During the Great War, artillery caused two-thirds of all casualties. Locating enemy batteries was therefore important so that counter-battery fire could silence them. Surprisingly, the search leads to an old geometry problem!
Articles recommended for you.
The links between mathematics and the physical sciences are both ancient and profound. They find their most striking expression in the curves, trajectories and other loci obtained through experiment. Conic sections are especially prevalent, at every scale from the microscopic to the macroscopic.
Equidistance is introduced very early in geometry. Perpendicular and angle bisectors are the simplest examples. Let us go further and consider points equidistant from a line and a circle, from two circles, or even from two more general curves. How far can we take this?
Drawing paper, tracing paper, colored pencils, a little curiosity and some practical ingenuity... You now have everything you need to explore roulettes and rediscover a now-forgotten classic of dynamic geometry: plane-on-plane motion.
It took decades to uncover the geometric properties of cycloids and trochoids. The scholars who studied them began with physical or practical questions before turning to these remarkable curves themselves.
Discussion
Sign in to post a comment and talk with other readers.
No comments yet. Be the first to respond.
