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How round is your circle?


I found How round is your circle? a delightful blend of geometrical and engineering problems.
What I most appreciated is the historical perspective. It shows how problems arose from practical needs and curiosity, that their solutions were incremental, competed against one another, and were in many cases quite recent (less than a few centuries), and finally how those solutions enabled further discoveries and innovations. As a result of the specialization of knowledge and the accumulation of advanced tools, we can easily forget how simple things are actually not trivial at all.
Some highlights of the topics covered:

  • How to build a linkage that will draw a straight line?
  • How to mark graduations on the “first” ruler or sector (requires difficult angle divisions such as trisection)? A later chapter goes into the history and significance of slide rules with logarithmic and alternative scales.
  • How to draw a arc of a large circle (for instance to make a railroad curve)?
  • How to measure with precision (Vernier scales, magnifiers and fine-threaded screws)?
  • How to measure surface areas, and how planimeters work (tools to measure surfaces by drawing contours, surprising but effective)?
  • How to make shapes and volumes of constant width, and conversely how to measure departure from roundness (a hard problem)?

How round is your circle.jpg

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