How strong are the math skills of French soldiers?

Written by Chen Guanrong (City University of Hong Kong)

France's outstanding achievements and leadership in modern mathematics are well known. However, many people do not realize that in French history, even some military personnel were excellent in mathematics. Here are just a few familiar figures.

Descartes

René Descartes (1596-1650) is one of the founders of modern Western philosophical thought and a pioneer of modern European rationalism, a philosophical theory that human reasoning can be a source of knowledge. He proposed the idea of ​​"doubting everything". In particular, he is famous for his phrase "I think, therefore I am" (the original Latin is Cogito ergo sum, English is I think, therefore I am).

Descartes received a master's degree in law in 1616. Two years later, he joined the army as an officer and then participated in a war. After the war, he traveled around and visited many European countries. On the way, he met many famous scientists. With the brainstorming and personal efforts, he became a famous French philosopher and great enlightener. He was hailed as "the pride of the French" and even "the myth of the French nation." Descartes was also a mathematician and physicist. He was famous for the formulation of geometric coordinate systems. He was revered as the "father of analytic geometry" and was written into the history of mathematics.

L'Hôpital

French Marquis L'Hospital (1661-1704) was a student of the famous Swiss mathematician John Bernoulli (1667-1748). He was very talented and solved a cycloid problem proposed by French mathematician Blaise Pascal (1623-1662) when he was 15 years old. L'Hospital served in the military when he was young and was a cavalry captain. In 1696, after retiring and turning to mathematical research, L'Hospital published the famous book "The Infinitesimal Analysis of Curves". In Chapter 9 of the book, he introduced the analytical method of the problem of "finding the limit of a fraction when both the numerator and denominator tend to zero" that his mentor John Bernoulli told him in a letter two years ago. Perhaps because this book is the world's first calculus textbook, and especially because some people have the bad habit of not indicating the original author and source when reprinting literature, almost all mathematics books later called this method of finding limits "L'Hôpital's rule", which turned out to be a major misunderstanding in the history of mathematics.

Napoleon

Napoléon Bonaparte (1769-1821), the first emperor of the French Empire, was a military commander who needed no introduction, but many people do not know that he was also a member of the Mathematics Department of the French Academy of Sciences. The "Napoleon Triangle" is named after him. It is said that Napoleon's elementary mathematical skills once amazed his marquis, the great mathematician Pierre-Simon de Laplace (1749-1827). Of course, Napoleon admired Laplace's mathematical attainments and political abilities even more, and appointed him as Minister of the Interior.

Napoleon's exterior triangle theorem states: "If you construct equilateral triangles outward from each side of a triangle, their centers will form an equilateral triangle." This equilateral triangle is called the "Napoleon exterior triangle," as shown in Figure 1.

Figure 1. Napoleon's outer triangle

Dually, there is the Napoleon interior triangle theorem: "If you construct equilateral triangles inwards with each side of the triangle as the side, then their centers form an equilateral triangle." This equilateral triangle is called the "Napoleon interior triangle."

Figure 2. Using only a compass to divide a circle into four equal parts

Charles de Gaulle

Charles de Gaulle was the president of the Fifth Republic of France. After his death, his family erected a small stele in front of his tomb according to his wishes. On one side was engraved "Charles de Gaulle 1890-1970" and on the other side was engraved a Cross of Lorraine, which consisted of 13 equal small squares, as shown in Figure 3.

Figure 3. Lorraine Double Cross

The Lorraine Cross is a family emblem adopted by Godefroy de Boullion, Duke of Lorraine, France, since 1099. Charles de Gaulle was a heroic general who led the "Fighting French" to bravely fight against Nazi Germany under the banner of the Lorraine Cross during World War II. The general was also the first person to propose and solve the following interesting mathematical problem about the Lorraine Cross: "As shown in Figure 4, at point A of the Lorraine Cross, only a straight line is drawn using a pencil, a compass and a ruler to strictly divide the cross into two parts of equal area". This standard elementary geometry problem is not easy to solve, and is left for interested readers to think about. (Original article published in "Mathematical Culture", published with permission)

Figure 4. Bisection of the Lorraine Cross

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