''How Round Is Your Circle? Where Engineering and Mathematics Meet'' is a book on the mathematics of physical objects, for a popular audience. It was written by chemical engineer John Bryant and mathematics educator Chris Sangwin, and published by the

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...

in 2008.

Topics

The book has 13 chapters, whose topics include: * Lines, the thickness of physically drawn or cut lines, and the problem of testing straightness of physical objects *The construction of physical measuring and calculating devices including

ruler A ruler, sometimes called a rule, scale, line gauge, or metre/meter stick, is an instrument used to make length measurements, whereby a length is read from a series of markings called "rules" along an edge of the device. Usually, the instr ...

protractor A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (''gōnía'') 'angle' and μέτρον (''métron'') ' me ...

pantograph A pantograph (, from their original use for copying writing) is a Linkage (mechanical), mechanical linkage connected in a manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a se ...

planimeter A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape. Construction There are several kinds of planimeters, but all operate in a similar way. The precise way in whic ...

integrator An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output. Integration is an importan ...

s, and

slide rule A slide rule is a hand-operated mechanical calculator consisting of slidable rulers for conducting mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry. It is one of the simplest analog ...

s *

Mechanical linkage A mechanical linkage is an assembly of systems connected so as to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as pro ...

four-bar linkage In the study of Mechanism (engineering), mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-Kinematic chain, chain movable linkage (mechanical), linkage. It consists of four Rigid body, bodies, called ''bars'' or ''link ...

s, and the problem of converting rotary to linear motion, solved by the

Peaucellier–Lipkin linkage The Peaucellier–Lipkin linkage (or Peaucellier–Lipkin cell, or Peaucellier–Lipkin inversor), invented in 1864, was the first true planar straight line mechanism – the first planar linkage capable of transforming rotary motion ...

and by

Hart's inversor Hart's inversors are two planar mechanisms that provide a perfect straight line motion using only rotary joints. They were invented and published by Harry Hart (mathematician), Harry Hart in 1874–5. Hart's first inversor Hart's first inverso ...

*Geometric dissections,

straightedge and compass construction In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...

angle trisection Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and ...

, and mathematical origami *The

catenary In physics and geometry, a catenary ( , ) is the curve that an idealized hanging chain or wire rope, cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, ...

and the

tractrix In geometry, a tractrix (; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point (the ''tractor'') that moves at a right angl ...

, curves formed from physical forces, and their use in bridges and bearings * Approximation by rational numbers,

discretization In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numeri ...

and

pixelization Pixelization (in British English pixelisation) or mosaic processing is any technique used in editing images or video, whereby an image is blurred by displaying part or all of it at a markedly lower resolution. It is primarily used for censorshi ...

, gear ratios, and the approximations involved in

calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A calendar date, date is the designation of a single and specific day within such a system. A calendar is ...

systems *The roundness of objects, non-circular objects of constant width, including the

Reuleaux triangle A Reuleaux triangle is a circular triangle, curved triangle with curve of constant width, constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circle, circular dis ...

and certain coins, and their use in drilling square holes *Stability and

mechanical equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is ze ...

of objects, overhanging objects and the

block-stacking problem In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire , also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table. Statement The block- ...

superegg In geometry, a superegg is a solid of revolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis. It is a special case of superellipsoid. Unlike an elongated ellipsoid, an elongated sup ...

s, and objects with only one stable resting position (unfortunately not including the

Gömböc A gömböc () is any member of a class of convex set, convex, three-dimensional and homogeneous bodies that are ''mono-monostatic'', meaning that they have just one stable and one unstable Mechanical equilibrium, point of equilibrium when r ...

, which was discovered too recently to be included) The book emphasizes the construction of physical models, and includes many plates of the authors' own models, detailed construction plans, and illustrations.

Audience and reception

Doug Manchester characterizes the topic of the book as "recreational engineering". It only requires a standard background in mathematics including basic geometry, trigonometry, and a small amount of calculus. Owen Smith calls it "a great book for engineers and mathematicians, as well as the interested lay person", writing that it is particularly good at laying bare the mathematical foundations of seemingly-simple problems. Similarly, Ronald Huston recommends it to "mathematicians, engineers, and physicists", as well as interested members of the general public. Matthew Killeya writes approvingly of the book's intuitive explanations for its calculations and the motivation it adds to the mathematics it applies. However, although reviewer Tim Erickson calls the book "exuberant and eclectic", reviewers Andrew Whelan and William Satzer disagree, both finding fault with the book's lack of focus.

References

{{reflist, refs= {{citation , last = Erickson , first = Tim , date = April 2009 , issue = 8 , journal = The Mathematics Teacher , jstor = 20876459 , page = 640 , title = Review of ''How Round Is Your Circle?'' , volume = 102 {{citation , last = Huston , first = Ronald L. , journal = zbMATH , title = Review of ''How Round Is Your Circle?'' , zbl = 1166.00001 {{citation , last = Killeya , first = Matthew , date = February 20, 2008 , journal = New Scientist , title = Review of ''How Round Is Your Circle?'' , doi = 10.1016/S0262-4079(08)60491-1 , url = https://www.newscientist.com/article/mg19726442-300-review-how-round-is-your-circle/ {{citation , last = Manchester , first = Doug , date = June 2010 , journal = EE Times , title = The intersection of engineering and math (Review of ''How Round Is Your Circle?'') , url = https://www.eetimes.com/the-intersection-of-engineering-and-math/ {{citation , last = Satzer , first = William J. , date = January 2008 , journal = MAA Reviews , publisher = Mathematical Association of America , title = Review of ''How Round Is Your Circle?'' , url = https://www.maa.org/press/maa-reviews/how-round-is-your-circle-where-engineering-and-mathematics-meet {{citation , last = Smith , first = Owen , date = June 2008 , journal = Plus Magazine , title = Review of ''How Round Is Your Circle?'' , url = https://plus.maths.org/content/how-round-your-circle {{citation , last = Wagon , first = Stan , authorlink = Stan Wagon , date = September–October 2008 , issue = 5 , journal = American Scientist , jstor = 27859211 , pages = 420–421 , title = Applied geometry (Review of ''How Round Is Your Circle?'') , volume = 96, doi = 10.1511/2008.74.420 {{citation , last = Whelan , first = Andrew Edward , journal = Mathematical Reviews , mr = 2377148 , title = Review of ''How Round Is Your Circle?'' , year = 2009 Applied mathematics Popular mathematics books 2008 non-fiction books