Differential geometry

Abstract This research paper is on the topic of math in the movie Hidden Figures. In Hidden Figures, Katherine Johnson is a single, African-American female during the 1960s. She is everything a person does not want to be during this time. However, she helped solve the calculations to send man into space. One of the main points is describing the mathematical method, Euler’s Method, NASA and Johnson used to launch America into space and back. The second main point is how math is able to unite…

c. Pipe 3 (4mm Diameter) 9 6) Analysis of Results 11 7) Conclusion 11 8) References 11 9) Appendices 11 Executive Summary: Introduction: The aim of the experiment was to calculate the pressure drop in three different pipes of different geometries, and then compare this experimental value of pressure drop to its theoretical value with the use of the Darcy-Weisbach equation (The Engineering ToolBox, 2017). The pressure drop in a pipe…

Different numerical methods are used to integrate the differential governing equations. The choice of the numerical method which will be joined with the influence of calculations steps in terms of accuracy are discussed in results section. However, an equivalent circuit diagram, shown in figure 7, was established…

Fluid dynamics relating to bluff bodies, non-streamlined structures or streamlined bodies at large angles of attack, remains a critical focus of study within the fluid mechanics community. One particular area of interests involves the occurrence of fluid-induced vibrations, or more commonly known as vortex-induced vibrations (VIV’s), exerted on bluff bodies. Due to the production of vortex shedding beyond bluff cross sections, an alternating pressure distribution produces periodic fluctuations…

In the past chapter, the overall problem was outlined. A structural member is needed to react the load within the system and transfer it from shoulder to waist. All past concepts proposed had no direct route towards flexibility nor actuation, these are key factors in determining the initial concept. In this chapter, solutions for the compression column are investigated, and an initial concept is proposed. This initial concept is broken down into its constitutive parts, and a plan for…

Leonhard Euler was a famous eighteenth century physicist who was responsible for developing many concepts that are now part of modern mathematics. He is acknowledged for many of the articles and books that he wrote over his lifetime. Leonhard was one of the top mathematics of the eighteenth century and the greatest mathematician to come out of Switzerland (Leonhard Euler Biography n.pag). Leonhard Euler was born on April 15, 1707 in Basel Switzerland. His parents were Paul Euler and Marguerite…

in terms of the mass balance of the considered chemical species, heat and moment balance, with the rate constants given in Table 2: Table 1. The fixed bed multi-tubular reactor model used for benzen oxidation to maleic anhydride Mass balance differential…

I.1- INTRODUCTION: Conformational analysis is the study of the energy change, a molecule undergoes, as it rotates about one or more single bonds. The conformations of a molecule are those arrangements in space of the atoms which are not superimposeable upon each other. The basic idea behind conformational analysis is that molecules will have certain physical and chemical and thermodynamic properties that are dependent on the preferred conformations. in the modern chemistry, where it can…

This might have been the case too, if it weren’t for a series of coincidences leading to Huygens’s scientific debut. Firstly, he was introduced to Fermat’s Differential Geometry by a friend and mentor, and began to study this in great detail. Secondly, his father much of his influence in politics, so any residual influence Christiaan would have had from his father was lost. Lastly, and most importantly, Christiaan…

many of his creations have contributed central works in “almost all spheres of mathematics.” Some of the mathematical ideas Poincaré took so far as to publish dealt with, “topology, automorphic functions, theory of differential equations, integral equations, non-Euclidean geometry, and the relative theory, the theory of numbers, celestial mechanics, physics, and philosophy of mathematics and philosophy of science,” (Henri Poincare : Biography 3). His works were published in eleven volumes, and…