arXiv subjects

Dora Musielak

Publications and source records attributed to Dora Musielak.

6 recordsLinked to original sources

arXiv2023

Emilie du Chatelet and Euler: A Rare Convergence on the Hypotheses of Physics

Euler stressed the importance of hypotheses, which he thought were the only means of arriving at a certain knowledge of the physical causes, essential to establish the laws of physics. This thought was communicated to Emilie du Chatelet in response to hers when she debated the nature of forces, defending the Leibnizian concept of vis viva. After examining the Euler-Chatelet correspondence, I introduce a treatise discovered in 1844 where Euler provides the first analytical attempt to explain the difference between momentum and vis viva, and where he defined a new concept related to motion that can be considered the first idea of kinetic energy. These documents have received little attention. In this paper, I examine the topics Euler discussed in these manuscripts and place them in a context within the scientific and philosophical research of the seventeenth and eighteenth centuries that sought to establish the principles of nature, and that served as foundation for physics.

physics.hist-ph↗

arXiv2023

Dido's Problem. When a myth of ancient literature became a problem of variational calculus

When introducing the calculus of variations, we may invoke Dido's problem to illustrate the most fundamental variational problem: to find the curve of given perimeter which bounds the greatest area. This type of problem led mathematicians to invent solution methods of maxima and minima, and the genesis of variational calculus as a distinct branch of analysis. Dido's problem was inspired by the mythical tale of the foundation of Carthage (ancient city in North Africa) by a Phoenician princess as told independently by Roman poet Virgil, and by Latin historian Justinus in the first two centuries BC. Historians have debated the facts surrounding Carthage's birth; however, contemporary mathematicians have accepted the vague events described by Virgil in his Aeneid, adding details to Dido's story to extrapolate a few verses and use as a basis for the isoperimetric theorem. Was Leonhard Euler or Lord Kelvin who first interpreted Virgil's poem as Dido's problem of variational calculus? In this article I attempt to resolve a question of historical attribution to identify who first defined Dido's problem.

math.HO↗

arXiv2020

Germain and Her Fearless Attempt to Prove Fermat's Last Theorem

Two centuries ago, Sophie Germain began to work on her grand plan to prove the theorem of Fermat, the famous conjecture that $x^n + y^n = z^n$ is impossible for nonzero integral values of $x$, $y$, and $z$, when $n > 2$. At that time, this was an open question since nobody knew whether Fermat's assertion was true. Euler had proved it for $n = 3$ and $n = 4$. However, no one else had demonstrated the general case. Then Sophie Germain valiantly entered the world of mathematics in 1804, reaching out to Gauss (writing under the assumed name Monsieur Le Blanc) boldly stating that she could do it. Eventually, Germain conceived a formidable plan for proving Fermat's Last Theorem in its entirety, and in the process she obtained proofs of Case 1 for particular families of exponents. Her efforts resulted in Sophie Germain's Theorem that proves Case 1 of FLT for an odd prime exponent $p$ whenever $2p + 1$ is prime. Today, a prime $p$ is called a Sophie Germain prime if $2p + 1$ is also prime. It remains an unanswered question whether there are an infinite number of Sophie Germain primes. But there is more that Germain did in number theory, much of which was veiled by the mathematicians with whom she shared her work. This article provides historical details of Sophie Germain's efforts, written with the sole intention of paying homage to the only woman mathematician who contributed to proving the most famous assertion of Fermat.

math.HO↗

arXiv2014

Euler: Genius Blind Astronomer Mathematician

Leonhard Euler, the most prolific mathematician in history, contributed to advance a wide spectrum of topics in celestial mechanics. At the Saint Petersburg Observatory, Euler observed sunspots and tracked the movements of the Moon. Combining astronomical observations with his own mathematical genius, he determined the orbits of planets and comets. Euler laid the foundations of the methods of planetary perturbations and solved many of the Newtonian mechanics problems of the eighteenth century that are relevant today. In his study of the three-body problem, Euler discovered two of the five equilibrium points so-called the Lagrangian points. His pioneering work in astronomy was recognized with six of the twelve prizes he won from the Paris Academy of Sciences. In this article, we review some of Euler's most interesting contributions to astronomy.

math.HO↗

arXiv2014

The Marquise du Chatelet: A Controversial Woman of Science

No woman of science has lived a more controversial life nor possessed a most contrasting character than Gabrielle Emilie Le Tonnelier, Marquise du Chatelet. One one hand, she was a woman of great intelligence, a philosopher of science, a student of mathematics, and she was an ardent supporter of Newton and his new laws of physics. At the same time, Emilie du Chatelet was an aristocrat society woman who gambled, enjoyed parties, and had several extramarital affairs, provoking numerous scandals in her native Paris. She was a passionate woman who was at ease conversing with the nobles at the court and with the most renowned scholars of her time. Emilie du Chatelet did not develop theorems and she did not discover new scientific principles. However, she studied mathematics with Maupertuis and Clairaut to better understand the geometrical language in Newton's Principia. In this article, we review some important aspects of this controversial woman of science, exploring her relationship with the greatest scholars of her time.

math.HO↗

arXiv2014

Euler and the German Princess

In 1760, Leonhard Euler began to write beautiful Letters to a German Princess on Diverse Subjects of Physics and Philosophy. Much has been written about Euler and his work, but we wonder, who was the princess? How did she become involved with the greatest mathematician of her time? The princess was a fifteen year old named Friederike Charlotte von Brandenburg-Schwedt. In this article we explore her story and the nature of the letters.

math.HO↗