Projective geometry

M.C Escher was more than just an artist. He created art using patterns of identical shapes, that fit together with no gaps, and did not overlap, also known as tessellations. He went through many stages throughout his art, but his most lasting legacy are the tessellations he made and the mathematical impact they had. By using mathematical reasoning he was able to create the tessellations, but he had to look beyond just mathematics to dig deep into his tessellated optical illusions. M.C Escher…

Researching two math placement tests for this project was the easiest part. A math placement test is a test that students take before entering a math course in college. The placement test that I took was for Monmouth University in Monmouth, New Jersey. Monmouth is on my list of schools that I am applying to for the fall of 2018 along with James Madison, which is the other test I chose to research for this project. I took the Monmouth test not thinking I would be able to complete the assigned…

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…

possible. These drawings can help the administrator to better understand test takers’ self-perceptions and attitudes. In addition, it presents concerns or conflict within individuals. It also has flexible and subjective interpretation, as many other projective tests. Description Buck developed a quantitative scoring system which can offer a measure of explanations to the drawings. Also, basic personality features were provided and categorized into groups. The administrator would usually ask…

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…