The Pythagorean Theorem in 365 Proofs: Exploring the Nature of Mathematical Proof and the Cultural Legacy of the World's Most Famous Theorem
暫譯: 《畢氏定理的 365 種證明：探索數學證明的本質與世上最著名定理的文化傳承》
Gerwig, Mario, Ziegler, Günter M.
相關主題
商品描述
This book presents about 365 different proofs of the Pythagorean Theorem in a highly visual and accessible form, while also placing the theorem and its wide variety of proofs into both a mathematical and cultural context. Here, the theorem becomes a model for the discoveries of ancient mathematics, showing how mathematical truths build upon one another. The collection also gives students a unique insight into the methods of mathematics and its deductive structure.
The collection of proofs is based on the work of Elisha Scott Loomis (1852-1940), who gathered, systematized, and published hundreds of algebraic and geometric proofs. His work became a crystallization point for the intellectual and cultural history of mathematics, exemplarily condensed in the Pythagorean theorem. After more than 80 years, the Loomis collection is now published again in a thoroughly revised and expanded edition.
This book is a translation of the original German edition Der Satz des Pythagoras in 365 Beweisen by Mario Gerwig, published by Springer-Verlag GmbH Germany in 2021. It omits a chapter from the original edition that was tailored primarily to educational contexts in German-speaking countries. The translation was done with the help of artificial intelligence. The author has subsequently revised the text further in an endeavour to refine the work stylistically. Nevertheless, the book might read stylistically different from a conventional translation.
From the foreword by the National Council of Teachers of Mathematics (NCTM):
May this volume inspire teachers to bring the wonder of the Pythagorean Theorem to their students with renewed clarity and enthusiasm. And may it remind us all that even the most familiar theorems still hold surprises, inviting us to look again, reason again, and delight again in the power of mathematics.
From the foreword by Prof. Günter M. Ziegler (President of Freie Universität Berlin, Germany):
This book presents a great variety of proofs for a very specific, interesting and fascinating statement - from a historical source, expertly and critically commented. There is much to learn from this book: Learn about the variety of proofs, be inspired by them and take pleasure in them.
商品描述(中文翻譯)
本書以高度視覺化且易於理解的形式，介紹約 365 種不同的勾股定理證明，同時將這一定理及其多樣的證明置於數學與文化的脈絡中。在此，這一定理成為古代數學發現的典範，展示數學真理如何彼此建構而成。這套證明集也讓學生得以從獨特的角度深入了解數學的方法及其演繹結構。
這套證明集以 Elisha Scott Loomis（1852–1940）的著作為基礎。Loomis 蒐集、系統化並出版了數百種代數與幾何證明。他的作品成為數學思想與文化史的凝聚點，而這段歷史則以勾股定理作為典型的濃縮呈現。時隔 80 多年後，《Loomis 證明集》如今以經過全面修訂與擴充的版本再次出版。
本書是 Mario Gerwig 所著德文原版《Der Satz des Pythagoras in 365 Beweisen》的翻譯本，原版於 2021 年由 Springer-Verlag GmbH Germany 出版。本書省略了原版中的一章，該章主要針對德語國家的教育情境而編寫。本書的翻譯借助了人工智慧完成，作者之後又進一步修訂文字，力求提升作品的風格與表達。然而，本書在文體上可能與一般的傳統翻譯有所不同。
National Council of Teachers of Mathematics（NCTM）序言：
願本書激勵教師以煥然一新的清晰度與熱忱，將勾股定理的奇妙之處帶給學生。也願本書提醒我們，即使是最熟悉的定理，仍然蘊含著驚喜，邀請我們再次觀看、再次推理，並再次陶醉於數學的力量之中。
Günter M. Ziegler 教授（德國 Freie Universität Berlin 校長）序言：
本書以歷史資料為來源，並附有專業且批判性的評論，介紹了各式各樣的證明，用以闡述一個十分特定、有趣且引人入勝的命題。本書有許多值得學習之處：了解證明方法的多樣性，從中獲得啟發，並享受其中的樂趣。
作者簡介
Mario Gerwig has been a teacher of mathematics and chemistry at the Gymnasium Leonhard in Basel, Switzerland, since 2011, and is also a book and textbook author. He is president of the Gesellschaft für Lehrkunstdidaktik and earned his Ph.D. in 2014 on the topic Understanding Proof in Mathematics Education.
作者簡介(中文翻譯)
Mario Gerwig 自 2011 年起，便在瑞士巴塞爾的 Gymnasium Leonhard 擔任數學與化學教師，同時也是書籍及教科書作者。他是 Gesellschaft für Lehrkunstdidaktik 的主席，並於 2014 年以「數學教育中的證明理解」（Understanding Proof in Mathematics Education）為主題取得博士學位。
