Differential geometry

The last topics are, "...inverse method of tangents and differential equations." (Riddle 1) One major thing Agnesi is known for is her discovery of "Witch of Agnesi". The "Witch of Agnesi" is a curve she founded. After the publication of this textbook, in 1759 she was, "...appointed to the chair of mathematics and…

Gsell from 1776-1783, and Katharina Gsell from 1734-1773. Leonhard was a Swiss mathematician and physicist, which helped in him being one of the founders in pure mathematics. Euler contributed to analytic geometry and trigonometry. Euler's work also revolutionized the fields of calculus, geometry, and number theory. In Euler’s younger years, his father wanted him to be a clergyman. Which is a male priest, minister, or religious leader.Euler gained…

4.1 First Side by Side Geometry The first model shown in figure 3 was for twin tunnels already constructed at a centre to centre spacing of 3D. This model helped to identify the influence of construction sequence on surface and subsurface ground displacement upon excavating the first and second tunnels underneath the existing twin tunnels. Figure 3: First Side by Side twin tunnels 4.1.1 Surface Displacements The surface displacements at distances of 4.75m, 7.125m, 9.5m and 11.875m from the…

Odd numbers were thought of as female and even numbers as male.” Pythagoras’ Theorem and the properties of right-angled triangles seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, and it was touched on in some of the most ancient mathematical texts from Egypt , dating from over a thousand years earlier. One of the simplest proofs comes from ancient China, and probably dates from well before Pythagoras' birth. It was Pythagoras…

analysis of relations for heat transfer. However, simple empirical correlations with claimed accuracy for the average Nusselt number is used for heat transfer analysis in natural convection expressed as where and are the constants depending on the geometry of the surface and flow regime. For value of for laminar flow and turbulent flow are usually equal to and , respectively (Cengel, Y.A. 2007). 3.2 Basic Heat Transfer Heat is normally absorbed or rejected by a working substance at a…

Daniel Bernoulli was born on February 8th, 1700 in Groningen, Netherlands, and was known as the “Archimedes of his age”. His parents were Johann Bernoulli and Dorothea Falkner. His father was a medical doctor and a well known mathematician, and his mother was born from a wealthy family in Basel, Switzerland. Daniel had two brothers, Nicolaus and Johann (II), and also had an uncle, named Jacob Bernoulli, who was also a leading mathematician. When his uncle died, leaving the chair of mathematics…

the father of modern philosophy and the founder of analytic geometry, Descartes was the first to plot equations on a graph. He made curves a less frightening part of mathematics by developing the x-y plane which was officially deemed the Cartesian Coordinate Plane in his honor. After his death in 1649, Descartes’ 106-page essay titled La géométrie which was the first printed account of what we know now as coordinates or analytic geometry (C.H. Edwards). In many books he wrote, Descartes wrote…

interpretation of scientific methods and theories to modern science. His mathematical findings are famous on integration and calculus. The idea of analytical geometry came from the usage of integration which is a method to define areas of curve. Also, He wrote a book about the methods of fluxion in 1666 which is the first ideas of differential calculus. In the aspect of…

from the mass fraction of fuel burned. The instantaneous thermodynamic properties are computed by the established equations [20-21, 28]. The instantaneous gas properties are calculated by the simultaneous numerical integration of the differential equations. The differential equations governing the gas pressure and temperature are resulting from the first law of thermodynamic analysis. The instantaneous…

to a Greek philosopher named Pythagoras. Pythagoras is best known for discovering the Pythagorean Theorem. In fact, most people will know him best for the Pythagorean Theorem in relation to geometry or trigonometry. However, this is not his only claim to fame. Pythagoras studied music as well, and understood the arithmetical relationships between pitches. It is said that he discovered the relationship between number and sound. He believed that…