Hyperbolic geometry

Throughout the centuries, many people have tried to find shortcuts to make their lives simple. Usually described as lazy, mathematicians came along to see the patterns that no one else was able to see. These mathematicians helped reform their societies, and bring about equations that will help others calculate what they need faster. Upon these mathematicians, Pythagoras was most likely one of the most influential mathematicians that helped shape the way that people see shapes today. Through his…

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…

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…

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…

In this project I will talk about curves in three space, also known as curves in three dimensional space or 3 - D. Many of us are familiar with two dimensional space or 2- D. It is called two dimension space because it has two axes: the x-axes and the y-axes. Three dimensional space is represented by the symbol it is called three dimensional space because three axes are used to draw, and the three axes are: x, y, and z. Figure 01: Standard axes of 3 dimensions This is the standard axes…

December 11th, roughly. Five years and one month ago was the date that not only my life and surroundings changed and not to sound cliché, so did I as a person. I remember it vividly it was summer in South Africa, as our seasons are flipped to those in the states. Nevertheless it being summer I had a winter coat on because I knew it was winter in the U.S. but I didn't know how cold it would be so I dressed accordingly to how I felt it would be in a place where it snows. I remember going to get my…

Fear of the future is one phobia that every so often gets a grip of us all. Wilkinson continues to assert, "We look out into the future, trying our best to make wise decisions, only to find ourselves staring into the teeth of ferocious and widespread uncertainties. If only everything didn't depend on, well, everything else. How do we decide what kind of career path to pursue when it's not clear what industries will exist in 10 or 15 years? How do we plan our children's education when we can't…

Questions: Answer all questions given What kind of relationship did you see in your D vs T graphs (both hand and computer)? Do these relationships make sense? Explain! In the distance versus time graph for the hand graph, there is an exponential increase the in the distance traveled; as time progresses, the distance the car travels increases a little more, as the slope is not a straight line, but instead slopes upwards, with slopes later in the line being steeper than the slopes before. What…