Sine wave: cylinder net

A sine graph can be obtained as a “cut off at an angle” cylinder (or, simi­larly, with an ellipse drawn on it).

All you need to get a sine wave at home is a loaf of sausage. It is known that sausage must be cut at an angle — then the pieces are bigger.

Let’s slice the casing along the still uncut part of the sausage and flatten the casing. If the cutting angle is 45° to the cylinder axis (taking its radius as a unit), then one edge of the casing (the cylinder net) will be exactly a sine wave — the graph of func­tion $y=\sin x$! If the angle was arbi­trary, $\alpha ,$ the graph will be $y=\tg\alpha \sin x $.

A museum piece can be made by stretching a trans­parent film over two cylin­ders. The drive should be manual, so that the user can rotate it at a suit­able speed for obser­va­tion and stop to watch the sine wave roll off the cylinder.

Another “home­made” method of producing a sine wave as a cylinder net is a coil with pins inserted along an ellipse.

The choice of the coil is not acci­dental: the flange, with a prop­erly adjusted base width, avoids misalign­ment. With this imple­men­ta­tion, the holes in the base need to be cone-shaped and/or wider than the pins, as they must be able to slide in and out “at an angle” unhin­dered.


Erleb­nis­land Math­e­matik. Dresden, Germany.