Topology
Topology is a modern branch of geometry. It has been called qualitative geometry because instead of thinking about the traditional characteristics of an object (like angles, length, etc.), topologists study features that can’t be altered by stretching, twisting or shrinking the object. After any alteration all points in the object that were connected must still be connected and all points separated by a hole must remain separated. Topology also attempts to explain objects that cannot exist in three dimensions using mathematical equations, since it is nearly impossible to imagine such objects within our frame of reference. The dimension of an object can be thought of in two ways: intrinsic and extrinsic. The perception of a “creature” occupying, say a line, is one-dimensional, since he can only move in one dimension. However, we draw a line on a plane, so extrinsically it is two-dimensional (1). So how do objects occupying the same dimension differ topologically? A doughnut shaped object, called a torus, and a sphere are topologically different. Both of these objects are extrinsically two-dimensional, since we only deal with the surfaces of the object. There is no “inside.” The reason for the topological difference is the hole in the middle of the torus. No permitted alterations (stretching, twisting, shrinking) can be made to the sphere that will transform into a torus.
Topology emerged out of Euler’s work on graph theory in the early 1700’s. Leonhard Euler was born on April 15, 1707 in Switzerland. His father was a minister and wanted his son to follow in his footsteps. He sent his son to the University of Basel in 1720, when Leonhard was only 14. It was here that his interest and natural capabilities in mathematics really began to show. After completing his studies and showing very promising mathematical talent, Euler moved to St. Petersburg, Russia to teach mathematics, at the age of only 19. He remained in Russia for several years (4). And it was here that he made contributions to mathematics that would later be seen as the first steps towards topology. Graph theory studies how points are connected without giving any regard to the distance between them or the actual shape of the line connecting them.
According to Roland Shearer (1992) the release of non-Euclidean geometries at the end of the 19th Century copied the announcement of art movements occurring at that time, which included Cubism, Constructivism, Orphism, De Stijl, Futurism, Suprematism and Kinetic art. Most of the artists who were involved in these beginnings of Modern art were directly working with the new ideas from non-Euclidean geometry or were at least exposed to it – artists such as Picasso, Braque, Malevich, Mondrian and Duchamp. To explain human-created geometries (Euclidean, non-Euclidean), it is a representation of human-made objects and technology (Shearer
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.
Although Wells Fargo has maneuvered the recent crisis very responsibly and prudent, it is lumped together with other Wall Street firms and their failure during the crisis. Its’ reputation, as the reputation of any firm on Wall Street, has suffered. The trust in Wall Street firms is destroyed It is believed that the economic crisis was triggered by failures in leadership; we are in a so-called leadership crisis, meaning that the majority of the American public doesn’t have trust in their leaders anymore, and neither do employees trust their managers. This leadership crisis influences the productivity of banks, as can be seen at the falling stock value of Wells Fargo. Therefore, to guarantee enduring productivity, Wells Fargo has to adjust some managerial aspects because only a strong leadership provides a stable future and avoid another crisis.
Leonhard Euler was born in Basel, Switzerland as the first born child of Paul Euler and Marguerite Brucker on April 15, 1707. Euler’s formal education started in Basel where he was sent to live with his maternal grandmother on his father’s orders. Euler's father wanted his son to follow him in working for the church and sent him to the University of Basel to prepare him in becoming a pastor. He entered the University in 1720 to gain general knowledge before moving on to more advanced studies. Euler’s pastime was used for studying theology, Greek, and Hebrew in order to become a pastor like his father. During that time at the age of thirteen Euler started gaining his masters in Philosophy at the University of Basel, and in 1723 he achieved his master degree. On his weekends, Euler was learning from Bernoulli in several subjects because Bernoulli noticed that Euler was very intelligent in all types of mathematics and it also helped that Euler’s father was a friend of the Bernoulli Family, at the time Johann Bernoulli was Europe’s best mathematician. Bernoulli would later become one of ...
Escher’s work has significance far past its aesthetic value. As an untrained mathematician, he explored some of the most sophisticated constructs in topology and geometry before they were properly understood. His work is unconventional, mind-boggling, and inspiring.
Bernard Bolzano (1781-1848), presently a logician and mathematician of international repute, worked from 1805-1819 as a theological professor at the Prague University. This post he received immediately after he ended his mathematics and theology studies. In this period he had already published his first scientific study Betrachtungen über einige Gegenstände der Elementargeometrie (A reflection on some elementary geometry questions), which was his final dissertation study. In the study Lebensbeschreibung des Dr. B. Bolzano (Biography of Dr. B. Bolzano), he remembers, that it was not easy to dec...
Forgiveness is a gift given to someone who does not necessarily deserve it. It is not an instant decision given without thoughts and considerations. Rather, it is a process that is separated into different stages. These stages can happen so quickly that sometimes people don’t even realize that forgiveness is a process. Many times I have found myself in situations where it is difficult to forgive. For myself, this is when someone is not resentful for their actions. Although difficult, I believe that forgiveness is the only outlet for me to overcome anxiety and
True peace walks hand in hand with justice. Peace is not simply the fragile exhaustion that arises in the aftermath of conflict or the absence of war, relationships broken, when lives have been torn apart, homes demolished and infrastructures destroyed. Rather, the God-given peace that He desires for us is built on justice, where everyone and everything on earth is in a working relationship with each other and can obtain their God-given
Happiness as we have the peacefulness, it is a pleasure without rely on external things. It is called the peaceful of mind.
Euclid, otherwise known as “The Father of Geometry”, is who I shall be talking about in this paper. Place of birth? Place of death? Living conditions; child life, family backgrounds, etc? Educational background? What are his most significant contributions to the mathematical field? What is the relevance of those contributions to mathematics today? One interesting fact? Additional biographical information? Destiny Kirby is the only participant that’s writing this paper. My methods include; mostly online research and if I must, I will go to the library and check out a book about this mister Euclid. My results from researching will hopefully be useful information that I can use to complete
For Muslims peace is not a single dimensional or specific idea. Peace is to be at rest with one's own wants and desires and to have peace with the world around them. There is a mutual relationship between this inner peace and the peace with the wider world. Muslim’s believe that you cannot be at peace with yourself until you are also at peace with others. It will also not be possible to live at peace with others until there is a sense of peace with yourself.
Born in the Netherlands, Daniel Bernoulli was one of the most well-known Bernoulli mathematicians. He contributed plenty to mathematics and advanced it, ahead of its time. His father, Johann, made him study medicine at first, as there was little money in mathematics, but eventually, Johann gave in and tutored Daniel in mathematics. Johann treated his son’s desire to lea...
...notion that their quest is a spiritual one" (Goldstein 61). Once we reach the ideal inner peace is when we are truly able to understand the band of friendship that surrounds us. If we are able to maintain this philosophy, no trouble can exist to deteriorate our well-being. We will be able to enjoy life more and discover what our fears are hiding.
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.
Sir Isaac Newton contributed his whole life to the field of science . He invented calculus and provided a clear understanding of optics. But his most significant work had to do with forces, and specifically with the development of a universal law of gravity