You may have noticed poorly thought-out graphics on posters, logos, or even the British 2-pound coin, that feature a design of an odd number of gears interlocking (commonly three). While gears symbolize cooperation and innovation, it’s hard to take these designs seriously when you realize that any set of an odd number of gears interlocking cannot possible move.
After all, for gears to work, one gear has to turn one way and the other the opposite way. If there’s three, five, seven, or any other odd number of gears, one of them will end up interlocking with a gear going the wrong direction. In the interesting Numberphile video above, mathematician Henry Segerman talks about 3 gear systems and how, despite their seeming impossibility, can actually exist, with the help of a little ingenuity and 3D printing.