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Excerpt from A Double Discovery: The Square of the Circle The diagrams in this work are not found in any ancient or modern works, with the exception of the common circle and simple forms used for illustrating. The famous problem of Squaring the Circle is solved in Geometry. In the mathematical part, in place of unending decimals there is shown the absolute fraction now discovered that was searched for by the ancient Greeks, and the ancient problem is solved in Mathematics. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Based on the author’s experience as a researcher and teacher of lower-track students, Beyond Formulas in Mathematics and Teaching illuminates the complex dynamics of the algebra classroom. From within this setting, Daniel Chazan thoughtfully explores topics that concern all dedicated educators, how to really know one’s students, how to find engaging material, and how to inspire meaningful classroom conversations. Throughout, he addresses the predicaments that are central to the lives of teachers who work in standard educational settings. By highlighting teaching dilemmas, Chazan prompts readers to consider what their own responses would be in similar situations. With an eye to ways of restructuring roles and relationships, Beyond Formulas in Mathematics and Teaching is essential reading for educators seeking to enhance their teaching practices and understanding of students who may be estranged from school.