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Jim Tolpin could be described as a guy who can do math without having to do math--by using history. His deep grasp of geometry and pre-industrial design and layout techniques have provided us with lots of useful information, from how folks designed furniture without math and measuring tools and how to determine the proper dimensions for your own workbench.
Now Tolpin and co-author George Walker have a new book coming out, From Truth to Tools, that explains how geometry gives birth to tools, which in turn allow us to create furniture and structures. As an example, here's an excerpt from the book that illustrates "how the carpenter/geometers of antiquity used the simplest of tools…to solve for an unknown distance:"
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It's pretty cool stuff! The $25, 208-page book is mostly illustrated like you see here, as it's easier to grasp things visually. And if you want to take a longer look, publisher Lost Art Press has made a 27-page sample available as a free PDF download.