...back, read and enjoy this project. (1) History of European Mathematics During the centuries in which the Chinese, Indian and Islamic mathematicians had been in the ascendancy, Europe had fallen into the Dark Ages, in which science, mathematics and almost all intellectual endeavour stagnated. Scholastic scholars only valued studies in the humanities, such as philosophy and literature, and spent much of their energies quarrelling over subtle subjects in metaphysics and theology. From the 4th to 12th Centuries, European knowledge and study of arithmetic, geometry, astronomy and music was limited mainly to Boethius’ translations of some of the works of ancient Greek masters such as Nicomachus and Euclid. All trade and calculation was made using the clumsy and inefficient Roman numeral system, and with an abacus based on Greek and Roman models. By the 12th Century, though, Europe, and particularly Italy, was beginning to trade with the East, and Eastern knowledge gradually began to spread to the West. Robert of Chester translated Al-Khwarizmi's important book on algebra into Latin in the 12th Century, and the complete text of Euclid's “Elements” was translated in various...
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...and Zero Have you ever wondered about the origins of prime numbers or the numeral zero? The ancient philosophers and mathematicians from such early civilizations in Egypt, Greece, Babylon, and India did. Their efforts have provided the basic fundamentals for mathematics that are used today. Prime Numbers A prime number is “any integer other than a 0 or + 1 that is not divisible without a remainder by any other integers except + 1 and + the integer itself (Merriam-Webster, 1996). These numbers were first studied in-depth by ancient Greek mathematicians who looked to numbers for their mystical and numerological properties, seeking perfect and amicable numbers. (O’Connor & Robertson, 2009) In 300 BC, Greek mathematician, Euclid of Alexandria proved and documented in his Book IX of the Elements that prime numbers were infinite. He started with what he believed to be a comprehensive list of prime numbers, created a new number, N, by multiplying all of the prime numbers together and adding 1. This resulted in a number not on his list and not divisible by any of his prime numbers. N therefore had to be either prime itself or be a composite number that was a product of at least two other prime numbers not on his list. In 1747, a mathematician named of Euler demonstrated that all even numbers were perfect numbers. However, one hundred years later in 200 BC, Eratosthenes of Cyrene, a famous Greek mathematician known for his studies regarding prime numbers as well as for...
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...9:55 – 11:15 Math III – 1 1:00 - 2:20 Math III - 2 I. Objective: * Compare values of the different denominations of coins and bills through P1000 Value: Gratitude II. Subject Matter: Comparing values of the different denominations of coins and bills through P1000 References: BEC PELC – I A. 4. 3. Materials: Philippine money, play money, flashcards, charts III. Procedure: A. Preliminary Activities: 1. Drill: Write greater than, less than or equal to the following a. P50.00 __ P100.00 b. 2 ten peso bills __ P30.50 2. Review: Write the money values in symbols. a. nine hundred fifty pesos and fifty centavos b. seven hundred seventy-eight pesos and twenty five centavos 3. Motivation: Did you also receive Christmas gifts from your godparent? What did you say after you receive such gift? B. Developmental Activities: 1. Presentation: a. Last Christmas Edmar’s godparents gave him P500 P100P100 P50 . Allyssa’s godparents gave her P1 000 Edmar received P750 while Alyssareceived P1000. Let us compare the amounts. Use >, < or =. Which is more, 750 or 1000? Which is less? 2. Guided Practice Compare the following. Write >, < or = 1. P 955 ____ P 595 2. P 1 000 ____ P 100 3. P 99 ____ P59 4. P 678...
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...project to roman_numeral_soln (this is the BlueJ project you will be submitting). You can rename the project by renaming the folder from roman_numerals_buggy to roman_numeral_soln after extracting the zip file. The purpose of this code is to convert Arabic numerals into Roman numerals. Make an instance of RomanNumerals and invoke the method toRoman(int n). Enter a number in the Arabic notation and it will convert it to a Roman numeral. For example “17” will be converted to “XVII”.You will notice a test suite that we provide with the code. Run the test suite by right-clicking on RomanNumeralsTest and choosing Test All as shown in Figure 6.3 of the book. Alternatively, you can click on the Run Tests button as shown in Figure 6.2 of the book, if you have enabled the ‘Show unit testing tools’ preference. To enable it, go to Tools > Preferences > Miscellaneous, and select ‘Show unit testing tools’. You will notice a total of eight tests of which two fail. Your first task in this assignment is to study the given code, identify why the two tests fail, and correct the code. On studying the code further, you will notice a few more bugs/limitations in the provided code (i.e. the provided code will not give the correct Roman numeral conversion for some numbers). Identify them and correct the code to handle those situations also. Also, the test suite itself has a bug, i.e. it will flag an error in a particular case even when the code gives the right answer. Identify that situation...
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...ENG 205 Ms. Tabor Assignment for 1.19.16: “Organizing Your Information” Pablo Millan 1. Advantages of Outlining * Helps you organize your ideas; * Presents your material in a logical form; * Shows the relationships among ideas in your writing; * Constructs an ordered overview of your speech; * Groups ideas into main points. * Improves creativity 2. Basic Roman numeral Outline It is the most common type of outline. It emphasizes topics and subtopics by means of Roman numerals, letters, and Arabic numbers. Basic format for the Roman numeral outline: I. Major section A. First-level subsection 1. Second-level subjection a. Third-level subsection 1) Fourth-level subsection It is not common that your object need four subdivisions, but diving it this way allows to have more details about the topic if it was necessary. You should stop when there is no way to make another division into at least two items. The first-level heading or the major section is going to be the main topic of the subject. Once you have decided which are going to be the primary sections, you look for minor divisions with each section. 3. This outline is not ready to insert the information since we are not making the right division of the subject. All information we can appreciate at the second-level subsection possess the same value and they are all integrated in just one group. 4. The Decimal Numbering System...
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...knew that he would succeed him so Phillip II prepared Alexander for a military and political future. He was very well educated by the Greek Philosopher, Aristotle. Aristotle taught Alexander not just the basics but opened his interest to science, medicine and philosophy. After Phillip II was assassinated, Alexander became king of Macedonia at the age of twenty. As stated Alexander was groomed from an early age and was given control of the cavalry at the important battle of Chaeronea. He secured Macedonia’s frontlines, put down the Greek rebellion, then set his eyes on the rest of the world. He began his campaign (entered Asia Minor) with 37,000 men of which 5,000 were cavalry and had his first confrontation and victory against the Persian Empire at a battle at the Granicus River which almost cost him his life. By the following spring, 334/335, the western half of Asia Minor was controlled by Alexander. At the Battle of Issus, the Persian troops outnumbered Alexander’s and his men. However, the numerical advantage the Persian’s had was cancelled because the battle was on a narrow field and resulted in another success for Macedonia. Alexander then turned south, and by the winter of 332 BCE, Alexander dominated Egypt, Palestine and Syria. He took the title of pharaoh of Egypt and founded the first cities named after him. (Alexandria) as the Greek administrative capital of Egypt which remains one of Egypt’s and Mediterranean’s most important cities. He then moved into ancient...
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...today. Art can reveal an extensive amount of information regarding the culture and background of the society, which it was created. To examine artwork in relation to the culture of the each society, the artwork must be analyzed in variety of ways. The artwork that will be examined will be the Parthenon from the Classical Greece period, The Scraper from the Hellenistic Period, and the tombs from the Etruscan Civilization. The Parthenon is a great example of the Doric style of architecture from the Classical Greek period, as shown in Figure 1. The Parthenon was built by Perikles, the great Athenian leader. It was built on the highest point and was the largest building on the mainland. (Benton & DiYanni, 2008, pp. 66-121) The Parthenon was made of marble and was built in 447-432 BCE. Parthenon is a temple dedicated to the Goddess Athena. ("The Parthenon") An image of Athena made out of gold and ivory stands in the Parthenon. (Benton & DiYanni, 2008, pp. 66-121) The Greeks believed she helped them defeat the Persian Empire during the Persian Wars. The Parthenon is known to symbolize wealth and power of the Athenians. Tax money of the people was used to pay for the building. Ironically, the building was used as a state treasury, which held tax money that the Dalian League collected. The society was proud of its culture and political achievements. ("The Parthenon") The society also formed the first Democracy. The society saw themselves rising to the same level as the Gods...
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...Based on the representations shown in Discovering the Global Past, chapter three, the Greek and Egyptian cultures both value strong men, and women who needed their men. However, one difference that the Egyptians and Greeks have in their values is simplicity. The Egyptians favored elaborateness and the Greeks preferred simplicity. Both the Greek and Egyptian cultures value strength in their men. The images of the Greek men show these men in the prime of their abilities. The well muscled bodies depicted in the images show vitality and power that men in their prime have. The image "Theseus and the Amazons" shows strong and militarily powerful men defeating the Amazons. Competition of any kind, athletic or militaristic, was a way for men to prove themselves in Greek society. If a man showed arete he had honor (Burger, 49). Because of the Greek's chase of arete, men had to be strong both physically and intellectually in order to win. When Greek artists depicted men, the only men worthy to make art of were strong men with arete, so looking at the Greek culture, strong men were valued. The Egyptian images two and three show powerful men as well. In image two, showing Nebamum hunting, Nebamum is larger than his wife and servant. He is also closer to the foreground of the image with the other two in the background. Another instance of the man being larger and more forward is with image three. King Ramesses II is much larger than his wife, with Nefertari only coming up to his...
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...respectfully disagree. I don't think fashions truly ever really fade. There is always something “coming back in style.” There is one particular style that never really seemed to go away and is still prominent in 21st century high fashion. Greek style dresses have endured the test of time and have become a bit of a staple of modern fashion. The early Greeks made the peplos style famous, but European influence called it the “Empire Waist”; dresses that were long and loose fitting but gathered under the bust. Today, modern wedding dresses are almost always made with some version of an empire waist, and New York Fashion Week's catwalks are littered with remnants of Greek style. No offense to Mr. Saint-Laurent. A peplos is a full-length Greek garment worn by women before 500 BCE. The cloth was manufactured as a tube of fabric that was folded inside out from the top down, then gathered at the waist and fastened at the shoulders in either a strap or with pins. The top of the tube draped down to the waist giving the appearance of a second piece of material. A similar style that would have been worn by both men and women was a chiton[1]. The chiton was a heavier garment made of wool or linen and was held on with a fibula, which was an ancient Greek brooch.[2] Men's styles of chitons were either knee length, or body length based on the status, age, and profession of the individual, and were often worn with a cloak called a himation. The chiton was the outfit of Aphrodite because of how...
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... Page 1 Mr.Brown Honors World History 14 April 2013 Roman and Greeks Correlations There are many differences between the Greeks and Romans. There are so many similarities between the two because Romans adopted the Greek religion and everything they did in life. One difference between them is the religion even though the Romans adopted it there are differences. Another difference is architecture like the Greeks the Romans also did gods for their architecture, but there are many differences. The last difference would have to be art while the Greeks did body the Romans did nature and power. Even though they were the same almost there are many different correlations. First one thing that was the same with the Greeks and Romans but had different attributes was architecture. One difference between their architecture was the materials. The early classical period of Greece used bronze. bowserguy62 When they started to advance they used white marble and painted it. The Romans also used white marble to make their architecture however they didn’t paint it. Another example is their styles and inspiration. Greeks often did depictions of their gods in heroic nudes and mainly the male figure was idealized. Even though the Romans did do gods they often did nobles or emperors that were naturalistic. Greeks did sculpture in architecture and also did free- standing sculpture just like the Romans did. When it they did free-standing...
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...roamed all over Asia and Europe as a supernatural figure. In presenting and describing the military and personal life of this legendary man, Cantor draws his information from the contemporary writings on the Alexander. He uses the cultural and psychological studies to portray that Alexander was not an ordinary person in the ancient world. The author portrays Alexander the Great as person liked to conquer new empires. In writing this biography, Alexander clearly explains the relationship that existed between Alexander the great and his father, Philip II of Macedon, his bisexuality, and his oedipal involvement with his own mother. In addition, traces the efforts of this great man in attempting to unite the Persian and Greek worlds, west, and east using the famous Greek hero Achilles of the Trojan War as his model. Furthermore, Cantor explores the superstitious nature of Alexander towards the gods of Egypt and Greece. Cantor biography artistically balances between the public life and private life as he...
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...Country Analysis - Greece Bordering the Aegean Sea, Ionian Sea and the Mediterranean Sea in southern Europe,Greece is a country of mostly mountains with ranges extending into the sea as peninsulas or chains of islands. From wet winters, to hot and dry summers, greece is a popular tourist destination. With nearly 4.5 million people in the Athens area, Greece is populated with nearly 10 million people in which a parliamentary democracy exists. 300 people are elected whom form the parliament which conducts the legislative duties of the government.The political party collects approximately 151 seats in the parliamental duties of the administration. The president automatically becomes prime minster and then gets appointed to become cabinet ministers. The actual ‘president’ is elected by the parliament for a five year term. The current ‘chief of state’ is President Karolos Papoulias and the head of government is Prime Minister Antonis Samaras. As you are aware, Greece’s economy isn’t doing too well lately. Greece has a capitalist economy which means it has an economic system based on private ownership of capital. 40 percent of the countries GDP is accounted from a public sector. Tourism provides fifteen percent, in which we will discuss later. Between 2003 and 2007 the economy grew nearly four percent per year. This is partially due to the 2004 Olympic games which also resulted in an increased availability of...
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...poet composed both works. The Greeks attributed both of the epics to the same man, and we have little hard evidence that would make us doubt the ancient authorities, but uncertainty is a constant feature of scholarly work dealing with Homer's era of Greek history. The Greeks hailed him as their greatest poet, as well as their first. Although the Greeks recognized other poets who composed in Greek before Homer, no texts from these earlier poets survived. Perhaps they were lost, or perhaps they were never written down‹Homer himself was probably on the cusp between the tradition of oral poetry and the new invention of written language. Texts of the Iliad and the Odyssey existed from at least the sixth century BC, and probably for a considerable span of time before that. These two great epic poems also had a life in performance: through the centuries, professional artists made their living by reciting Homer, performing the great epics for audiences that often know great parts of the poem by heart. It is impossible to pin down with any certainty when Homer lived. Eratosthenes gives the traditional date of 1184 BC for the end of the Trojan War, the semi-mythical event which forms the basis for the Iliad. The great Greek historian Herodotus put the date at 1250 BC. These dates were arrived at in a very approximate manner; Greek historians usually used genealogy and estimation when trying to find the dates for events in the distant past. But Greek historians were far less certain...
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...heroic values- the strength, skill, and valor of the dominating warrior. Such was the earliest meaning of arête, “excellence” or “virtue”, a term whose meaning changed as values changed during the course of Greek culture. To obtain arête- defined by one Homeric hero as “to fight ever in the forefront and outdo my companions”- and the undying fame that was its reward, men would endure hardship, struggle, and even death. Honor was the just reward for one who demonstrated arête, and the greatest of human injustices was the denial of honor due to a great hero. Homer makes such denial the theme of the Illiad,- the disastrous results of Achilles’s decision to withdraw from battle after he had been denied honor by King Agamemnon. P. 107 In fifth-century Athens, scholars estimate that one out of every four persons was a slave. Some were war captives and others were children of slaves, but most came from outside Greece through slave dealers. No large collections of slaves were used on agricultural estates. Small landowners might own one or more slaves, who worked in the fields alongside their masters. Those who owned many slaves often hired them out to private individuals or to the state, where they worked alongside Athenian citizens and received comparable wages. P. 113 The Greeks were the first to formulate many of the European culture’s fundamental concepts of politics, philosophy, science, and art. How was it that a relatively small number of people could leave such a great legacy...
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...was one of the very important part of the civilization. For all the cultures habitation and finding food is depend on the environments that they placed on and all the cultures are in relation with each other. A Senegalese social scientist Cheikh Anta Diop has a theory about the roots of the civilization. He supports that Ethiopians and the Egyptians played a key role in the processing of civilization by their developments in science, art and religion. These developments were required for the adaptation of the people. The Greeks interiorized the elements of civilization which they inspired from Egyptians, continued to develop them and spread them to the Eurasians. The Greek philosophers and scholars thoughts were shaped by the Egyptians. Their style of architecture was similar with the Egyptians’. They also effected from Egyptians’ literature like fables. One of the French writers, La Fontaine, inspired from a Greek writer, Aesop. Diop also claim that Greeks impressed their gods from Egypt. He proved that with the foreign sources which were mostly written by Egyptians. Apart the theory of Diop, there is a big relation between religion and civilization. People had found supernatural solutions or explanations for natural problems like climate change, volcanic eruptions or darkness and lightness and they also have a supernatural solution for fertility – mother goddess which was a symbol of fertility – which was very important for the people who have...
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