Skipping Stones by Math

One of my most beautiful childhood memories was stone skipping with my dad. It always seemed mysterious to me when the rocks bounced smoothly on a calm sea on a warm summer day.

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Skipping stones is a worldwide phenomenon. Eskimos skip rocks on ice and Bedouins on the smooth sand. In England, stone skipping is known as "ducks and drakes"; in France, as "ricochet"; in Ireland, as "stone skiffing"; and in Denmark as "smutting." Stone skipping is mentioned in the works of Shakespeare and even Homer. The British King's bouncing gold coins on the Thames River in 1583 was the first public event on skipping stones. From Hindi to Russian to Chinese, every language has a unique word or term for skipping stones. This may be because everyone wonders how a stone can glide across the water after throwing one. Of course, the secret to a successful skipping is to choose a suitable stone with a smooth surface, not too heavy nor too light, and the water should be as calm as possible, for wavy water prevents stones from bouncing further.

Stone skipping is usually a promising application area of mathematics and physical sciences. Yet, Lazzaro Spallanzani (1729–1799), an Italian Catholic priest, is the first person to make a scientific explanation of how stones bounce on water. After him, there seemed to be a long gap in research until a French physics professor, Lyderic Bocquet, brought this subject to the scientific field in an article published in 2002 and then in another article in 2004. Dr. Bocquet attributed his interest to this topic because of his child. Similar to the father-child memoir mentioned at the beginning of our article, one day, Dr. Bocquet was skipping stones on the seashore with his six-year-old son when his son asked: "Dad, how is it possible? How does the stone skip on water?" Simple questions do not have simple answers. Bocquet reflected on this question, and his scientific interest grew on this topic. Thus, the professor's first thing was to design small catapults that skipped stones on the water. Later, using these catapults, he bounced the rocks and continued his scientific work.

At the end of his research, he found many factors affecting whether a stone sinks or skips. Commonly known factors are the weight of the stone, its surface, and water stillness. Although everyone is on the same page for the importance of the surface…