Wait a second!
More handpicked essays just for you.
More handpicked essays just for you.
The importance of Euclidian geometry
Euclid's contributions to geometry
Euclid's contributions to geometry
Don’t take our word for it - see why 10 million students trust us with their essay needs.
Recommended: The importance of Euclidian geometry
From the beginning of time there have been many anomalies in humanity. With the advancement of techniques, tools, and knowledge, our understanding of the world aspires to clarify our curiosities. The most beneficial to factors throughout our history would include our knowledge of numbers. Numbers hold great possibilities and bring forth answers to the most complex systems of life. Our mathematics is incorporated into basic aspects of our daily lives, allowing us to unlock our potentials and give keys to uncover the hidden secrets in the universe.
There are many applications to mathematics such as triangulating polygons. Triangulation is a surveying technique in which a region is divided into a series of triangular elements based on a line of known length so that accurate measurements of distances and directions may be made by the application of trigonometry. (Company, 2009) Since its discovery, triangulation has lent the world many beneficial advantages.
Polygons exist as multi-sided shapes. These shapes can be subdivided into many non-overlapping triangles. These triangles connect corners to corners, creating diagonals that section it off. These sections are called convex hulls. The many uses of algorithms allow anyone to calculate these triangular hulls. The mathematics behind triangulating polygons was originated in Alexandria by the man, Euclides. Euclides was a Greek mathematician who was highly revered as the “Father of Geometry.”
Euclides possessed a mysterious personal life, because his life was not documented and often confused with others. He taught many children mathematics during the reign of Ptolemy. His father and grandfather were thought to be Greek, but this is not certain considering the confusion between him...
... middle of paper ...
...'s Formula. Retrieved from ENRICH: http://nrich.maths.org/1384
Company, H. M. (2009). Triangulation. Retrieved from TheFreeDictionary by Farlex: http://www.thefreedictionary.com/triangulation
csunplugged. (2010, October 30). Santa's Dirty Socks (Divide and Conquer Algorithms). Retrieved from Youtube: http://www.youtube.com/watch?v=wVPCT1VjySA
lecture, P. T. (1993). Triangulations and Arrangements. McGill University.
Math Open Reference. (2009). Euclid. Retrieved from Math Open Reference: http://www.mathopenref.com/euclid.html
Suksak, P. S. (2010, November 30). Catalan Numbers Presentation 2. Retrieved from Slide Share: http://www.slideshare.net/PaiSukanyaSuksak/catalan-number-presentation2
Teter, M. (2000, March 15). Sonar a way of seeing sound. Retrieved from Cornell Center for Material Research: http://www.ccmr.cornell.edu/education/ask/index.html?quid=260
What is trigonometry? Well trigonometry, according to the Oxford Dictionary ‘the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.’ Here is a simplified definition of my own: Trigonometry is a division of mathematics involving the study of the relativity of angles and sides of triangles. The word trigonometry originated from the Latin word: trigonometria.
Study of Geometry gives students the tools to logical reasoning and deductive thinking to solve abstract equations. Geometry is an important mathematical concept to grasp as we use it in our life every day. Geometry is the study of shape- and there are shapes all around us. Examples of geometry in everyday life are- in sport, nature, games and architecture. The game Jenga involves geometry as it is important to keep the stack of tiles at a 90 degrees angle, otherwise the stack of tiles will fall over. Architects use geometry everyday- it is essential when designing buildings- shape, angles and area and perimeter are some of the geometry concepts architects
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
I assume the point of teaching this skill was to help apply it to real life situations, but sadly, triangles simply aren't the same thing as world
Abstract geometry is deductive reasoning and axiomatic organization. Deductive reasoning deals with statements that have already been accepted. An example of deductive reasoning is proving the sum of the measures of the angles of a quadrilateral is 360 degrees. Another example of deductive reasoning is proving the sum of the angles of a trigon is equal to 180 degrees. From this we get, any quadrilateral can be divided into two trigons. Axioms, which are also called postulates, are statements that can be proved true by using deductive reasoning.
On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry. M.C. Escher used his knowledge of geometry, and mathematics in general, to create his tessellations, some of his most well admired works.
Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in the early twentieth century. Although it appears simple, the Sierpinski Triangle is actually a complex and intriguing fractal. Fractals have been studied since 1905, when the Mandelbrot Set was discovered, and since then have been used in many ways. One important aspect of fractals is their self-similarity, the idea that if you zoom in on any patch of the fractal, you will see an image that is similar to the original. Because of this, fractals are infinitely detailed and have many interesting properties. Fractals also have a practical use: they can be used to measure the length of coastlines. Because fractals are broken into infinitely small, similar pieces, they prove useful when measuring the length of irregularly shaped objects. Fractals also make beautiful art.
Tubbs, Robert. What is a Number? Mathematical Concepts and Their Origins. Baltimore, Md: The Johns Hopkins
Euclid is one of the most influential and best read mathematician of all time. His prize work, Elements, was the textbook of elementary geometry and logic up to the early twentieth century. For his work in the field, he is known as the father of geometry and is considered one of the great Greek mathematicians. Very little is known about the life of Euclid. Both the dates and places of his birth and death are unknown. It is believed that he was educated at Plato's academy in Athens and stayed there until he was invited by Ptolemy I to teach at his newly founded university in Alexandria. There, Euclid founded the school of mathematics and remained there for the rest of his life. As a teacher, he was probably one of the mentors to Archimedes. Personally, all accounts of Euclid describe him as a kind, fair, patient man who quickly helped and praised the works of others. However, this did not stop him from engaging in sarcasm. One story relates that one of his students complained that he had no use for any of the mathematics he was learning. Euclid quickly called to his slave to give the boy a coin because "he must make gain out of what he learns." Another story relates that Ptolemy asked the mathematician if there was some easier way to learn geometry than by learning all the theorems. Euclid replied, "There is no royal road to geometry" and sent the king to study. Euclid's fame comes from his writings, especially his masterpiece Elements. This 13 volume work is a compilation of Greek mathematics and geometry. It is unknown how much if any of the work included in Elements is Euclid's original work; many of the theorems found can be traced to previous thinkers including Euxodus, Thales, Hippocrates and Pythagoras. However, the format of Elements belongs to him alone. Each volume lists a number of definitions and postulates followed by theorems, which are followed by proofs using those definitions and postulates. Every statement was proven, no matter how obvious. Euclid chose his postulates carefully, picking only the most basic and self-evident propositions as the basis of his work. Before, rival schools each had a different set of postulates, some of which were very questionable. This format helped standardize Greek mathematics. As for the subject matter, it ran the gamut of ancient thought. The
Addition, especially of small numbers, is a process that can be done over many repetitions. Sometimes, it produces interesting patterns. One such pattern is in Pascal’s Triangle, where each row can be constructed by adding the numbers on the row above. This particular pattern is significant in that, among other things, it shows a representation of the coefficients of a binomial expansion to a particular power.
It is constructed by taking an equilateral triangle, and after many iterations of adding smaller triangles to increasingly smaller sizes, resulting in a "snowflake" pattern, sometimes called the von Koch snowflake. The theoretical result of multiple iterations is the creation of a finite area with an infinite perimeter, meaning the dimension is incomprehensible. Fractals, before that word was coined, were simply considered above mathematical understanding, until experiments were done in the 1970's by Benoit Mandelbrot, the "father of fractal geometry". Mandelbrot developed a method that treated fractals as a part of standard Euclidean geometry, with the dimension of a fractal being an exponent. Fractals pack an infinity into "a grain of sand".
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know whether they are true or not. The first one is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. This is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The next type of information is that Euclid was born at Megara. But this is not the same Euclid that authors thought. In fact, there was a Euclid of Megara, who was a philosopher who lived approximately 100 years before Euclid of Alexandria.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
Abstractions from nature are one the important element in mathematics. Mathematics is a universal subject that has connections to many different areas including nature. [IMAGE] [IMAGE] Bibliography: 1. http://users.powernet.co.uk/bearsoft/Maths.html 2. http://weblife.bangor.ac.uk/cyfrif/eng/resources/spirals.htm 3.
Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclicalphenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.