Measurement

Measurement is a work by mathematician Paul Lockhart following his A Mathematician's Lament. The simplified Chinese edition was translated by Wang Lingyun and published by Posts & Telecom Press under the Turing New Knowledge imprint; the original English title is Measurement. At roughly 286,000 characters, the book is divided into two major parts. Part One, "Size and Shape," begins with abstract geometric figures and proceeds through mosaic patterns and angle measurement, proportional scaling and ratios, length, area, and volume, the method of exhaustion and its applications, polygons and trigonometry, conic sections and projective geometry, and mechanical curves. Part Two, "Time and Space," starts from the intuition of motion and discusses coordinate systems and dimension, vector representation and relative motion, the measurement of speed, and differential calculus and its many applications. With "measurement" as its thread, the book reorganizes concepts such as proportion, area, volume, coordinates, speed, and calculus along the path of humanity's understanding of the world, emphasizing that mathematics is exploration and play rather than a pile of formulas and drill exercises. In the opening pieces "Reality and Imagination" and "On Mathematical Problems," the author expounds his understanding of the nature of mathematics, while the closing "Some Encouragement for the Reader at the End" returns to attitudes toward learning and teaching. The book features numerous diagrams and concrete examples in plain, lively language, with no exercises or standard answers; it does not aim to train techniques but hopes readers will rebuild mathematical intuition by drawing, measuring, and imagining, and appreciate the unexpected beauty and order behind shapes, patterns, and motion.