Hyperbolic geometry Essays

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, they will be congruent (Cornell). Finally, in Hyperbolic geometry, two triangles will have the same

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

Some roulette players use a sequenced betting system. The set of numbers in the sequence determines the size of the bet in a system known as the Fibonacci roulette betting system. As you might have noticed, the name is taken from one of the greatest mathematicians of the Middle Ages. That's because this betting system is actually based on his homonymous number sequence—the Fibonacci numbers. A Bit of History Leonardo Fibonacci, also known as Leonardo of Pisa, presented to the world a sequence

Activity 21 emphasizes the different classifications of triangles. Triangles are three-sided polygons classified by the length of each side and the measurement of each angle. An Equilateral triangle has sides that are all the same length. Isosceles triangles have at least two congruent sides. The length of the sides of a Scalene triangle are incongruent. A Right triangle has one ninety-degree angle and two forty-five degree angles to equal one hundred and eighty degrees. An Acute triangle has three

A) 1) 10th Grade Geometry – Right Triangle Trigonometry 2) a. Students will learn how to use trigonometry ratios to find unknown lengths and angles. b. Students will learn how to find angles of elevation and depression in real world scenarios. c. Students will learn how to find the area polygons and triangles using trigonometry ratios. 3) a. CCSS.MATH.CONTENT.HSG.SRT.D.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

In \cite{Romauera92}, Romaguera pointed out that if $X=\mathbb{R}^+$ and $p : X \times X\to \mathbb{R}^+$ defined by $p(x, y) = \max\{x, y\}$ for all $x, y \in X$ then ${CB}^p(X)=\emptyset$ and the approach used in Theorem \ref{THM201} and elsewhere has a disadvantage that the fixed point theorems for self-mappings may not be derived from it, when ${CB}^p(X)=\emptyset$. To overcome from this problem he introduced the concept of mixed multi-valued mappings and obtained a different version of Nadler's

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