix Answers to Problems Index. Beautiful crocheted items that enhanced interior furnishing generations ago are once again in the needlecraft spotlight. For this outstanding collection of classic crochet patterns, needlework authority Mary Carolyn Waldrep has selected for today's needleworker a variety of attractive designs that first appeared in now-rare thread-company instruction leaflets of the 1930s through the '50s. Included in The Crocheter's Treasure Chest are patterns for a lovely tablecloth with a rose motif, a floral-patterned refreshment set (comprising coasters and a larger doily), an elegant series of wide edgings displaying scallops, florals, and filet mesh; a tea-cart cloth with lacy petal designs; a magnificent "Cameo" bedspread; the "Chrysanthemum," a charming tablecloth composed of delicate medallions beautiful enough to complement any table arrangement; and dozens of other eye-catching pieces. A complete list of necessary materials accompanies each pattern, while more than 65 illustrations and detailed, row-by-row instructions guide beginning and advanced needleworkers through each step of the crocheting process. Here's a rich anthology of heirloom-quality designs that crocheters are sure to find inspirational and irresistible. This superb text introduces number theory to readers with limited formal mathematical training. Intended for use in freshman- and sophomore-level courses in arts and science curricula, in teacher-training programs, and in enrichment programs for high-school students, it is filled with simple problems to stimulate readers' interest, challenge their abilities and increase mathematical strength. Contents: I. Introduction II. The Euclidean Algorithm and Its Consequences III. Congruences IV. The Powers of an Integer Modulo m V. Continued Fractions VI. The Gaussian Integers VII. Diophantine Equations Requiring only a sound background in high-school mathematics, this work offers the student an excellent introduction to a branch of mathematics that has been a strong influence in the development of higher pure mathematics, both in stimulating the creation of powerful general methods in the course of solving special problems (such as Fermat conjecture and the prime number theorem) and as a source of ideas and inspiration comparable to geometry and the mathematics of physical phenomena. Cover; Title Page; Copyright Page; Contents; Introduction; Tablecloths and Placemats; Mayfair Dinner Set; Poinsettia Tablecloth; Sundial Tray Mat; Pond Lily Tablecloth; Empire Medallion Tea Cloth; Chrysanthemum Tablecloth; Filet Luncheon Set; Daisy Ring Tablecloth; Tulip Tablecloth; Sunset; Gazelle Luncheon Set; Lily of the Valley Tablecloth; Rose Filet Cloth; Lace Medallion Luncheon Set; Bedspreads; Starbright; Golden Wedding; Chevy Chase; Marguerite; Popcorn Pinwheel; Filet Medallion Bedspread; Cameo; Textured Beauty; Berkeley Square; Nocturne; Gracie Square; Prophecy; Doilies; Sea Shells Detailed step-by-step instructions and clear illustrations for 80 projects that add lovely accents to domestic items: elegant edgings, "Diamonds and Arrowheads" bedspread, "Enchantress" tablecloth, more. For crocheters at all levels.