The golden braid (mind stretch) Math source: Finn & Thiffeault 2018. Topological Optimisation of Rod-stirring devices. #math #goldenratio #braids

The Golden Ratio sometimes shows up in the weirdest places. Imagine three rods stirring taffy. Over time, the moving rods trace out strands that weave together to create braids. You can describe any motion of the three strands using just two basic moves called braid generators. If the strands are labeled one, two, and three, then one move swaps one and two, and the second move swaps two and three. Strans can only swap if they are next to each other. These two moves and their reverse directions build every possible three strand braid. Now here's the intriguing part. The taffy gets stretched each time the rods move. If you search for the three rod sequence that forces the strongest guaranteed stretching each cycle, you find it is one swaps with two, two swaps with three in the reverse direction, repeating over and over. This particular braid has a stretching factor equal to the golden ratio. A golden braid hidden within some mixed up taffy.