It just automatically happens! Actually I was just messing around with the pen block and I made this!
The Euler spiral was first thought of as a math problem by James Bernoulli in 1694. It was finally worked out calculated and described by the Swiss mathematician Leonhard Euler in 1744. Euler was looking at how elastic springs behave. He anted to find a curve where the resistance to bending and the curve itself got stronger in a straight line as the length increased. He did this by making series expansions and setting limits on integrals , now called Fresnel integrals to show exactly how a line could slowly twist into a balanced double spiral. Because the curve had an gentle change the shape was discovered again two more times. First in 1818 by Augustin-Jean Fresnel who used it to figure out how light bends when it goes through an opening. Then again in 1890 by Arthur Talbot, a civil engineer. Talbot used the spiral in building railroads and roads to solve a safety problem. He needed a way to help trains move smoothly from a path, to a tight curve controlling the force that pushes them outward so passengers don't shake around.
