#Trammel of archimedes how to

While this next one is an elaborate device, it is based on the same theory (but draws much more precise ellipses). (Chalk would be placed in the holder on the left end of the cross-beam.) Here is a simple trammel dating from the late 19th century and probably used in the classroom. The museum has eight ellipsographs in its mathematics collections. There are also much more intricate devices that will draw ellipses and they all fall under the title of ellipsographs. Trammels are deceptively simple machines that produce something profoundly mathematical. That's right! The trammel is a device for drawing ellipses! You can go to YouTube and type in any of the names above and you will find videos and animations of this wonderful little device in action ( this one is fun), and even directions for making your own if you are handy. Don’t you think it looks good?īut why have I linked these two items, the 'do-nothing' machine and the ellipse? The answer is in the mathematical name for the machine: the elliptic trammel.

#Trammel of archimedes how to

You can draw a perfect circle simply by using a single pin.Įven though I had known theoretically how to draw an ellipse since I first learned about conic sections, I had never actually done it! I was surprised that it worked so well right out of the box. Notice in my creation below that the total length of string does not change, so the distance from the two pins (foci) to the pencil is always the same (r1+r2 in the diagram above). The easiest way to do this is to draw one (please try this at home-you will feel a great sense of accomplishment) using a piece of string, two pushpins and a pencil. So what exactly is an ellipse? Apart from its mathematical equation, which you can look up if that vital piece of knowledge escapes you, it can be defined very simply as the set of all points whose combined distance from two points (the foci, F1 and F2 above) remains constant. You may even recall that a circle is a special case of an ellipse where the two foci become one (see image below of an ellipse and all its relevant measurements). Archimedes explored these geometric objects at length and was the first to give us some idea of their uses. The conics are the circle, the ellipse, the parabola, and the hyperbola. You remember those, the four curves that arise when you cut a cone with a plane. Envision yourself drawing conic sections. Now I want to take you from your halcyon days of childhood toys to the more capricious days of ninth- or tenth-grade Algebra II class. He gave us, among other amazing things, the Archimedes screw, still used in many developing countries to raise water the theory of density, where he famously-though maybe not actually-cried 'Eureka!' when he discovered while soaking in the bath that King Hieron II's crown was not made of pure gold and the legendary burning mirrorsand other defensive works that kept the Romans out of Syracuse for three years during the Second Punic War.

I mean, how sad? Why give a child a toy that by its name has no intrinsic value? Why not call it the 'what does this do?' machine and let them explore it until it has some meaning? To me, it is an elliptic trammel, often referred to as the Trammel of Archimedes after the ancient Greek mathematician Archimedes of Syracuse (c. 287 BC – c. 212 BC).Īrchimedes is my personal math hero. As a child, you may have played with a simple wooden toy called a 'do-nothing' machine or simply a 'grinder.'Īs a mathematician, I find that name a very poor choice.