Abstract: - Leonhard Euler is considered to be one of the greatest mathematicians of all time. He made incredible discoveries to many subject areas, but most were to the field of mathematics. In this paper we explore Euler’s mathematical contributions including formulas/identities, concepts and notations. We see how Euler’s formula came to be and the story behind it along with Euler’s identity. We then explore Euler’s approaches to the Basel and Seven Bridges of Königsberg problems and his solutions to these. Lastly, we see Euler’s influence in current mathematical notations. Key-Words: - Euler, notations, formulas, Basel, Königsberg 1 Introduction Leonhard Euler was born on April 15th, 1707 in Basel, Switzerland. His father, Paul Euler,…
Leonhard Euler lived form 1707-1783. During his life time he published eight hundred sixty six pages and books to only be surpassed by Paul Erdos later on. His complete work is ninety volumes. Remarkably, most of his outputs were from his last two decades of being alive while his completely blind (www.usna.edu). His most famous contributions to the world of mathematics was his equation or better known as the Leonhard equation which is V+R-L=1. Where V is equal tothe number of vertices (nodes)…
Daniel Bernoulli, proclaimed to be the greatest out of all the Bernoulli in his family, made the basis for the kinetic theory of gases, applied the idea of Boyle’s law, worked on elasticity with Leonhard Euler, the development of the Euler-Bernoulli beam equation, and one of the most important Bernoulli’s Principle which is critical to aerodynamics. At the beginning of Daniel’s life he wasn’t allowed to choose what he wanted to be or be able to pursue the career he wanted, but this shaped the…
the 1720’s, was a theory of harmony based on the fact that he heard many harmonics sounding simultaneously when each note was played. Rameau’s Treatise on Harmony created a stir that began a revolution in music. Musicians began to notice other harmonics sounding in addition to the played, fundamental tone, notably the 12th and 17th, which are the 12th and 17th steps in the scale of a given note, respectively. In the 18th century, calculus became a tool, and was used in discussions on vibrating…
Daniel. “Bernoulli's principle was named for Daniel Bernoulli (1700-1782), a Swiss mathematician”(Martin, “Bernoulli’s Principle”). This mathematician was born on January 29, 1700 in Groningen, the Netherlands. His death occurred on March 17, 1782. During his lifetime, he worked as a professor at the University of Basel in 1733. His principle is all about calculating the flow of fluids. “His Hydrodynamica, published in 1738, is considered his most important work”(Swetz, “ Mathematical Treasure:…
for x≤z≤x+h. Therefore, (A(x+h)-A(x))/h=f(z). We find that, as h→0, f(z)→f(x). This happens, as we decrease the thickness of x+h, z will become close to x. Infinite series: For a while, let us revisit the Achilles’ paradox that Zeno stated. If Achilles continued running, and his distance left to cover keeps halving repeatedly, then we can ask a question; will he eventually catch the tortoise? Or more mathematically, will Achilles cover a full hundred metres at the end of his run? And how will…
approximate the curvature relationship, but it was Daniele whom introduced the following approximation which is still relevant nowadays. (d^2 w)/(〖dx〗^2 )= - M/EI (2.1) Where w, M and EI are vertical deflection, applied moment and flexural stiffness of the beam respectively. By the derivation of this equation Daniel Bernoulli was successful in determining the deflection of Galileo’s…