It took some amazing minds to send astronauts to the moon, and of the many ingenious ideas they came up with, one involved some pretty neat optical tricks.
The Alignment Optical Telescope played a crucial role in the Apollo missions, as the measurements astronauts took from it were used to align the gyroscopes contained in the Inertial Measurement Unit (IMU), the device that tracked the Lunar Module's position in space, the same sort of device still used in modern commercial aircraft. Taking the measurement required finding two angles, one of which could measured directly from the scope, and one that had to be inferred based on its distance from the center, which was proportional to the second angle. Measuring this distance took some further ingenuity, however, as covering the glass in concentric circles would obscure too much of the scope. A rotatable straight line would be an option, but it would be nowhere as precise as an angular measurement. Think of it this way: Take a 12-inch ruler. Now, take a 36-inch yardstick, and wrap it into a spiral that is 12 inches wide. Even though both can measure outward in the radial direction a total of 12 inches, the yard stick has triple the resolution.
And thus, the solution was created: an Archimedean spiral. In math, an Archimedean spiral is the locus of points that is generated by a point moving at a constant rate while its radius vector also rotates at a constant rate. In other words, put your finger on a surface. Start moving it outward from the center at some fixed speed, but at the same time, rotate it around the center at some constant rate. Your finger is tracing out an Archimedean spiral. It turns out that this was the yardstick the engineers were looking for. Check out the above video for more!
Lead image credit: NASA