Non-Euclidean geometry Essays

Mathematics is a discipline whose basic ingredients are numbers, shapes, and algebraic relationships. Logical reasoning is used to study the properties of these objects and develop connections between them. The results can be used to understand and analyze a vast array of phenomena arising in all of the sciences, engineering and everyday life. For this reason, mathematics is often called the "language of science.” We support mathematics achievement for all learners by providing guidance and technical

The painting done by Jim Dine called Dexter’s Four Robes and the painting by James Lechay called Sky, Sea and Samos are two paintings that are vastly different, but both exhibit similar and different Elements and Principles of Design. I will analysis both paintings and compare as well as contrast the similarities and differences of each painting. I will than explain my opinion on which painting I believed is more visually appealing and what I liked and disliked about each painting. The Elements

different forms of geometry. Euclidean geometry is probably considered the most understood and well-known form of geometry and is taught widespread among school systems today. However, many non-Euclidean geometries including Spherical, Hyperbolic, and Fractal geometry also play an important role in the world of mathematics as well. As if four forms of geometry were not enough, there is also another branch of geometry that plays a big role in real world mathematics application: Taxicab geometry. In my opinion

The twelfth century translators that went through Spain, Sicily and many other places opened up opportunities for science and math scholars of the time. Without those translators, many major works including Ptolemy’s Almagest, Euclid’s Elements of Geometry, and Avicenna’s The Canon of Medicine would not have been translated and the knowledge of those works would not have been shared for many years. The translation movement is truly one of the main causes that allowed the Scientific Revolution to

This was a major contribution to our modern society as the Pythagorean Theorem is still in use today in mathematics, and is one of the major aspects of Euclidean geometry. Finally, Euclid was a contributor modern understanding of mathematics, specifically geometry. According to the University of New Mexico’s NonEuclid page: “Euclidean geometry was named after Euclid, a Greek mathematician who lived in 300 BC. His book, called "The Elements", is a collection of axioms, theorems and proofs about squares

1. Make a protractor. To do this, use a compass to draw the outline of a half circle on a firm poster board. 2. Cut the new half circle out. 3. Using a pencil and a protractor, label the degrees from 0 to as far as the half circle goes. 4. Cut out a small half circle on the straight edge of the new protractor, this will be the spot where the nose goes. 5. Next, put a colored ( does not matter what color) tack at 0 degrees. This creates a focus point to ensure the person is not accidentally looking

The endolymph in the semi-circular canals moves at the opposite direction to the rotation of the body. The three axes the semi-circular canals can detect angular rotation are the anterior vertical, the posterior vertical and the horizontal planes. When angular rotation occurs in any of these planes, the endolymph in the semi-circular canals moves the opposite way to the body movement, causing the cupula to be moved and therefore the hair cells in the semi-circular canals will also be pushed in the

In Mrs. Myers Honors Math class we started an assignment called The Stained Glass Art Project. We started off by watching a video on artistic choice that talked about color choices, lines, forms, shapes, textures, value, and space. After that, we were all given the same equations and were told to make points out of them. We chose 0, 2, 4, and 6 for the x-axis and we kept them the same for all the eleven equations. Before we plotted the points we had to figure out where our origin and scale factor

In Euclidean triangles, all of the interior angles add up to equal 180° however in Hyperbolic triangles, the interior angles add up to equal less than 180° (Cornell). This is due to the fact that all of the lines are curved (Quora). Continuing, in Euclidean triangles, if two triangles are similar, then they only have to have equivalent angles and not necessarily congruent sides. In Hyperbolic geometry, if two or more triangles are considered similar,

Introduction Leonhard Euler is one of the great mathematicians, who made many remarkable contributions to mathematics. I got to know him when I was learning natural logarithm in math class, which is one of his achievements. He discovered many theorems including polyhedron formula, which states that the number of any polyhedron together with the number of vertices is two more than the number of edges (Kirk, 2007). This formula is widely used in mathematical practice and in real life as well. As polyhedron

Pythagoras Pythagoras is a famously known controversial ancient greek philosopher. Pythagoras is known as the first pure mathematician. Though much information about pythagoras mathematical achievements is not known, because unlike other greek mathematicians, pythagoras had no book or writings. The information known about pythagoras today, was recorded a few centuries after his death. Pythagoras is the son of Mnesarchus, he was born on a greek island in 570 BC. Pythagoras was known to be married

René Descartes created Cartesian coordinates in order to study geometry algebraically. This form of math involves a plane with a horizontal axis and a vertical axis, named X and Y. As in geometry, both axes, as well as the plane, go on into infinity. Along the axes, points are numbered so that with only two numbers (for example -5, 7) one can know exactly where on the chart to look. This is very useful in computer programming because a computer screen is set up similarly to the Cartesian coordinate

for AP calculus that 's why some schools offer other math alternatives to help. The author also explains that students are required to take the basic math courses that will lead them up to Ap calculus. For example, they need to learn algebra and geometry to be able to do

Leonhard Euler, a pioneering Swiss mathematician and physicist, was very successful in his life due to his discoveries in infinitesimal calculus and the graph theory. Preeminent mathematician of the eighteenth century, Leonhard Euler, has been believed to be one of the greatest mathematicians to ever live. Euler has been given recognition for introducing much of the modern mathematical terminology and notation, mostly for mathematical analysis, such as the notion of a mathematical function. His

1. There is a need for studentsto understand and be able to construct geometric figures using a compass and straightedge. By Hayley McMillon 2. ~Summary~There is a need for students to understand and be able to construct geometric figures using astraightedge and compass. I chose to defend this argument, because I believe that studentsshould be able to understand and make constructions using a compass, straightedge, andpaper. Although, drawing programs are great resources, there is nothing better than

Mathematics, Philosophy and Theology: Pascal’s Braid Throughout history, there have been many great thinkers. They have sprawled among many disciplines, from philosophy to physics. Nevertheless, some of these have made important contributions to many fields at the same time. One of these cases is that of Blaise Pascal, who was deeply influential in mathematics, philosophy and theology. In a sense, one could say that these three disciplines were intertwined in his work. By studying the loftier aspects

Abstract: This paper is a report about the ancient Egyptians mathematics. The report discusses the unique counting system and notation of the ancient Egyptians, and their hieroglyphics. One of the unique aspects of the mathematics is the usage of “base fractions”. The arithmetic of the Egyptians is also discussed, and how it compares to our current methods of arithmetic. Finally, the geometrical ideas possessed by the Egyptians are discussed, as well as how they used those ideas. Introduction

is 3,4,5. As early as in the 8th grade I started feeling that knowing at least a few commonly used Pythagorean triples allows solving various geometry problems with a bigger ease. For example, it helps you spot right triangles and solve for the third side in a triangle. This proved to be a valuable skill when dealing with comparatively primitive geometry problems in elementary school. In this exploration I will investigate two ways how a Pythagorean triple can be generated. First, the Euclid’s

culture used Geometry? Well, geometry was used in every single culture, but sometimes geometry was use differently. For example, Ancient Babylonians used geometry 's calculations to track Jupiter in the night sky, and the ancient Egyptians used geometry to help them build their pyramids the right way. Those are just two examples, geometry is used very differently around the world. There wasn 't just one person who invented geometry because every culture had someone who discovered geometry. All the

Ancient Greece was a collection of many different city-states. Greece was broken up because of the geography. Greece was a mountainous area. It was hard for Greeks to build up an empire because all of its city-states were separated by mountains. Although the Greeks were naturally separated they were able to make a great impact on the modern world and customs. Their interest in mathematics, athletics, architecture and art is something that is still shaping cultures today. Mathematics was a very