The steepest descent line we know is actually a cycloid. Only on the steepest descent line, this cycloid is reversed. The so-called cycloid is the trajectory formed by a certain point on the circumference when the circle moves along a straight line, and the trajectory passed by a certain point on the circle is called cycloid. What is this called in the history of mathematics? Steepest descent line? In fact, a well-known problem of the Great Wall was first put forward by the famous Italian scientist Galileo in 1630. Galileo thought through his research that the steepest descent line should actually be an arc, but unfortunately this answer is incorrect. As time goes by, more than 60 years have passed. 1June, 696, a John from Basel, Switzerland? Bernoulli raised this question again in Teacher's Magazine. He openly challenged mathematicians all over Europe. This is a unique new concept, but it is very easy to understand and attracted mathematicians all over Europe at that time. However, the people who can give the correct answer in the end are also famous giants in the history of mathematics. This also makes this challenge the most exciting fair and open challenge in the history of mathematics. In fact, mathematicians at that time were no strangers to this curve. Pascal and Huygens had studied this important curve at that time. But most people still don't think that this line is actually the steepest descent line that people have tried their best to pursue before.

Among many excellent mathematicians, John's solution should be the most beautiful. He used Fermat's principle to compare the motion of the ball with the motion of light. Fermat's principle has other names? The shortest light? Principle, that is to say, when light propagates, it always chooses a path with a short optical path. That's it? Steepest descent line? That is, the speed of light increases with the decrease of height. Using this analogy, John also successfully worked out that this curve is actually the cycloid mentioned above.