Émile Lemoine

Émile Michel Hyacinthe Lemoine: A Pioneer in Geometry

Imagine a world where geometry was not just about drawing lines and circles but about finding the simplest way to construct them. This is exactly what Émile Michel Hyacinthe Lemoine did, a French civil engineer and mathematician who lived from 1840 to 1912. His work laid the foundation for modern triangle geometry, and his contributions are still celebrated today.

The Journey of a Mathematician

Lemoine’s education at the Prytanée National Militaire and École Polytechnique set him on a path that would eventually lead to groundbreaking discoveries. He taught mathematics at the prestigious École Polytechnique, where he honed his skills in geometry and algebra.

The Lemoine Point: A Mathematical Gem

One of Lemoine’s most notable contributions is the proof of the existence of the Lemoine point. This point, also known as the symmedian point, is a fascinating concept in triangle geometry. It’s like finding the perfect balance point in a triangle where all the symmedians (lines that are reflections of medians over the angle bisectors) meet.

Géométrographie: The Art of Simplicity

Lemoine developed a system called Géométrographie, which aimed to simplify geometric constructions using just a compass and straightedge. This was like creating a language where every construction could be described in the simplest terms possible. He listed five main operations: placing a compass on a point or line, drawing a circle, placing a straightedge on a line, and extending a line with a straightedge.

De la mesure de la simplicité

In 1888, Lemoine presented his paper at the Association Française in Oran, Algeria. The title of his paper was intended to discuss mathematical concepts in general but due to time constraints, it focused on simplifying geometric constructions using a compass and straightedge. This work was groundbreaking because it introduced a methodological system for judging the simplicity of constructions.

Continuing His Legacy

Lemoine’s contributions did not stop there. He published several other papers that year, including “Sur la mesure de la simplicité dans les constructions géométriques” and “La Géométrographie ou l’art des constructions géométriques.” His work on transformation continue also related mathematical equations to geometrical objects, further enriching the field of geometry.

Founding a Journal

In 1894, Lemoine co-founded the journal L’intermédiaire des mathématiciens with Charles Laisant and served as its first editor for several years. This was like creating a platform where mathematicians could share their ideas and discoveries.

The Lemoine Point and Circle: More Discoveries

Lemoine’s work on the Lemoine point also included the concept of the Lemoine circle, which proves the concurrency of symmedians. This is like finding a hidden treasure in geometry where all these lines meet at one perfect spot.

Conjectures and Theories

Lemoine’s conjecture that every odd number greater than 3 could be expressed as 2p + q, where p and q are prime numbers, was a fascinating idea. His refined Lemoine conjecture extended this to odd numbers greater than or equal to 9 with additional constraints. These conjectures were like puzzles waiting to be solved.

Recognition and Legacy

Lemoine’s contributions have been recognized as laying the foundation for modern triangle geometry, and he received the Francœur prize in 1902. His work on Géométrographie, study of concurrencies, and definition of points in triangles continue to influence mathematicians today.

Émile Michel Hyacinthe Lemoine’s legacy is a testament to the power of simplicity and innovation in mathematics. His work continues to inspire mathematicians, much like finding the simplest path through a complex problem.