# Free Foundations Of Geometry Essays

chronological order -399 pythagoreans discover irrational numbers -240 Eratosthenes determines circumference of earth -230 Archimedes determines fromulas for the area of a secton of a parabola formulas for the area of a section of a parabola -200 Appollonius studies conic sections -200 Euclid writes Elements -100 Hipparchus develops the trig tables 825 Al-Khowarizmi uses Zero 1525 Rudolff introduces the radical sign 1535 Tartaglia solves cubic equations 1545 Square roots of negative numbers 1557...

Eratosthenes Eratosthenes Eratosthenes was born in Cyrene which is now in Libya in North Africa. His teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of Chios who had studied under Zeno, the founder of the Stoic school of philosophy. Eratosthenes also studied under the poet and scholar Callimachus who had also been born in Cyrene. Eratosthenes then spent some years studying in Athens. The library at Alexandria was planned by Ptolemy I Soter and the project came to fru...

History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the scienc...

History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasingly as the scienc...

Beowulf7 Bernard Bolzano (1784-1848) Bernard Bolzano was a philosopher and mathematician whose contributions were not truly recognized until long after his death. He is especially important in the fields of logic geometry and the theory or real numbers. Bernardus Placidus Johann Nepomuk Bolzano was born in Prague, Bohemia, (which is now part of the Czech Republic), on October 5, 1781 as the fourth child out of twelve children. His mother was a German-speaking native of Prague, his father a deale...

Descartes vs hume Exploring the Epistemologys of Rene Descartes and David Hume Beginning in the 17th century, traditional ideas were being questioned by the new beginnings of science. Although many of the accomplishments during this scientific revolution were in astronomy and mechanics, very important advances along the whole borders of knowledge were also taking place. The revival of skepticism, brought about by these new concepts, had many philosophers seeking answers to questions such as: ...

hubble THE JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY OF CANADA JOURNAL DE LA SOCIT ROYALE D ASTRONOMIE DU CANADA Vol. 83, No.6 December 1989 Whole No. 621 EDWIN HUBBLE 1889-1953 By Allan Sandage The Observatories of the Carnegie Institution, Pasadena, California, U.S.A. (Received September 22, 1989) Hubble\'s role. This year marks the centennial of the birth of Edwin Hubble. There can be no doubt that future historians, writing about the scientific advances of this age will describe the 20th c...

leonhard Euler Leonhard Euler\'s father was Paul Euler. Paul Euler had studied theology at the University of Basel and had attended Jacob Bernoulli\'s lectures there. In fact Paul Euler and Johann Bernoulli had both lived in Jacob Bernoulli\'s house while undergraduates at Basel. Paul Euler became a Protestant minister and married Margaret Brucker, the daughter of another Protestant minister. Their son Leonhard Euler was born in Basel, but the family moved to Riehen when he was one year old and ...

leonhard Euler Leonhard Euler\'s father was Paul Euler. Paul Euler had studied theology at the University of Basel and had attended Jacob Bernoulli\'s lectures there. In fact Paul Euler and Johann Bernoulli had both lived in Jacob Bernoulli\'s house while undergraduates at Basel. Paul Euler became a Protestant minister and married Margaret Brucker, the daughter of another Protestant minister. Their son Leonhard Euler was born in Basel, but the family moved to Riehen when he was one year old and ...

PANTHEON Once an ordinary building in Rome originally built in 27 BC by the statesman Agrippa, now a wonder of the modern world. After two fires and 145 years, the emperor Hadrian built the dome and round hall, which the Pantheon is known for today. Around 128 AD, the Pantheon was finished, disregarding some minor alterations made in the early third century. The Pantheon stands elite, possessing appearance, size, and architecture of unparalleled equality. Lined with Corinthian columns, the porch...

pascals life Magnetischer Verein and its journal were conceived, and the atlas of geomagnetism was published. From 1850 onwards Gauss\'s work was that of nearly all practical nature. He disputed over a modified Foucalt pendulum in 1854, and was also able to attend the opening of the new railway link between Hanover and Gottingen, but this outing proved to be his last. The health of Carl Gauss deteriorated slowly and he died in his sleep early in the morning of February 23, 1855. Carl Gauss\'s in...

Pasteur PASTEUR, Louis (1822-95). The French chemist Louis Pasteur devoted his life to solving practical problems of industry, agriculture, and medicine. His discoveries have saved countless lives and created new wealth for the world. Among his discoveries are the pasteurization process and ways of preventing silkworm diseases, anthrax, chicken cholera, and rabies. Pasteur sought no profits from his discoveries, and he supported his family on his professor\'s salary or on a modest government all...

Music and Math Music is the harmonization of opposites, the unification of disparate things, and the conciliation of warring elements...Music is the basis of agreement among things in nature and of the best government in the universe. As a rule it assumes the guise of harmony in the universe, of lawful government in a state, and of a sensible way of life in the home. It brings together and unites. - The Pythagoreans. Every school student will recognize his name as the originator of that theore...

pythagorean Pythagorean Philosophy and its influence on Musical Instrumentation and Composition Music is the harmonization of opposites, the unification of disparate things, and the conciliation of warring elements... Music is the basis of agreement among things in nature and of the best government in the universe. As a rule it assumes the guise of harmony in the universe, of lawful government in a state, and of a sensible way of life in the home. It brings together and unites. - The Pythagore...

Anaxamander With his discoveries, Anaxamander of Miletus attempted to bring the realm of the unreal to the world where common man could conceive it. As successor and pupil of Thales of Miletus, Anaxamander worked on the fields of geometry, natural science, and astrology. The culmination of his life attempted to define the indefinite or undetermined. He was the first to discover and apply the theory of the unlimited. For a philosopher of this time period, he had many radical ideas. Anaxamander be...

Cartesian Doubt In his first meditation, Descartes sets out with amazing clarity and persistence to clear himself of every false idea that he has acquired previous to this, and determine what he truly knows. To rid him of these rotten apples he has developed a method of doubt with a goal to construct a set of beliefs on foundations which are indubitable. On these foundations, Descartes applies three levels of skepticism, which in turn, generate three levels at which our thoughts may be deceive...

descartes3 The Move from Doubt to Certainty; A Look at the Theories of Descartes and Locke Descartes is interested in the certainty of his existence and the existence of other people and things. Descartes beliefs vary from those of Socrates. Descartes argues that knowledge is acquired through awareness and experience. Using this approach, Descartes moves through doubt to certainty of his existence. He asks himself various questions about the certainty of his existence and solves them through cl...

History of Physics Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and ...

Life and Times of Sir Isaac Newton Newton, Sir Isaac (1642-1727), mathematician and physicist, one of the foremost scientific intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where he went to school, he began to attend Cambridge University in 1661; he was elected a Fellow of Trinity College in 1667, and a Lucasian mathematics professor in 1669. He stayed at the university, lecturing most of the years, until 1696. During these Cambridge years, in which Newton was at the...

Newtons Life as we know it At his birth on Christmas day, 1642, in Woolsthorpe, Lincolnshire, England, Newton was so tiny and frail that he was not expected to live. Yet despite his boyhood frailty, he lived to the age of 85. As a delicate child, he was a loner, interested more in reading, solving mathematical problems, and mechanical tinkering than in taking part in the usual boyish activities. Until the time Newton entered Cambridge University in 1661, there was little inkling as to his mental...

Pasteur PASTEUR, Louis (1822-95). The French chemist Louis Pasteur devoted his life to solving practical problems of industry, agriculture, and medicine. His discoveries have saved countless lives and created new wealth for the world. Among his discoveries are the pasteurization process and ways of preventing silkworm diseases, anthrax, chicken cholera, and rabies. *BR* Pasteur sought no profits from his discoveries, and he supported his family on his professor\'s salary or on a modest governmen...

The Golden Ages Greece Rome and China The Golden Ages : Greece, Rome, and China The Golden Ages of Greece, Rome, and China were periods when certain cultures reached many achievements in certain fields. These fields could include drama, poetry, sculpture, philosophy, architecture, math or science. Their achievements in education, technology, and government have greatly influenced modern society. The artistic and literal legacies of these periods continue to instruct and inspire people today (Be...

Sir Issac Newton Sir Isaac Newton (1642 - 1727) Isaac Newton was born in Lincolnshire, on December 25, 1642. He was educated at Trinity College in Cambridge, and resided there from 1661 to 1696 during which time he produced the majority of his work in mathematics. During this time New ton developed several theories, such as his fundamental principles of gravitation, his theory on optics otherwise known as the Lectiones Opticae, and his work with the Binomial Theorem. This is only a few theories...

Bayes Theory REVIEW OF RELEVANT LITERATURE AND RESEARCH I first became interested in Bayes\' Theorem after reading Blind Man\'s Bluff, Sontag (1998). The book made mention how Bayes\' Theorem was used to locate a missing thermonuclear bomb in Spain in 1966. Furthermore, it was again used by the military to locate the missing submarine USS Scorpion (Sontag, pg. 97) that had imploded when it sank several years later. I was intrigued by the nature of the theory and wanted to know more about it. Wh...

Carl Gauss Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world. Carl Gauss was born Johann Carl Friedric...

Eratosthenes Eratosthenes Eratosthenes was born in Cyrene which is now in Libya in North Africa. His teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of Chios who had studied under Zeno, the founder of the Stoic school of philosophy. Eratosthenes also studied under the poet and scholar Callimachus who had also been born in Cyrene. Eratosthenes then spent some years studying in Athens. The library at Alexandria was planned by Ptolemy I Soter and the project came to fr...

Womens Contributions to Mathematics Abstract Women in the world of mathematics is a subject that people rarely hear about. The only time people do is if its a female math teacher. But what many do not know is that women have made extremely important contributions to the world of mathematics. Women have been documented to be involved in mathematics, since as early as the fifth century A.D. Women such as Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy Noether, Ruth Moufang and Sun-Yung Alice...

History of Math History Of Math History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be re...

Descartes and Locke The Move from Doubt to Certainty; A Look at the Theories of Descartes and Locke Descartes is interested in the certainty of his existence and the existence of other people and things. Descartes beliefs vary from those of Socrates. Descartes argues that knowledge is acquired through awareness and experience. Using this approach, Descartes moves through doubt to certainty of his existence. He asks himself various questions about the certainty of his existence and solves them ...

Doudt In his first meditation, Descartes sets out with amazing clarity and persistence to clear himself of every false idea that he has acquired previous to this, and determine what he truly knows. To rid him of these rotten apples he has developed a method of doubt with a goal to construct a set of beliefs on foundations which are indubitable. On these foundations, Descartes applies three levels of skepticism, which in turn, generate three levels at which our thoughts may be deceived by erro...

The Move from Doubt to Certainty A Look The Move from Doubt to Certainty; A Look at the Theories of Descartes and Locke Descartes is interested in the certainty of his existence and the existence of other people and things. Descartes beliefs vary from those of Socrates. Descartes argues that knowledge is acquired through awareness and experience. Using this approach, Descartes moves through doubt to certainty of his existence. He asks himself various questions about the certainty of his existe...

What was Plato8217s worldview and how do humans exist within it Plato lived in a very exciting time in history. The post-Socratic era had merits for exploration totally new to him. The idea that science and reason could be applied to more than static issues such as logistics and geometry, allowing the thinking men of the time the opportunity to examine the world around them with structured thought. He, like his mentor, was not happy with what science gave as answers to life. Though it gave a st...

Covalent BOnding and Molecular Geometr Covalent Bonding and Molecular Geometry Objective The objective of this exercise is to help in understanding the geometric relationships of atoms in simple molecules and the relationship of hybridization to the geometry present. Discussion In the last 30 years, data obtained from spectrometric measurements, X?ray and electron diffraction studies, and other experiments have yielded precise information about bond distances, angles, and energies. In many case...

Isaac Newton Sir Isaac Newton was born on December 25, 1642 in Woolsthorpe, near Grantham in Lincolnshire, England. Newton is clearly the most influential scientist who ever lived. His accomplishments in mathematics, optics, and physics laid the foundations for modern science and revolutionized the world. Newton studied at Cambridge and was professor there from 1669 to 1701, succeeding his teacher Isaac Barrow as Lucasian professor of mathematics. His most important discoveries were made during...

discourse on method by descartes DISCOURSE ON THE METHOD OF RIGHTLY CONDUCTING THE REASON, AND SEEKING TRUTH IN THE SCIENCES PREFATORY NOTE BY THE AUTHOR If this Discourse appear too long to be read at once, it may be divided into six Parts: and, in the first, will be found various considerations touching the Sciences; in the second, the principal rules of the Method which the Author has discovered, in the third, certain of the rules of Morals which he has deduced from this Method; in the fourth...

Existence of God Rene Descartes (1596-1650) Rene Descartes (1596-1650) is one of the most important Western philosophers of the past few centuries. During his lifetime, Descartes was just as famous as an original physicist, physiologist and mathematician. But it is as a highly original philosopher that he is most frequently read today. He attempted to restart philosophy in a fresh direction. For example, his philosophy refused to accept the Aristotelian and Scholastic traditions that had dominat...

Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world.Carl Gauss was born Johann Carl Friedrich Gauss, on t...

History Of Math History of Math Mathematics, study of relationships among quantities, magnitudes, and properties and of logical operations by which unknown quantities, magnitudes, and properties may be deduced. In the past, mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or of the generalization of these two fields, as in algebra. Toward the middle of the 19th century, however, mathematics came to be regarded increasing...

Imperialism Pablo Picasso was probably the most influential modern painterof the 20th century. Born in Spain, he lived in France much of his life painting, sculpting, making ceramics, and doing graphic artwork. His style was quite avant-garde and unique, and he changed it many times during his career. Picasso was one of the artists to lay the foundations for Cubism, a style that used angular, cube-like structures to depict people and things. He loved to shock the public with his strange, powerfu...

Christianity in a Postmodern World Christian Belief in a Postmodern World: The Full Wealth of Conviction Others have tried to do what Diogenes Allen, Professor of Philosophy at Princeton Theological Seminary, does in his book but none with his breadth or effectiveness. That is, others have attempted to exploit for theism\'s benefit the hard times now befalling the modern world\'s emphasis on scientific reasoning and pure rationality, which for quite a while had placed Christianity (and religious...

The Move from Doubt to Certainty; A Look at the Theories of Descartes and Locke Descartes is interested in the certainty of his existence and the existence of other people and things. Descartes\' beliefs vary from those of Socrates. Descartes argues that knowledge is acquired through awareness and experience. Using this approach, Descartes moves through doubt to certainty of his existence. He asks himself various questions about the certainty of his existence and solves them through clear though...

Descartes First Meditation Descartes\' First Meditation Descartes believes that knowledge comes from within the mind, a single indisputable fact to build on that can be gained through individual reflection. While seeking true knowledge, Descartes writes his Six Meditations. In these meditations, Descartes tries to develop a strong foundation, which all knowledge can be built upon. In the First Meditation, Descartes begins developing this foundation through the method of doubt. He casts doubt upo...

Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world. Carl Gauss was born Johann Carl Friedrich Gauss, on ...

Issac Newton Sir Isaac Newton Sir Isaac Newton was born in Lincolnshire, near Grantham, on December 25, 1642. His education took place at Trinity College, in Cambridge where he lived from 1661 to 1696. Here is where he studied physics and astronomy, and created calculus. Newton became interested in mathematics in the autumn of 1663 when he tried to read an astrology book but could not understand it because he had little knowledge of trigonometry and geometry. What got his mind going was when he ...

The Application Of Fractal Geometry To Ecology The Application of Fractal Geometry to Ecology Principles of Ecology 310L Victoria Levin 7 December 1995 Abstract New insights into the natural world are just a few of the results from the use of fractal geometry. Examples from population and landscape ecology are used to illustrate the usefulness of fractal geometry to the field of ecology. The advent of the computer age played an important role in the development and acceptance of fractal geometry...

History Of Physics Early PhysicsPhysics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had a knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics.Thales of Miletus (636BC. - 546BC.)Thales is ...

Earthquake Loads & Earthquake Resistant Design of Buildings Earthquake Loads Earthquake Resistant Design of Buildings 1. 1 2. Summary 2 3. Earthquake Design - A Conceptual Review 2 4. Earthquake Resisting Performance Expectations 3 5. Key Material Parameters for Effective Earthquake Resistant Design 3 6. Earthquake Design Level Ground Motion 4 6.1. Elastic Response Spectra 4 6.2. Relative Seismicity 5 6.3. Soil amplification 6 7. Derivation of Ductile Design Response Spectra 7 8. Analysis and Ea...

HISTORY OF PHYSICS Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and ...

Early Civilization Mesopotamia and Ancient Egypt Mesopotamia and Ancient Egypt are both cradles of civilization. Both contributed greatly to human development through their achievements, failures, peoples, scientific accomplishments, philosophies, religions, and contributions. Mesopotamia is a rich flat plain created by deposits from the Tigris and Euphrates rivers. At the southern end of this plain developed the first recognizable civilization, in the area known as Sumer. In 3000 B.C. Sumer con...

Imperialism Pablo Picasso was probably the most influential modern painterof the 20th century. Born in Spain, he lived in France much of his life painting, sculpting, making ceramics, and doing graphic artwork. His style was quite avant-garde and unique, and he changed it many times during his career. Picasso was one of the artists to lay the foundations for Cubism, a style that used angular, cube-like structures to depict people and things. He loved to shock the public with his strange, powerfu...