Non-Euclidean geometry

mathematics at Kazan University for nineteen years, devised a method for finding roots of a polynomial and published a plethora of material on algebra, numerical analysis, astronomy and probability. His most important discovery was the idea of non-Euclidian geometry, the thought of which was met with scorn and derision during his lifetime, but one that would go on to be a cornerstone for our modern understanding of…

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…

All the scenes in the play were short and barely any characters were called by name. They also did not go in order of the pamphlet that spells “Shakespeare.” Throughout my paper, I try to describe each scene to the best of my ability with the info of which play they are acting out or about just the scenes in general. The beginning of the play began with people cleaning up the stage with brooms. The three people were slouched over sweeping close together. This showed medium topography and close…

Lists 3 visual elements of art and design (the "building blocks") you think Munch employed when he created The Scream. These visual elements must be chosen from those featured in Chapter 3 and the PowerPoint presentation. 1. After you list the 3 visual elements, you must then write a 300-word long thread that describes the characteristics of each element AND explains why they were chosen by Munch to createThe Scream. 2. Pay particular attention to the most obvious visual elements of The Scream.…

Determining Subject Matter I worked with the CT to identify the topic that would be appropriate for this assignment. After reviewing the upcoming lessons and considering the timeline, we agreed that I would teach the students about coordinate planes, including the parts of the plane, how to plot points, find the distance between points, and reflect points across axes. The timing of this topic is fitting since the students just completed a unit on number lines, integers, and rational numbers.…

The Van Hiele Levels of Geometric Reasoning describes how students learn geometry. It was a theory worked on by Pierre Van Hiele and his wife, Dina Van Hiele-Geldof. They were Dutch researchers and teachers. They came up with this theory at the University of Utrecht in the year 1957. The Van Hiele’s did multiple research experiments and it took years for them to complete this thesis. Shortly after the thesis was complete, Dina passed away (Šafránková, 2012, p. 72). These levels have five…

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…