Quilters have been practicing geometric principles for centuries. Since straight seams are easier to sew than curved ones, the grid naturally evolved as the basis for their designs. This book is a resource for experimenting with traditional patchwork quilt patterns. It provides students a hands-on understanding of geometric concepts. It contains…

Pattern manifests itself in many ways through properties such as symmetry, repetition, translation, and illusion. This guide, appropriate for use with grades 6-12, presents patterns that are formed entirely by straight lines, yet appear to contain or be formed by curves. Exploring these geometrical shapes offers an opportunity to discover various…

The Golden Section, also known as the "Golden Mean" and the "Divine Proportion," is a ratio found in art and nature that has mathematical properties. This book explores these geometric and algebraic properties in a variety of activities. Construction problems, designs using the pentagon and pentagram, and opportunities to work…

This book contains transparency masters, duplication masters, and activities for teaching tessellating art. Part 1 gives instructions and information for creating transparencies from the paper masters in this book. Part 2 provides the transparency masters along with detailed instructions about when and how to use each of the transparencies.…

This book explores a class of geometric patterns called tessellations, a pattern made up of one or more shapes which completely cover a surface without any gaps or overlaps. Focus in on one of the more elementary types of tessellations and investigation of them through concepts basic to art, geometry, and design. The seven chapters look at which…

Discusses the use of flexible straws for teaching properties of figures and families of shapes. Describes a way to make various two- or three-dimensional geometric shapes. Lists eight advantages of the method. (YP)

Describes the stages of a process of reflective thinking. Investigates how geometrical models can be used in learning and teaching mathematics in connection with the process. Identifies two models for children of age four to eight: constant path in the space of shapes and continuous path of varied polygonal shapes. (Author/YP)

Uses pentominoes to examine the concepts of congruence, similarity, transformations, tessellations, networks, perimeter, area, and volume in a problem-solving, cooperative learning environment. Discusses the construction of three-dimensional pentominoes. (YP)

This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and…

The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)

The activities presented in this guide are designed for elementary age students, and intended to provide hands-on, integrated learning experiences. A learning station format is indicated for open ended activities which include a "Preliminary Activity: Free Exploration First!", an "Introductory Activity: Architect/Builder", and…

Discusses six activities from concrete to abstract related to geometric patterns. The stages of the activities are familiarization, starting point, walkabout, do-it-yourself, and investigation. Provides pictures of diverse patterns. (YP)

This updated reprint of a classic work presents design analysis of geometric patterns and information helpful to constructing mathematical drawings of industrial and achitectural features. Both simple and complex designs are given. Problems combine both algebra and geometry. The work is divided into six chapters which are further divided into…

Discusses the golden ratio and how to make golden triangles using recursive Logo programs. Presents some outputs of the Penrose tile patterns. (YP)