Bridge Mathematics

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Teachers occasionally define projects about mathematical curves to be found in bridges.  This is a topic that has to be treated with care.  While it is true that some "mathematical" curves, notably the straight line, are found in some bridges, we should always be aware that in many cases, the shapes are the indirect result of calculations which are often complex, and are not the primary consideration.  We should also ask what we mean by a "mathematical curve".

We might simply mean a curve which can be represented by a formula, such as a parabola, represented by y = ax2 + bx + c, or an ellipse, represented by an equation of the form (x/a)2 + (y/b)2 = 1.  But any shape that is the result of calculation, however complicated, can be called mathematical.  Mathematics lies behind far more phenomena than we usually suppose.  Solving the once popular Rubik's cube was an exercise in group theory, for example.

Before people began to understand forces in a logical and mathematical way, many shapes were the result of trial and error, of experience.  They were often "geometrical" because the shapes were simple to draw and make.  Straight lines and arcs of circles are probably the simplest shapes to use, and they account for a vast proportion of structural shapes before modern science began.  If a structure is made thicker and stronger than it needs to be, the exact shape is less important than it is if everything is refined to the minimal strength.

A well known example of a "mathematical bridge" is found in Cambridge, England.  This bridge owes nothing to mathematics, and is not even a distinguished structure.  Cambridge has produced brilliant mathematicians and beautiful mathematics, but this is not evident in most promotions to tourists.

But we should not then say that medieval builders did not understand the behaviour of forces: they simply knew what worked, though they sometimes went beyond the bounds of the possible, and things fell down.  For the same reason, we wouldn't say that a brilliant snooker player, tennis player or cricketer does not understand the physics of balls - they simply understand in a way that is not expressible by mathematics.

What is far more important than seeking out the examples where "geometry" seems to apply, is to gain an appreciation of the reasons behind the shapes we see.  This can be gained by thinking about the forces that are experienced by a structure.

Nevertheless, a project about circles in bridges can form the basis of a useful and interesting investigation, as we have to limit the work in some way, rather than look at every possibility.

See also Bridge Mathematics II.


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