Is it possible to make mathematical drawings that help to understand mathematical ideas, proofs, and arguments? The [Author];s of this book are convinced that the answer is yes and the objective of this book is to show how some visualization techniques may be employed to produce pictures that have both mathematical and pedagogical interest. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece, and India, but only in the last thirty years has there been a growing interest in so-called ``proofs without words''. Hundreds of these have been published in Mathematics Magazine and The College Mathematics Journal, as well as in other journals, books, and on the internet. Often a person encountering a ``proof without words'' may have the feeling that the pictures involved are the result of a serendipitous discovery or the consequence of an exceptional ingenuity on the part of the picture's creator. In this book, the [Author];s show that behind most of the pictures, ``proving'' mathematical relations are some well-understood methods. As the reader shall see, a given mathematical idea or relation may have many different images that justify it, so that depending on the teaching level or the objectives for producing the pictures, one can choose the best alternative.

The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. Mathematical drawings related to proofs have been produced since antiquity in China, Arabia, Greece and India but only in the last thirty years has there been a growing interest in so-called 'proofs without words.' In this book the authors show that behind most of the pictures 'proving' mathematical relations are some well-understood methods. The first part of the book consists of twenty short chapters, each one describing a method to visualize some mathematical idea (a proof, a concept, an operation,...) and several applications to concrete cases. Following this the book examines general pedagogical considerations concerning the development of visual thinking, practical approaches for making visualizations in the classroom and a discussion of the role that hands-on material plays in this process.

Covering the essential math concepts learned in the first years of school, Amazing Visual Math brings a whole new dimension to learning. Amazing Visual Math is an interactive hands-on experience that makes math fun. Key curriculum subjects including shapes, patterns, telling time, lines of symmetry, addition, subtraction, measurement and more are explained through over 50 interactive elements throughout the book including pop-ups, flaps, and pull the tab elements, making an otherwise tedious subject entertaining. Ideal for developing manual dexterity skills and sharpening visual learning skills, Amazing Visual Math is a hands-on experience kids won't want to put down. Supports the Common Core State Standards.

Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this timeless subject. WOODEN BOOKS are small but packed with information. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.

Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. With downloadable resources and a 16-page full-color insert, it includes numerous illustrations, computer-generated graphics, photographs, and art reproductions to demonstrate how mathematics can inspire art. Basic Math Topics and Their Visual Aspects Focusing on accessible, visually interesting, and mathematically relevant topics, the text unifies mathematics subjects through their visual and conceptual beauty. Sequentially organized according to mathematical maturity level, each chapter covers a cross section of mathematics, from fundamental Euclidean geometry, tilings, and fractals to hyperbolic geometry, platonic solids, and topology. For art students, the book stresses an understanding of the mathematical background of relatively complicated yet intriguing visual objects. For science students, it presents various elegant mathematical theories and notions. Comprehensive Material for a Math in Art Course Providing all of the material for a complete one-semester course on mathematics in art, this self-contained text shows how artistic practice with mathematics and a comprehension of mathematical concepts are needed to logically and creatively appreciate the field of mathematics.

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the first-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.