Differential geometry

M.C. Escher’s art has always been fascinating to look at; his tessellations especially. I was first introduced to him by my psychology teacher when we looked at optical illusions, and then, once again in art class when he was introduced as an amazing artist, rightfully so. Being a fan of his art, I was amazed to find I could translate it in math terms as well; tessellations turn into geometric ratios and formulas. From psychology, to art, to math, M.C. Escher’s art has been widely acclaimed as…

I used to believe that geometry wasn’t possible without algebra, that geometry was essentially a representation of algebra. I didn’t have an experience of geometry that focused on the creativity and ingenuity that I’ve come to now know. Chapter 6 of Journey Through Genius reiterates how impressive the discipline of geometry truly is. Cardano’s solution to the general solution was astonishing, to me, because of the literal use of geometry to find the appropriate algebraic identities and the…

and built in two ways: one with solely using operational amplifiers and other using transistors as differential amplifiers. Electrocardiography (ECG)/ Background The heart is one of the vital organs in the human body. The heart behaves like a pump that circulates blood and oxygen around the body in order for the human body to function flawlessly. Waste products are removed from the body…

investors will not pay for risk premiums, and defined by following stochastic differential equations: (1) (2) Where: S(t) represents the price process of an underlying assets. V(t) is the variance of the corresponding instantaneous returns. And the initial condition S(0), V(0) should be strictly positive. r is the risk-free return rate…

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)…

Johnny Martinez Period 7th Pythagorean Theorem The Pythagorean Theorem also known as Pythagoras’s theorem is a relation in Euclidean geometry that are the tree sides of a right triangle. It’s the sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse. The equation use for it is A squared plus B squared equals C squared.The Theorem relates the lengths of the three sides of any…

If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…

Supply chains that are complex are commonly modeled as linear programs (LPs). They can effectively trade off broad range of criteria. To model FMCG supply chains accurately, one must include discrete aspects of decision making, which requires solving a mixed-integer program (MIP). It has become significantly important for managers, given the widespread use of linear models today, to be able to develop good, efficient models to aid them in the decision-making process. Three important factors;…

of the Kaufmann Desert House by Richard Neutra, the first thing that was drawn to my attention was all the similar geometry, specifically the L shaped geometries. They were all different shapes and sizes, and were facing all different directions, There was a sense of repetition embedded within the floor plan. A central axis stood out, and it was obvious that all the L shaped geometries were rotated around this central axis, and then shifted off of it. Diagram one is all about identify the…

Title: Application of Self-Organization Neural Network Technique (SOM) to Optimize Finite- Element Partial Differential Equation (PDEs) Results in Square-Shaped Structures Analysis. The finite-element method (FEM) is a computationally method for solving partial differential equations (PDEs) with specific boundary conditions over a domain. When we applying the FEM to a domain, it has to divide to a finite number of elements and nodes. The collections of the elements and nodes form the…