Pythagoras Essays (Examples)

It was then notated that if triangle ABC is a right triangle, with a right angle at C, then c2 = a2 + b2. Earlier, the converse of this theorem appears to have been used. This became proposition number 47 from Book I of Euclid's Elements ("Pythagorean," 2007).
Although this theorem is traditionally associated with Pythagoras, it is actually much older.

More than a millennium before the birth of Pythagoras, four Babylonian tablets were created demonstrating some knowledge of this theorem, circa 1900-1600 B.C.. At the very least, these works represent the knowledge of at least special integers known as Pythagorean triples that satisfy it.

In addition, the hind papyrus, created around 1650 B.C., shows that Egyptians had knowledge of the theorem as well. However, the first proof of this theorem is still credited to Pythagoras, despite the fact that some scholars believe it was independently discovered in several different cultures ("Pythagorean,"…

Socrates and Pythagoras
Pythagoras:

Pythagoras was born in 569 BC in Samos, to Mnesarchus of Tyre and Pythias of Samos. Mnesarchus was a merchant and so Pythagoras had the opportunity to visit many lands as a child traveling with his father. Besides these facts there is very little that is known of the childhood of Pythagoras. There is no doubt that he would have been properly educated and there is evidence to show that Pythagoras was influenced by three philosophers the most important of which was Pherkydes. Another person to influence his life was Thales and it is believed that it was Thales that stoked the interest of mathematics in Pythagoras. The pupil of Thales Anaximander is believed to have contributed many ideas in geometry and cosmology that were to influence the views of Pythagoras. Pythagoras as a young man moved to Egypt and remained there till the Persians invaded Egypt and…

This idea was accepted by most of the philosophical schools of the time, including the Atomists.
Plato took quite a different approach and found that ideas, as noted, and saw idas as existing outside of human consciousness. Plato's doctrine of recollection holds that learning is the remembering of a wisdom that the soul enjoyed prior to its incarnation, another aspect of the idea that there are ideal forms "remembered" by the soul in this world, and this is actually a mythical statement of this view that neither reason nor the intelligible order that it reveals is alien to the human soul. The soul is seen as existing before life here on earth and as remembering the ideals it knew before birth. Protagoras would not have engaged in this sort of argument, jus as he avoided arguments about the existence of the gods as being outside of sensory experience.

3. Plato's ideas…

The twenty-one pieces of the work, minus the Overture, are divided into two acts, 8 pieces in the First Act, and 13 in the Second. 8 to 13 is an example of the Golden Ratio. There are also 49 entrances in The Magic Flute, divided up as 19 in Act I and 30 in Act II. This too is an example of the Golden Ratio. Furthermore, the Overture contains a division between 81 bars and 130, yet another Golden Ratio.
Golden Ratio is thus contained within Golden Ratio, an image of the endless repetition of the primordial forms. Each individual part of the Creation is complete unto itself. One can take apart the Cosmos and find perfect miniature "worlds" that can be put back together to form a coherent whole. According to the Classical canon of art, the human body is built upon the Golden Ratio. By drawing lines through…

Philosophy and Psychology of the Mind and Body
Throughout human history, philosophers, doctors, and most recently, psychologists, have attempted to understand the relationship between the mind and body and how it results in human beings' awareness and perception of reality. At least since the golden age of Greek philosophy, thinkers have been aware of an ostensible distinction between the mind and body, a distinction that nonetheless allows for some intermingling such that physical issues affect the mental state just as mental issues may result in physical symptoms. Thus, if one desires to truly understand how contemporary estern psychologists and philosophers consider the nature of consciousness via the interaction between mind and body, one must trace the history of these concepts starting with the Greek philosophers, moving through the Middle Ages and the Renaissance and on to the eighteenth and nineteenth centuries, when psychology first began to develop as a formal discipline.…

Parmenides is one of Plato's most important dialogues, according to both ancient and modern scholars, and focuses on the critique of the theory of forms, based on the influence of pre-Socratic thinkers such as Pythagoras, Parmenides, and Heraclitus. The theory of Forms is founded on the assumption that a higher, spiritual realm of Forms, or Ideas, exists beyond the world of physical things.
The realm of Forms has a hierarchical order, the highest level being that of the Form of Good. The physical world, as perceived by the senses is in constant flux, therefore making knowledge derived from it variable and restricted. The realm of Forms, however, is only apprehensible by the mind and is eternal and changeless. Each Form is actually a pattern of a certain category of things in the physical world -- things which are only an imperfect copy of the perfect Forms.

Although in the Phaedo dialogue, Socrates…

Joyce's Ulysses
Claude Rawson is best known as a scholar of Jonathan Swift and the eighteenth century, but Rawson's has also used the savage irony of Swift's modest proposal for a series of essays which consider Swift's invocation of cannibalism in light of a longer tradition (in Anglo-Irish relations) of imputing cannibalism literally to the native Irish as a way of demonizing their "savagery" or else to implying a metaphorical cannibalism to describe the British Imperial exploitation of those native Irish. Rawson reapproaches these Swiftian subjects in a more recent essay entitled "Killing the Poor: An Anglo-Irish Theme" which examines what Rawson calls the "velleities of extermination" in a text like Swift's "Modest Proposal" (Rawson, 300). Rawson examines how Swift's ironic solution of what to do with the poor of Ireland (eat them as food) undergoes, in various later iterations by Anglo-Irish writers including Shaw and ilde, transformation into a rhetorically…

He looks at thee methods: histoy (melding infomation about the divese geogaphical oigins of algeba with the poblems themselves), multiple epesentations (using notation, naative, geometic, gaphical, and othe epesentations togethe to build undestanding), and the object concept of function (teaching functions without genealizing about how taits of an individual elate to taits of a goup). The aticle seves to offe some inventive solutions to a common poblem in math education: How to make mateial elevant and compelling to a beadth of students.
Matinez, a.A. (2010). Tiangle sacifice to the gods. 1-11.

The aticle looks at Pythagoas, paticulaly the mythology suounding his life and his most famous discovey, the Pythagoean theoem. It calls into question the histoical evidence on which mathematics teaches base thei teaching of this theoy. The autho points out how vey little is known about Pythagoas and how he has been canonized by the math discipline because his theoy…

Nature Closer to the Ancient than the Renaissance View?
In his book, The Idea of Nature, Collingwood analyzes the principle characteristics of three periods of cosmological thinking in the history of European thought: Greek, Renaissance, and the Modern. By taking such an approach, Collingwood makes it possible for his readers to distinguish the similarities as well as fundamental differences between the modern view of Nature and that of Greek and Renaissance cosmology. But, perhaps Collingwood's work is more valuable because it demonstrates how both Greek and Renaissance schools of thought have made the modern view of nature possible. In other words, the modern view of nature has evolved from both Greek and Renaissance cosmology, with each period laying the foundation for the next to build on. To that extent, an assertion that the modern view of Nature more closely resemblances one period rather than another cannot, strictly speaking, be made…

He died four years before Peurbach's matriculation, leaving the University without an astronomy lecturer. However, his library and instruments were probably accessible to Peurbach.
While it is known that Peurbach travelled throughout Europe between the years 1448 and 1453, there is no record of the precise dates. At the time, he also had an international reputation as an astronomer of note, despite the fact that he had not publications at the time. He did however lecture in Germany, France and Italy.

After lecturing at Bologna and Padua, these universities offered him permanent appointments as lecturer, but Peurbach turned these down. During his travels he also met the leading Italian astronomer of the time, Giovanni Bianchini, in Ferrara. Bianchini also offered Peurbach a post at an Italian university. Peurbach however remained unwilling to be tied to any specific institution of learning and turned down the offer. In 1453, Peurbach returned to Vienna…

One of the most enduring legacies of the Pre-Socratic concern with the source of all sentient life is atomism, advocated by Democritus. The definition of atoms as things "that cannot be cut up or actively divided up and split," seems more like a precursor to modern physics rather than philosophy (80) Sophists such as Critas asked questions, not about the natural world, but the moral and political life of citizens and acted as "independent, often itinerants teachers of wisdom," and above all conveyers of "political skills" that were of vital importance in a free-for-all democracy like ancient Athens, where the ability to "speak well" and persuasively was a vital survival skill (6;96). The Sophists were rivals to Socrates because they claimed that morality was based in convention, and did not exist outside of social institutions like language.

The diversity of the Pre-Socratic philosophers highlights the complexity of what constituted philosophy in…

Pythagorean Triple is a term derived specifically from the theorem that a right triangle displays the equation. This theorem, named aptly the Pythagorean Theorem, states that "in any right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides" (Mack, 2010). How do the two relate? A Pythagorean Triple is simply the term derived for a, b, and c, provided that 1) a, b, and c are positive integers and 2) a, b, and c fulfill the equation. Silverman's Number Theory chapter on "Pythagorean Triples" has highlighted the relevant proof for the equation of the Pythagorean Theorem. What further equations can be used to find subsequent Pythagorean Triples?
The primitive Pythagorean triple begins with set T (3,4,5). Already, set T. fulfills both the requirements 1) and 2) as stated above; that the numbers in the set are positive integers and, with the use of…

Ethnography
There is no such thing as a time machine. Ancient history can only be understood by modern peoples through the cultural documentation that was left behind. ritings from the period of the New Testament exist but they do not provide information into every aspect of everyday life. Consequently, historians and scholars must analyze the documents that are in existence in order to gain a greater understanding into the world's past. One technique that makes it possible for current populations to understand ancient texts is the use of literary ethnography. This procedure is the endeavor to use qualitative means to learn about and to better understand various cultural documentation and ideology which mirror that culture's society. Particularly of importance to ethnography is the ways and means of knowledge acquisition of a culture and also the system of meanings and which dictate that culture, such as language and the roles of…

Goethe and Marlowe, Faust
The Faust myth provides a writer with a chance to explore religious issues through the theme of damnation, while also allowing the writer to identify with the damned protagonist through a shared sense of ambition. This is palpable in both Marlowe's and Goethe's different versions of the Faust legend -- in both cases, it seems like the ambitious "striving" (to use a crucial Goethean word for Faust's essential nature) of the main character is mirrored by the author's ambition to present broad swathes of human and indeed divine experience on stage or into the reader's imagination. A comparison of the endings of these two different handlings of the Faust legend will, I think, illustrate crucial differences between not only Goethe's and Marlowe's differing literary ambitions, but also their different religious or spiritual worldviews.

In reality Marlowe's Faustus seems like Marlowe himself -- someone who is interested in gaining…

" James a.S. McPeek
further blames Jonson for this corruption: "No one can read this dainty song to Celia without feeling that Jonson is indecorous in putting it in the mouth of such a thoroughgoing scoundrel as Volpone."

Shelburne

asserts that the usual view of Jonson's use of the Catullan poem is distorted by an insufficient understanding of Catullus' carmina, which comes from critics' willingness to adhere to a conventional -- yet incorrect and incomplete -- reading of the love poem. hen Jonson created his adaptation of carmina 5, there was only one other complete translation in English of a poem by Catullus. That translation is believed to have been Sir Philip Sidney's rendering of poem 70 in Certain Sonnets, however, it was not published until 1598.

This means that Jonson's knowledge of the poem must have come from the Latin text printed in C. Val. Catulli, Albii, Tibulli, Sex. Aur. Propertii Opera omnia…

" ell's article underlines the thinking behind Raphael's masterpiece. It is not simply an imagined portrait of famous people; rather it is a philosophical treatise, in symbolic form, of what it meant to be a great man, as embodied in these different figures.

Glenn Most, in his 1996 article "The School of Athens and its Pre-text" from Critical Inquiry agrees that the central question of the School of Athens is "How can an artist represent pictorially an intellectual activity like philosophy? In the School of Athens, Raphael chooses to do so by depicting the manifold set of ratiocinative and discursive activities performed on a sunny day in a splendid building by a large number of adult male philosophers… because Raphael's image has embedded itself so deeply in our visual unconscious. It requires an effort of the historical imagination to recognize that this was not an inevitable, or even a likely, way…

Support for the figure being Diogenes rather than Socrates has been found in the fact that he is prone, and alone, which seems to suggest Diogenes' status as an antisocial Cynic -- he also called himself a 'dog.' However, the painting seems to depict in chronological order in the development of ancient philosophy, of the viewer moves his or her gaze from foreground to background and from left to right. This would suggest that the figure is Socrates. The bowl besides the lying figure if it is Socrates could symbolically signify his drinking of hemlock also suggests the death of Christ. Raphael, a Neo-Platonist in his philosophy, thus gave particular importance to Socrates' martyrdom (Bell 1995).
The artwork, as a glorification of the human, is sublimely Renaissance in nature, and typical of the period but it is also unique in the way that it celebrates philosophers and their intellectual arts,…

e can consider 'The School of Athens' as a 'visualization of knowledge.'" in addition to Plato and Aristotle, Euclid and Pythagoras are present among others. Lahanas even suggests that the painting may be a reproduction of Plato's Academy. This concept would emphasize a commitment to learning, as well as an interest in antiquity and classical learning. The architecture depicted is a "modification of Bramante's first design for St. Peter (Lahanas).
The combination of classical scholars, emphasis on learning, and suggestion of St. Peter's draws together all of the relevant characteristics of the Renaissance. First, Raphael most obviously alludes to the Renaissance's interest in antiquity with the identifiable Greek scholars. That two of the most prominent classical philosophers are prominent, suggesting not only their importance, but also the importance of the classical period. In addition, the situation in which the philosophers are located places an emphasis on the importance of learning…

Also, men oppose her for reasons of jealousy, he stresses, not because they really think that she is acting in an anti-Christian manner. Thus while Socrates Scholasticus himself never even entertained any point-of-view remotely considered heretic, including Gnosticism and Manichaeism as well as Arianism, he never condoned violence and was able to see how personal and political biases could fuel hateful actions masking as 'anti-heretical' actions like the murder of a woman preacher. Although he on a few occasions used the term "evil" is in regards to the Arians, and he gave ample attention to the benefits of the creation of the creed of Nicene, praising its ideals, more often than not Socrates Scholasticus used cool and factual language to describe controversies. Sometimes even the Arians who denied the consubstantiality of the Son with the Father and Trinitarian notions of God are given a chance, through excerpts, to 'speak'…

Euclid of Alexandria: 325 .C. ~ 265 .C. (?)
The dates are not exact as little is known about Euclid's life. It is generally believed that he studied under the students of Plato and it is known that he established a school of mathematics and taught at the library in Alexandria. His most well-known work is The Elements, which is a wonderfully organized development of the plane and solid geometry, geometric algebra, theory of proportions, number theory, and the theory of irrational numbers known then. The work is divided into 13 books and contains 465 propositions. eginning in ook I with 5 postulates, 5 common notions, and 23 definitions, Euclid develops the basic properties of plane geometry from the construction of an equilateral triangle in Proposition 1 to his beautiful proof of the Theorem of Pythagoras in Proposition 47 (the book closes with a proof of the converse of the Pythagorean…

Egyptian Hieroglyphics and Other Ancient Symbols on 18th, 19th and 20th Century Surface Pattern Design and Their Influences on Contemporary Design
Hieroglyphics are a system of picture-writing, from the Greek, literally meaning "sacred carvings"; these symbols were used extensively on the walls of Egyptian tombs and temples, as well as columns and in written texts (Cavendish 1970). This paper will provide an analysis of the influence of Egyptian hieroglyphics and other ancient symbols on 18th, 19th and 20th century surface pattern design and their influences on contemporary design, taking account of the impact on design practice of digital techniques today. A discussion of designers from these periods illustrating their work will be followed by suggestions for critical analysis, and an examination of possible philosophical questions to be considered related to a future professional practice. A summary of the research will be provided in the conclusion.

Review and Discussion.

Background and Overview. According…

In sports terms, to which most Americans can relate, it is the idea of passing backward in soccer in order to move forward with the ball. Also, in arguments, it is making a concession to keep the communication going. In labor disputes, it is compromising to find a middle ground. Many times one has to yield, back down, empty oneself before overcoming, feeling straight, filling up.
James Autrey wrote, eal Power: Business Lessons from the Tao Te Ching that covers a prime way that this paradoxical thought of Tao Te Ching can be understood by the modern manager -- as a means of gaining the most valued and elusive prize in business: power.

Autrey responds to the questions, What exactly is power, and where does it come from? Does power automatically come with authority? Does it come from one's superiors, or do people create it for themselves? And why is it…

Beginning with the major arch of the Stanze that frames the entire piece, there recedes a series of concentric circles that focus down to the archway that frames the two central figures. This can be seen as a nearly literal rippling effect of the wisdom of these two great thinkers off into space, and into the mind of the viewer. Working from largest to smallest, we can see that the pattern is ultimately infinite since it ends with the focal point discussed in the previous paragraph. This seems to reflect the philosophy that the more focused a philosophy comes, and the finite the topics, the closer it gets to circling back again into the infinite.
The integration of a dialectic of ideas is achieved through an intricate working of visual lines. The strong diagonals of the heads of the two statues and the heads of the two major figures creates…

The text deals at length and often with a great variety of matters which bear on the human condition, but there are matters which would certainly have no place in a modern treatise on politics"
Therefore, it is rather hard to determine the extent to which Plato used this means of communication, the dialogues, to point out to the actual necessities of the society he lived in and the aspects that needed changes. In particular, the arguments he provides from the realities of the time are provided by Plato to merely support his own line of thought related to the philosophical ideas on happiness and justice.

An aspect that firmly relates to the way in which the "Republic" is constructed and that uses the arguments on the ideal state is related to the role the state may have in providing its citizens (here, the term "citizen" must be understood as "the…

St. Anthony is recognized as the head of the monastic family. His date of birth was in 251 and somewhere in Egypt. His parents died when he was only sixteen years old. He remained to be the guardian of his younger sibling, Dious. Six months after the demise of his parents, he went to the church to hear the word of our lord. 'If you would be perfect, go sell all you have, given to the poor and come follow me.' (Matthew 19:21)
He regarded to this advice as a personal message sent to him God himself. From the fortune his family left behind, he sold 300 acres land that was fertile and the proceeds he gave the poor remaining with a little for taking care of his sister. He left the sister to be taken care of by the community of virgins. This allowed him to be free and…

Music on Vocabulary ompetence, Writing, Reading omprehension and Motivation in English Language Learning in High-School
EFFETIVENESS OF MUSI ON VOABULARY

The Effectiveness of Music on Vocabulary ompetence, Writing, Reading omprehension and Motivation in English Language Learning in High-School

Most English language learners in high schools show poor vocabulary competence. The main reason for this is the limited level of exposure to the language. It is generally understood and practically acknowledged that words form the basic unit of language structure. Therefore lack of sufficient vocabulary constrains students from effectively communicating and freely expressing their ideas.

Vocabulary competence is critical to developing reading comprehension skills. Lack of vocabulary development is detrimental to the development of metacognitive skill that is important in comprehending advanced texts. omprehension is a major component of development of vocabulary, reading to learn. Therefore, reading comprehension it is quite challenging for students lacking adequate knowledge of meaning of words.

In addition, inadequate vocabulary…

master guru/student relationship is nothing new in human history and evolution. In more ancient times, curious folks would search for knowledge and wisdom in this form of relationship at least since the days of Pythagoras, Lao-Tse and numerous others spread throughout the world. More primitive cultures sought the advice of the eccentric medicine man or shaman to gain insight into their worlds. Today's master/student relationship seems to culminate within graduate schools organized by the large and powerful college and university institutions that compose the formal education system. The purpose of this essay is to analyze the PHD movie and contrast this story to my own personal experiences with this subject.
College is an institution. It is a self preserving organization with clear and explicit hierarchies. Entrance into this special group requires certain accreditation. The PHD is this golden ticket to enter this realm and become a guru within academic society.…

Sophocles' Oedipus the King
Look up and/or reflect on the meaning of:

Tragedy: A tragedy is any event which causes great suffering and stress, such as the death of a loved one or a natural disaster. In the context of Greek literature, tragedy was the most popular form of theatre, with storytellers relying on the rhetorical technique of tragic irony to create emotionally resonant tales of lost love and territorial conquest.

Philosophy: The overall study of the human condition, reality, metaphysics, and other pursuits of higher intelligence.

Psychology: The scientific study of the human mind, including cognitive function, perception, attention, emotion and behavior.

Logic: The fundamental application of reasoning to the pursuit of problem solving, a function which only the human mind is known to hold the capacity to perform.

Ethics: The branch of philosophy which postulates certain standards which should be used to guide proper human conduct.

Mathematics: The abstract study of numerical value, spatial relationships,…

lives of Archimedes and Carl Friedrich Gauss, two of the greatest mathematicians of all time, through a point by point comparison of their childhood and education, mathematical contributions and the influence their work has on the science of mathematics.
Childhood and Education

Archimedes (287 BC to 212 BC) lived most of his life in Syracuse, Greece. This son of an astronomer and mathematician was born into a distinguished family and was able to comfortably devote his life to mathematical research.

Carl Friedrich Gauss (1777-1855) was born into a humble German family. His early mathematical promise marked him as a prodigy and eventually earned him admission to university.

Major Mathematical Ideas

The mathematical work of Archimedes centered on the theoretical, particularly geometry. His greatest mathematical contribution involved measuring areas and segments of plane and conic sections.

Gauss's work centered on number theory. Unlike Archimedes, Gauss also used ventured into applied mathematics like astronomy and geodetic research.

Influence…

Ancient Philosophy
Though it is acknowledged that the words and ideas of Socrates have been filtered though the thoughts of those that followed him, namely Plato, as Socrates wrote nothing himself, it is also clear that the interpretation garnered by the ancients has been profoundly felt throughout western culture. It is also clear that the body of work that survives in fragmentation recorded as prior to the Socratic philosophical revolution is a strong basis for that which followed, it can also be described as simpler or at least less complex. The main difference according to the writings of the post Socratic philosophers between Socratic ethics and pre-Socratic ethics are twofold. On the one hand the idea that philosophical questions are not and cannot be seen as finite and on the other the establishment of Socrates as the supreme model of the philosophical life and all its trappings. The impact that these…

Chinese Mathematics
In ancient China, the science of mathematics was subsumed under the larger practice of suan chu, or the "art of calculation." The Chinese are believed to be one of the first civilizations to develop and use the decimal numeral system. Their early mathematical studies have influenced science among neighboring Asian countries and beyond.

This paper examines the history of mathematical knowledge in China. It looks at the early Chinese achievements in the field of mathematics, including the decimal system, calculation of pi, the use of counting aids and the application of mathematical principles to everyday life. It also examines the influence of Indian and later, European mathematical knowledge into Chinese mathematics.

Early China

Unlike the ancient Greeks who prized knowledge for its own sake, much of the scientific studies conducted in ancient China were spurred by practical everyday needs. Because of its geographic location, China was prone to devastating floods, particularly along…

Proof, a NOVA episode aired on PS [...] review the video, with a focus on what the video tells us about how people learn to do mathematics. Compare and contrast this with your own experiences with mathematics, particularly your approach toward learning about new mathematical problems and trying to solve them. "The Proof" is more than just a video about solving a complex mathematical problem. It is a story of determination, setting goals, and finding out that solutions come from many different places and ideas. You have to be open to new ideas when you try to solve anything, whether it is a complex mathematical problem, or a personal problem. The proof is really about keeping an open mind, and looking at all the angles of a problem.
The Proof

The Proof" is an interesting look at one man's obsession with proving (or disproving) a theory (Fermat's Last Theorem), written over…

Skepticism is defined as a school of philosophical thought where a person doubts the beliefs of another person or group. hile one person might believe wholeheartedly a certain political perspective or believe completely the dogma of a religion, a skeptic would have doubts about these beliefs or about the stories related to religion. Not only do they doubt organized religion, they also doubt the validity of socially constructed morals and laws. Sometimes they doubt the world as they witness it because they are unsure of the truth of reality as they perceive it through the senses (Butchvarov 1998). Like many philosophies, skepticism has origins in Ancient Greece. Pyrrho of Elis is credited with founding the philosophy, a branch of which was later named Pyrrhonism in his honor. The philosophy was expanded into countries throughout the known world, up to and including the early modern world. During the Enlightenment, skepticism branched…

Plato and the Platypus
Philosophers in the Enlightenment era would come up with various new means to popularize ideas. Denis Diderot conceived the first encyclopedia in this period, which was an attempt to systematize all world knowledge in an accessible way. But also, in another innovation, Voltaire would offer as a refutation of the optimistic philosophy of Leibniz -- which held that "this is the best of all possible worlds" -- a new form of philosophical argument: the extended comedy (Cathcart and Klein, 17). Voltaire's short book Candide is essentially an extended refutation of Leibniz's view of God (or perhaps any view of God), but it makes its points through satirical humor. In some sense, Thomas Cathcart and Daniel Klein are following in the footsteps of Voltaire by attempting to shed light on philosophical ideas through the medium of humor in their work Plato and a Platypus alk Into A Bar.…

Pythagorean Theorem
Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?

Solving for x, the solution involves plugging in the binomials mentioned in the problem using the Pythagorean theorem. The Pythagorean theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagorean theorem is expressed in the following equation: a2 + b2 = c2

The problem gives information about the other two sides; in…

Map of New orld
They say that the winners of wars write history books. hen it comes to maps of the world prior to the full discovery and conquering of the world, it could be said that the desired winner of the war and/or conquest of the world write the maps. Indeed, the maps of that day are somewhat, if not wildly, inaccurate. They indeed reflect the desires and presumptions that the mapmakers of those days made. hile there were clear and obvious inaccuracies, the mistakes and projections made are very telling and can teach a number of lessons about that day and the people that existed within the same.

In looking at the requested source material as well as a few other sources, it becomes clear that some assumptions were made that were clearly wrong and/or they were extremely well-assuming. Indeed, the travel of Columbus proves that. here he was planning…

Dark Age and the Archaic Age
Having watched the lectures for the prior learning unit on video, I was prepared to enjoy the video lecture presentation for this learning unit. I previously found the presentation of lectures in the video format to be very convenient because I could observe at my own pace, rewind if I missed part of the lecture, have flexibility about when I was viewing the lecture, and not be distracted by the behavior or questions of other students. I acknowledged that there were some negatives to the video-learning environment, such as missing out on the organic and natural question and answers that develop in a live classroom setting, but had decided that missing those was an acceptable trade-off given the other benefits that I was receiving from the video lecture environment. Therefore, I was surprised to find that I did not enjoy the video lectures for this…

If this is indeed the case, Leach is within his rights to appeal for an overturn of his conviction. The Fourth Amendment protects travellers from unwarranted police searches, which appears to be what happened in this case.
The Fourth Amendment then protects the rights of individuals to reasonable expectation of privacy. While Archibald Leach voluntarily yielded his luggage for investigation, the search itself was not conducted in a legal manner if there was neither warrant, reasonable suspicion or probable cause. The case does not mention any of these, based upon which the conclusion can be that Leach has sound grounds for appeal.

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Criminal Law Lawyer ource. (2009). earch Warrant. http://www.criminal-law-lawyer-source.com/terms/search-warrant.html

Farlex, Inc. (2009). Probable Cause. The Free Dictionary. http://legal-dictionary.thefreedictionary.com/Probable+cause 'Lectric Law Library's Lexicon. (2009). "Confession." http://www.lectlaw.com/def/c274.htm

Rice, Beverly. (2009). When can the police stop and frisk you on the street? upreme Court Articles. http://www.legalzoom.com/legal-articles/when-police-frisk-you.html

Walker, Jayme . (1998, Dec 1). Moving and touching stowed…

Jazz dance is an integral part of American history. The various types of jazz dance all come from a fusion of African and European traditions, which is why jazz dance symbolizes American culture itself. According to Tilton's film Jazz Dance, jazz dance first evolved in the Deep South and spread as far as Europe before returning home to America. Jazz dance is not monolithic, and it is important to recognize the differences between types of dancing such as tap and swing in order to understand the contexts in which the dances were or are used. For example, some dances became popular in theater, while others were more comedic. Jazz dance might not seem to have a political or even an economic dimension, but it certainly does. The impact of jazz dance on American society has been felt on almost every dimension including political, economic, and social realms. In particular, jazz…