Computational geometry Essays

Geometry- Faces, Edges, and Vertices, (Newport News Public Schools, 2015) follows the 4E lesson plan model. The four components of this model include; engage and hook, explain and model, explore and apply, and evaluate. The lesson is designed to meet the Virginia Standards of Learning “2.16 the student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism)” (Virginia Department of Education, 2010). The following

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

Paul Erdős, one of the most famed mathematicians of the 20th century, lived quite a remarkable and unique life. Perhaps second only to Leonhard Euler as the most prolific mathematician of all time, Erdős was born in 1913 to a Jewish family and raised in Budapest, Austria-Hungary. Just days before his birth his two sisters died of scarlet fever. Unfortunately, Paul’s early hardships continued when his father was taken away to a Soviet gulag leaving him with just his mother who had to work full-time

Math Placement Exam Summary For my math placement exam project, I decided to do problems from the Ithaca College math exam. The 25 problems I did were mostly Algebra 1, Algebra 2, and some Geometry. I had a lot of trouble with a lot of the questions, because I either didn’t know how to do them or I haven’t learned the material yet. The other placement exam came from Barton College. This exam had problems in areas such as Algebra 1, Algebra 2, Probability, and Statistics. This exam had a significant

The Fundamental Theorem of algebra doesn’t have anything to do with the start of algebra rather it does have something to do with polynomials. It is the theorem of equation solving. It was first proved by Carl Friedrich Gauss (1800) as such the linear factors and irreducible quadratic polynomials are both the building block of all polynomial. The linear factors is the polynomials of degree 1 .The Fundamental Theorem of Algebra tells us when we have factored a polynomial completely. A polynomial

Pierre de Fermat was born August 17, 1601 in Beaumont-de-Lomagne, France. After pursuing his bachelor in civil law from the University of Toulouse, he spent a great deal of time researching calculus and corresponding with other mathematicians. Fermat was perhaps best known for the “integrity of his commitment to the cause of mathematical truth” [1] and sought to establish himself as a legitimate mathematician aside from his main profession as a lawyer. He was rather political about his work and frequently

affordable for very wealthy people. It is thought that while studying here Euclid developed a love and interest in Mathematics. Euclid is recognised as one of the greatest mathematicians in history and is often referred to as ‘The Father of Geometry’. Geometry is a strand of mathematics with a question of shape and sizes. It was not until the 19th century that any other

Proving De Moivre’s theorem using mathematical induction 000416 - 0010 Luis Blanco Tejada Mathematics Standard Level 2nd of October of 2015 Introduction When I first encountered De Moivre’s theorem I was quite skeptical with my math teacher, as it seemed too easy, difficult to believe blindly. To solve my doubts I will use this exploration as its aim is to proof by induction De Moivre’s theorem for all integers; using mathematical induction. De Moivre was a French mathematician exiled in England

Lesson Plan 2 September 24, 2015 Mathematics Kindergarten 30 Minutes Preliminary Planning Topic/Central Focus: Students will continue learning about 2D shapes with the key focus being on the attributes of triangles in this lesson. They will also learn that triangles can be represented by many real world objects. They will show them triangles can be represented in many different orientations Prior Student Knowledge: The students have been working with shapes and have been assessed on their

The Ancient Greeks laid foundations for the Western civilizations in the fields of math and science. Euclid, a Greek mathematician known as the “Father of Geometry,” is arguably the most prominent mind of the Greco-Roman time, best known for his composition in the area of geometry, the Elements. (Document 5) To this day, Euclid’s work is still taught in schools worldwide. In addition to advancements in math, ancient Greeks also made vast strides in the area of medicine. Hippocrates, a Greek physician

As you probably noticed in the image I included [Fig 1] there are symmetric geometric shapes throughout the vase. Inca designs were always geometrical and conventional seen in various pieces of art. They had repeated squares and cross-hatching rows of triangles, scrolls, parallel lines, and drawings of people and / or animals (Gutierrez). In my image of the vase, you can see rows on triangles on the very bottom of the vase [Fig 1]. It was a common pattern used by the Inca’s along with the use of

Bergess was a beautiful city in Bastug's eyes. Most people wouldn't agree with him but to Bastug, the city was something special. It was so alive. He had never seen anything of the like. Narrow, dirty streets, tall buildings, people bustling around even in the night. He loved that he could disappear into the crowd so easily. He loved that the buildings were so close to each other, that you could jump from one rooftop to the other. Even the nobles didn't have too spacious holdings: since space was

Noah Kokkinos Mrs. Dreyer Roots of Thought Honors 1 March 2016 The Blind Mathematician In the time of the Enlightenment, mathematics was in for a big change in the way it functioned. At this time, mathematics in Europe had the best of the best working together in academies to conjecture and prove theorems and advance mathematics. Being a mathematician in this era meant solving long, grueling problems that would usually plague all but one person who could solve it and free their friends from the

“The highest form of pure thought is in mathematics.” – Plato. One of the first things everyone learns when they are growing up is math. It impacts our lives in many different ways each and every day. Without the brilliant mathematicians who formed the ideas and concepts that we use and teach in this day and age it’s hard to imagine where we would be as a mathematical society today. One of most prominent mathematicians known is Plato. The ancient Greek philosopher, Plato, was born in approximately

Abstract: This paper is a report on collected material relating to the influence of mathematics, particularly geometry, on Native American Indians, as well as their contributions in several related areas within mathematics. Research findings lead to the understanding that Indian contributions are great, and their culture is heavily influenced by geometrical designs which have remained over the centuries. Aside from geometrical contributions, it is noteworthy that American Indians had an affinity