## Maya Pythagorean Theorem

has been alleged that the Maya long count calendar is based on the idea of a 3-4-5 right angle triangle, and involves extending the Pythagorean Theorem to a power of 3, instead of 2. The start date on their calendar, by the reckoning of modern archaeologists, is August 11 of 3114 BC, thus predating Pythagoras. The expression obtained by raising the Pythagorean Theorem to the power of 3 is as such: , where the dash in indicates the position in the sequence. The given expression describes the relationship

## Math: Old Babylonian Math

the most common proof used to prove the Pythagorean Theorem uses the Babylonian methods of geometric algebra. Text D shows how advanced the Old Babylonian society really was. Having the ability to solve for the dimensions given a diagonal and the area is complicated, and the method to solve for these dimensions uses the Pythagorean Theorem. Text D is just a microcosm of how far the Pythagorean Theorem was taken by the Babylonians. They not only used the theorem in advanced problems, but also began the

## Pythagorean Relationship Essay

Question 3 - Pythagorean Relationship by Justine Chan, Yolanda Shi, Audrey Lam and Chloe Chan Introduction: What is the Pythagorean Theorem? The Pythagorean Theorem is a special theory invented by the mathematician Pythagoras which states a relationship between the three sides of a right-angled triangle, or an angle with one intersecting point of two lines being 90 degrees. The Pythagorean Theorem states that the square of the longest side (mathematically referred to as the “hypotenuse”) is equivalent

## Pythagorean Triple Essay

Introduction A Pythagorean triple is an ordered triplet of positive integers (a,b,c) such that: a^2+b^2=c^2. It is evident that such integers correspond to the sides of a right triangle, a, b being the catheti (legs) and c being the hypotenuse of the triangle. The most well known Pythagorean triple 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

## Short Essay On Pythagoras

Pythagoras essay by Grainne Carey Pythagoras was born in Samos Greece around 570 BC .He is said to be the purest mathematician. He was an Ionian Greek, mathematician and philosopher. He is best known for the Pythagorean theorem. He was the son of Mnesarchus and Pythais. It is said his father Mnesarchus was either a gem-engraver or a wealthy merchant. It was said when his mother was pregnant that she would give birth to a man supremely beautiful, wise and beneficial to humankind. He

## Pythagorean Triangles Research Paper

Angle Triangle and the Pythagorean Triples Written by Nana Ekua Opoku INTRODUCTION It can be said that the Pythagorean Triple was derived by the Greek Philosopher and Mathematician Pythagoras and it is closely associated to the right angled triangle. The Pythagorean triple represents three positive integers namely a,b and c where a^2+b^2=c^2and they can be written as (a,b,c) It can be said that the Pythagorean Triples were derived from Pythagoras’ theorem, a very simple theorem which is widely used

## Euclid: The Alexandrian School Of Mathematics

The famous theorem ‘Pythagoras’ was proved on his first book. On the other hand, he defined divisibility, prime numbers, GCD and also proved several properties of these notations. Euclid came up with the algorithm for finding gcd of two numbers using repeated division

## Leonhard Euler's Polyhedron Formula

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

## Cartesian Coordinates Lab Report

INTRODUCTION: The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate

## Foliation Theory Research Paper

of Riemannian manifold is a geodesic line. In the work (Helgason S., 2001) it is proved a remarkable theorems on the geodesic lines. In the case of a foliated manifold, this question is complicated by the fact that a geodesic line of foliated manifold is not necessary geodesic line of the manifold. We have the following theorem which is a analog of classic theorem of Riemannian geometry. Theorem-1. Let be a smooth complete Riemannian manifold of dimension with a smooth foliation of dimension

## Why Do We Study Math Essay

AlKhwarizmi is one of a famous mathematician person in the world. He was in the sixth century, and Khwarizmi has left many publications in astronomy, geography, science of the most important algebra book and a lot. His book algebra, which consists of two main sections contains the first two algebraic theory, which is dedicated to the theory of algebraic equations and calculations, and to resolve the various issues by this theory, and applied to engineering problems. In addition, he has a lot of theories

## Sun Shadow Problem Solving Reflection

In this unit we learned about trigonometric functions which are related to a triangle’s angle/angles (specifically a right triangle) and are used to find the length of a triangle’s side or the side of an object that involves a right triangle. We learned to use an angle of the triangle of find the hypotenuse, the adjacent side, and the opposite side. The right angle is always across the hypotenuse, which is the longest side of a triangle. The opposite is the side that is across from the angle being

## Golden Ratio In Nature

Golden Ratio in Nature Introduction The Golden ratio is represented with the Greek letter phi ( or ) and has a value of approximately 1.618. The Golden ratio creates a special fascination that has caught the attention of mathematical minds for 2,400 years. The Golden ratio can be found in many areas such as art, architecture and nature, making it a very special value that I have found interest in exploring. Mathematics of the Golden ratio The Golden ratio is represented as a mathematical ratio

## Mathematical Approach To The Rubik's Cube

The Mathematical Approach to the Rubik’s Cube The Mathematical Approach to the Rubik’s Cube How was the Rubik’s Cube formed? One may ask. The Rubik’s cube is one of the most famous applications of a large field of mathematics known as group theory (more specifically permutation group theory), and has several applications in a variety of fields. I chose this topic as I have an interest towards the Rubik’s Cube, and would like to know if there is a mathematical way to solve it. Since, Rubik’s

## Carl Sagan's Pi: The Transcendental Number

Pi: The Transcendental Number The Greek symbol ԉ is used to denote an important mathematical constant. Simply put, it is the ratio of the circumference of a circle to its diameter. This ratio has been found to be constant, no matter what the size of the circle. Pi is an Irrational Number, which means that it can’t be written as a fraction. It is an unending decimal number. The number 2/7, when written in the decimal form is also unending. But after 6 digits, it repeats itself. It is 0.285714285714285714…

## Theories Of Metaphors

In previous chapter I mentioned the meaning, definition and different theories of metaphor that gives fundamental role in the development of mathematical understanding. I start this part by presenting the role of metaphors in the development of mathematical understanding found in literature, and reviewing categorizations and analysis of metaphors done by different researchers. However, many of the researchers who studied metaphors argue that all of our thinking is fundamentally metaphorical. With

## Ancient Egyptian Mathematics

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

## Fibonacci Roulette Betting System Essay

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

## Archimedes Contributions

TION Archimedes was a supreme mathematician of his time period. His contributions in geometry enhanced the subject of mathematics. He invented a extensive selection of machines such as pulleys and the Archimidean screw pumping device. According to the encyclopedia britannica “Archimedes (287 - 212 B.C.) was born at Syracuse of Sicily as a son of the astronomer Pheidias. It is said that Archimedes was a relative of Hieron, the king of Syracuse.” Archimedes as a youngster learnt many things from

## Evariste Galois: Group Theory

Group theory A major branch of modern discovered by mathematician Evariste Galois, group theory is the mathematical language of symmetry. It is the concept that is most associative with Rubik’s cube due to its invariant symmetry and the interdependence of it components. In mathematics, a “group” is a set of elements and a rule to combine those elements which satisfies certain properties. The elements of a group can consist of numbers, symmetries of a shape, or the elements themselves can be the different