From the early peoples who marvelled at the geometry of nature -- the beehive and bird's nest -- to ancient civilisations who questioned beautiful geometric forms and asked 'why?', the story of geometry spans thousands of years. Using only three simple tools -- the string, the straight-edge and the shadow -- human beings revealed the basic principles and constructions of elementary geometry. Weaving history and legend, this fascinating book reconstructs the discoveries of mathematics's most famous figures. Through illustrations and diagrams, readers are able to follow the reasoning that lead to an ingenious proof of the Pythagorean theorem, an appreciation of the significance of the Golden Mean in art and architecture, or the construction of the five regular solids. This insightful and engaging book makes geometry accessible to everyone. Readers will be fascinated with how the knowledge and wisdom of so many cultures helped shape our civilisation today. String, Straight-edge and Shadow is also a useful and inspiring book for those teaching geometry in Steiner-Waldorf classrooms.
Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles
Author: Robert Hahn
Publisher: SUNY Press
Explores Thales’s speculative philosophy through a study of geometrical diagrams. Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Plato’s Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahn’s book will enrich the study of ancient philosophy and mathematics alike.
An Encyclopedia of the Pacific Rim's Earthquakes, Tsunamis, and Volcanoes
Author: Bethany D. Rinard Hinga Ph.D.
The author examines natural disasters around the Pacific Rim throughout history together with scientific data context to produce enlightening—and highly readable—entries. • Features approximately 100 alphabetically arranged entries with insights into specific disasters, technology, key geographic features of the area, significant people, cultural beliefs, and more • Includes a general introduction and overview of the geography and tectonic activity in the Pacific Rim countries • Offers both historical and scientific information • Explains complex natural phenomena and scientific concepts using nontechnical language and clear illustrations • Provides relevant cross-references to related topics as well as to articles, books, and websites that offer further information
Composing Archimedes' Lever, the Equation, and the Sentence as an Interdisciplinary Unity
Author: James H. Bunn
This book examines the idea of ‘good education’ which is thought to include a scientific and technical component, a mathematical component, a writing component, and an ethical and aesthetic component. Bunn proposes a new three-way intersection in these teachings: the basic sciences and mechanics of levering on a seesaw, the basic formulations of patterning an algebraic equation, and the basic rules for writing a sentence in English. In all three forms of inquiry, balance is the mainstay through which problems in US middle school education are brought together and analyzed.
The Ancient Beginnings of Science From Pre-Science to the Age of Greece, With Modern-Day Applications By: Ronald A. Brown For more than 2,500 years, it has been assumed that science and mathematics originated solely in ancient Greece; however, this assumption is now known to be invalid. Recently available knowledge has shown that the ancient Hindus must also be included as one of the earliest precursors of modern mathematics and science, according to a set of criteria developed by Ronald A. Brown, namely the trifecta of philosophy, theory, and abstract mathematics. This trifecta implies that only the early Hindus and Greeks are true forerunners of modern science as they alone were the first to recognize that nature is rational and can, therefore, be understood by human reason. The ensuing developments, including selected modern topics, are discussed in historical detail, and demonstrate that the role of history is to clarify what is significant, what remains after having distilled out what is not essential.