Topology
The two main figures of Topology, the spheroid and the torus. Shown together like this, they create the symbol for the sun in ancient times (2, 1).
The field of mathematics encompasses many different sub-fields which have been studied and researched for a very long time. One of the most intriguing divisions of mathematics is topology. Topology, the mathematical study of the properties of objects which are preserved through deformations, twistings, and stretchings (4, 1), is rooted far back in time; so far back that it outdates all recorded history (2, 1). Modern topological mathematics was introduced in the late 19th century by a mathematician named Henri Poincare` (2, 2).
Poincare` Pictures
Henri Poincare` was born in Nancy, France in 1854. He received his education at The Ecole Polytechnique and the Ecole Superieur des Mines in Paris (8, 1). Poincare` then spent from 1879 to 1896 lecturing and teaching an array of fields ranging from physical and mathematical mechanics to celestial mechanics at both the University of Caen and the University of Paris. Although Poincare` was considered a physicist, his greatest accomplishments came in the fields of topology, differential equations, and probability, all mathematical fields (8,1). Poincare`’s greatest exposure to the public came in 1887, when King Oscar of Sweden announced that he would award 2,500 crowns to any man who could prove the stability of the orbital dynamics of our solar system. This was a great problem for the mathematicians of the day, and a very significant problem for every being on our Earth (2, 2). If the stability of the orbits could not be proven, one could not rule out the possibility of Earth being hurtled into space by the influence of the other p...
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...logy and its functions.
Works Cited
Fauvel, John. Möbius and his Band, Oxford University Press, New York, 1993.
Gilmore, Tom. Mathematics of Topology, http://www.tomgilmore.com/z_top.htm, 4 pp., 12/5/99.
Klein, http://history.math.csusb.edu/Mathematicians/Klein.html, 2 pp., 12/9/99.
Möbius Strip, http://www.treasure-troves.com/math/MoebiusStrip.html, 4 pp., 12/9/99.
Paper Strip, http://cut-the-knot.com/do_you_know/paper_strip.html, 5 pp., 12/14/99.
Poincare, http://euler.ciens.ucv.ve/English/mathematics/poincare.html, 2 pp., 12/9/99.
7. Poincare, Henri, http://www.treasure-troves.com/bios/Poincare.html, 1 p, 12/9/99.
8. Poincare, Jules Henri, Microsoft Encarta 1999 ed., Microsoft Inc.
9. Tarot FAQ Version 2, http://lonestar.texas.net/~r3winter/tarotfaq.html, 12/10/99.
Topology, http://www.treasure-troves.com/math/Topology.html, 3 pp., 12/9/99.
shapes its being continuously, where its actions make intuitive sense, and where it can finally
Albert Einstein’s discoveries and theories have had a positively enormous effect on the world. Some of Einstein’s biggest impacting discoveries and theories are the theories of Special and General relativity, the Theory of Relativity, Brownian motion, the discovery of the photon, and Einstein’s creation of the equation E = MC^2. Perhaps Einstein’s most beneficial discovery is his formulation of E = MC^2 which is crucial for space-flight and can help today’s scientist in gathering knowledge about our universe.
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen, Geometry, Houghton Mifflin Company. Boston, ©1988.
Johannes Kepler was a German astronomer and mathematician ho discovered that planetary motion is elliptical. Early in his life, Kepler wanted to prove that the universe obeyed Platonistic mathematical relationships, such as the planetary orbits were circular and at distances from the sun proportional to the Platonic solids (see paragraph below). However, when his friend the astronomer Tycho Brahe died, he gave Kepler his immense collection of astronomical observations. After years of studying these observations, Kepler realized that his previous thought about planetary motion were wrong, and he came up with his three laws of planetary motion. Unfortunately, he did not have a unifying theory for these laws. This had to until Newton formulated his laws of gravity and motion.
Throughout Albert Einstein’s lifetime he accomplished many amazing things that have an effect on people today. For example, in 1905, “often called as Einstein’s “miracle year”, he published four papers in the Annalen der Physik, each of which would alter the course of modern physics” (Michio,Kaku 13). Throughout Einstein’s four books, he “applied the quantum theory to light in order to explain the photoelectric effect, offered the first experimental proof of the existence of atoms, laid out the mathematical theory of special relativity, and proved the first mechanism to explain the energy source of the Sun and other stars”(13). Throughout 1905-1915 Einstein began to realize that his theory for relativity was flawed, because “it made no mention of gravitation or acceleration” (19). “In November of 1915, Einstein finally completed the general theory of reality” (20); “in 1921 he won the Nobel Prize in Physics” (Belanger, Craig. 1).
...is in fact when an individual has this boisterous yearning that they will do anything to fit a mold for stability, and in reality are unstable individuals. This community is not characterized by tradition and standards but is only a clandestine mold underneath it all.
Kepler strongly believed that God created the solar system like a puzzle. If he could somehow unlock the mathematics behind the solar system than everything else would come into place as well. Of course we know t...
Some examples that shows that one is responsible is when they have a job, a companionship, and are financially stable. Establishing connections within the world is important so one can have things they become responsible for. Being able to accomplish something from by one’s word shows their maturity in many scenarios. In my opinion, showing the obligation to acquire something is the most relevant when determining one’s consideration of adulthood. An adult is responsible for their own choices and are aware that their decisions can affect other people around them. The ability to balance out priorities like family, friends, work or school can be difficult but hitting the age of adulthood brings reason into a person. If a person is acknowledged to be responsible in another person’s point of view, it is most likely right to consider them as an adult despite of legal “laws” or accepted
As a student at Cambridge Newton found himself among surroundings which were likely to develop and enhance his powers. In his first semester Newton happened to discover a book on astrology, but cou...
Johannes Kepler was a German astronomer and mathematician who lived between 1671-1630. Kepler was a Copernican and initially believed that planets should follow perfectly circular orbits (“Johan Kepler” 1). During this time period, Ptolemy’s geocentric theory of the solar system was accepted. Ptolemy’s theory stated that Earth is at the center of the universe and stationary; closest to Earth is the Moon, and beyond it, expanding towards the outside, are Mercury, Venus, and the Sun in a straight line, followed by Mars, Jupiter, Saturn, and the “fixed stars”. The Ptolemaic system explained the numerous observed motions of the planets as having small spherical orbits called epicycles (“Astronomy” 2). Kepler is best known for introducing three effectual, applicable and valid laws of planetary motion by using the precise data he had developed from Tycho Brahe, a Danish astronomer, which helped Copernicus’s theory of the solar system gain universal reception (“Johan Kepler” 1). Nevertheless, he had made further effective contributions in the field of astronomy, which are valid to society and were used to change how the universe was perceived.
Osteoporosis is a disease in which the bones become so weak and brittle that even a cough can cause enough stress on the bone that it will cause the bone to facture. The most commonly broken bones are the hip, wrist, and the spine. Although it affects men and women of all races, post-menopausal Caucasian and Asian women are more commonly affected than those of other ethnicities and sexes. In fact, thirty percent of all post-menopausal women in the US and Europe will be diagnosed with Osteoporosis and at least 40 percent of those will suffer from a fracture in their lifetime.
While the idea of the word utopia is universal, the actual stories that derive from that idea can be very different in nature. The outcome, or even the basis of the story, relies completely upon the authors, or readers view of a prefect society. This is how progress is made, through ideas and thoughts of revolutionary writers in stories we have come to call "utopian."
Many scientists today revere Newton’s intellect because of his theory of gravity. Although this inevitably leads to many Whiggish accounts, the evidence from history gives a more nuanced view of his discoveries. In particular, Newton’s obsession of the occult and theology, the previous works from his predecessors, and the correspondences between his peers demonstrate that modern society overrated Newton’s ingenuity.
Becoming an adult, also known as young adulthood, is a very crucial stage in one’s life. This is the climax of physical and health processes. This is the point in life when we make plans of our futures. It is the time when we think of what life will be like as an adult and make plans for the future. Most importantly, it is when we lay the starting point for developmental changes that we will undergo throughout our lives. An adult is a person who is fully grown or developed. Some people believe that you become an adult when you are 18 years old, other believe you are an adult when you can legally buy and consume alcohol, that is, at age 21 in the United States. Others believe that you are an adult when you are supporting yourself
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.