Henry Ernest Dudeney/Modern Puzzles/124 - Drawing a Straight Line/Solution

by : $124$

 * Drawing a Straight Line

Solution

 * Prime.mover suggests:
 * You can always fold a piece of paper.

However, 's suggestion is more elaborate, as follows.


 * Dudeney-Modern-Puzzles-124-solution.png

The diagram shows a linkage of rods which are free to rotate at the points at which they are joined.

The geometry is such that:
 * the longer rods are both the same length
 * the shorter rods are all the same length
 * the distance $AB$ is the same as the distance $BC$.

The points $A$ and $B$ are pinned to the drawing board so as to be able to rotate around those pins.

A writing instrument is attached to $D$ so as to draw on the surface when it is moved.

When $D$ is moved, a straight line is drawn.

Note that it is not strictly necessary for the rods themselves to be accurately straight, merely that the distances between the hinges are correct.

Proof
It remains to be proved that the line drawn by the writing instrument at $D$ is straight.