# How Round Is Your Circle?: Where Engineering and Mathematics Meet

John Bryant and Chris Sangwin

How do you make a line appear straight? How can you tell whether a circle is truly round? These mathematical issues may appear to be straightforward or even minor, yet to an engineer, the solutions might spell the difference between success and failure. Your Circle: How Round Is It? enables readers to investigate many of the same fundamental issues practiced engineers face daily; it’s tough, practical, and enjoyable.

Chris Sangwin and John Bryant provide an example of how abstract mathematical models can be translated into practical ones. They lead readers through paper-and-pencil recreations of mathematical issues using basic geometry and trigonometry and demonstrate how to build real physical models yourself with step-by-step instructions. It is a powerful and engaging technique to demonstrate how applied mathematics and engineering combine to find solutions to issues, including maintaining a piston’s alignment within its cylinder and ensuring that automobile driveshafts rotate smoothly. It’s interesting how difficult it is to verify that a produced object is spherical. When does the width of a saw blade—or, for that matter, the width of a real line—have an impact on an engineer’s calculations? When is an accurate measurement required, and when will an estimate work? These are the kinds of issues that Bryant and Sangwin address and they bring a wealth of fascinating examples from engineering history to life. How Round Is Your Circle? which is profusely illustrated, illustrates some of the subtle complexity in commonplace objects.