Magical Practices in the Works of Homer - Literature Essay Samples

Homeric Epic has become a staple of the modern evaluation of the ancient Greco-Roman world. It is among the great literary works of history, having withstood the tests of time and remaining so widely popular. Whether we believe Homer was an individual, a group, or an evolution of oral tradition, it cannot be argued that any assessment of ancient Greek culture that does not include Homers works is incomplete. They reflect not only the culture of the time period, but also the specific viewpoints of those who lived during that time. In terms of magical practices, in the works of Homer it seems that magic is used as a device to portray the belief that Gods control the mortal world in terms of physical attributes as well as power, yet when it comes to nonphysical aspects of the world, the Gods leave control in the hands of those who dwell in it. Magic is used as a means of depicting what mortals can control when it comes to the physical world, war, strength, and power, the Gods deci de what outcomes will occur and how they come to be humans do not practice magic pertaining to such areas. But when magic is practiced, it relates to nonphysical areas of the mortal world, showing that mortals have control of this part of the world they live in. By illustrating this idea, magic is an invaluable element in Homers works, as it makes the duality of these spheres of control apparent.However, before one can evaluate magical practices in a literary work, history, or any other paradigm, it is essential to establish some criteria to differentiate magical practices from similar actions or ideas. For the purposes of analyzing magical practices in the works of Homer, the criteria presented by Sir James Frazer in his essentialist approach (also known as the etic perspective) seem to be well suited to distinguishing magic from things such as religion or science. Frazer purports other ideas in the essentialist approach, such as taking an outsiders perspective of cultural pra ctices, as well as the relation between magic, religion and science. For the purposes of this analysis, those ideas will be set aside, and only Frazers ideas regarding what indicates magic will be used. Frazer claims that magic is coercive in nature, meaning that the practitioner controls the forces involved in magic. He also claims that magical forces are impersonal that there are no personal characteristics or attributes associated with the forces controlled in magic. Compare this to religion, for example, which is supplicative (the practitioner asks for the forces involved to perform something, rather than forcing or controlling them to do it) and personal (the forces have names and personal characteristics, rather than being anonymous).Specifically in the Iliad and the Odyssey, there are cases that show the difference between magic and religion or other ideas. For example, Chryses prays to Apollo after his daughter is taken by the Achaeans, and Apollo responds by unleashin g a plague upon the Achaeans armies (Iliad, book 1). This is not magic, since the practitioner (Chryses) is acting supplicatively by praying to Apollo, who may not answer, as opposed to acting coercively. He also is summoning a personal force (Apollo) rather than an impersonal one. Another example is Machaon, one of the healers (along with his brother Podalirius) who uses scientific methods to heal wounds, such as surgery or poison removal (Iliad, book 11). The difference between science and magic, according to Frazer, is that science is correct, while magic is not. Yet another instance of non-magical practices is disguise, used repeatedly by Odysseus in the Odyssey. Toward the end of the story he infiltrates his own palace disguised as a beggar (Odyssey, book 17). Though disguise is an impersonal force, the practitioner is not wielding a force coercively; he is simply using his own faculties to disguise himself.Having established the difference between magic and other forces, we can search the Iliad for examples of human magical practice. The only two characters that can even be considered something close to magical practitioners are Machaon and Calchas. Machaon, as has already been explained, does not practice magic so much as use scientific methods to heal the wounded. Calchas is a prophet of the Achaeans who is proficient in reading bird signs (auspicy) and revealing the will of the Gods (Iliad, book 1). However, auspicy is a form of divination, which at best is arguably a form of magic. It focuses on time, communication, reflection, and intervention basically terms that reveal that it is focused on time and the gods, meaning that it puts little power in the hands of the practitioner or humans at all. Additionally, auspicy in specific is meant to reveal the will of the Gods. As such, it furthers the idea presented in the Iliad that Gods are in control of the physical world, since the humans are limited to simply trying to divine their will in the outcome of the war. In that sense, there is an utter lack of human magical practice in the Iliad, and those characters closely resembling magical practitioners are simply tools furthering the idea that Gods control physical aspects of the mortal world.The fact that there is a lack of magical practice in the Iliad indicates that whatever the focal point of the story may be, it involves the Gods control over that given area. It is simple to see that this focal point is strength and power. The Iliad is a story centered on the importance of raw strength and power. The opening lines of the story invoke the muses to sing of Achilles rage, thereby making the spotlight of the story one mans wrath and showing that the story centers on physical power (Iliad, book 1). If that does not make it obvious enough that the story centers on physical strength, the fact that the story is about a war should make it apparent that physical power is important in this work. After all, the story is named the Iliad, indicating that it is the story of the war of Ilium, or Troy. Additionally, lengthy descriptions of combat and death are pervasive throughout the poem. Yet another telltale sign of the focus on strength is that the epic piece in this poem is Achilles shield, representative of close combat (Iliad, book 18). Close combat is, of course, a symbol of strength and raw, physical power. The final sign that the Iliad is a story based around strength is that the victor in the end is Achilles, the strongest of all the warriors. All of these examples prove beyond a shadow of a doubt that the Iliad is focused on the importance of strength.Keeping in mind that strength is the underlying motif of the Iliad, we can assume that Homer intends to show that there is little human control over physical aspects of the world (mainly strength and power, and additionally life and death). This is strongly supported by the severe lack of magic practiced by humans in the Iliad, especiall y when contrasted with the Odyssey. Not only is there no magic practiced by humans, all of the power exhibited over life, death, war, and strength seems to be that of the Gods. They (mainly Zeus, Hera, and Athena) are constantly shifting the tides of battle, such as Poseidons empowerment of the Achaeans (Iliad, book 13), and Hera distracting Zeus to turn the tides of battle in favor of the Achaeans (Iliad, book 14). Another example is Apollos plague being unleashed on the Achaeans (Iliad, book 1) or his role in the death of Patroclus (Iliad, book 16). Additionally, it should be noted that the strongest mortals, and indeed the strongest one of all, Achilles, are all somehow descendants of the Gods.All of these point out not only that strength is the focus of the Iliad, but that the Gods are the force that controls that strength. The lack of human influence in this sphere is marked by the lack of magical practice done pertaining to these physical areas, and the immense activity t he Gods engage in relating to physical aspects of the world they change the tides of battle, affect life and death, and decide the fates of the warriors (e.g. Achilles fate to die by Paris arrow to his heel, Hectors fate to die by Achilles sword, etc). Perhaps the example most directly exemplifying this message is that Homer writes of how Apollo and Poseidon will destroy the walls erected by the Achaeans in the years following the war (Iliad, book 12). This shows exactly the point that the Gods are in control of the physical aspects of the mortal world creation, destruction, life, death, strength, and power.The Odyssey, on the other hand, is a story focusing on an opposing quality that of cunning. It is filled with disguise, trickery, and clever plans, rather than the combat and feats of strength that are omnipresent in the Iliad. The poem is rife with characters in disguise, such as Athena appearing to Telemachus as Mentes (Odyssey, book 1) or Odysseus dressing as a beggar t o avoid recognition (Odyssey, book 17). Cunning often prevails over strength, such as Odysseus clever tricks defeating the Cyclops Polyphemus superior strength (Odyssey, book 9). Additionally, the epic piece in this poem is Odysseus bow, representative of ranged combat (Odyssey, book 21). Close combat, at the time, represented more cowardly forms of combat, which of course can be related to cunning and trickery. And just as the strongest man is the victor in the Iliad, the Odysseys victor is Odysseus, the most cunning man in the story. All of these signs signify that cunning and more cerebral issues are the focus of the Odyssey.We can connect the focus on cunning in the Odyssey to the constant appearance of human and mortal magic. In contrast to the Iliad and its lack of magic in relation to the physical dominion, the Odyssey is full of magic, directly in relation to the mental, nonphysical dominion. For example, the Sirens song lures sailors to their death by tempting them t o approach the rock on which the deadly temptresses live (Odyssey, book 12). This is a perfect example of magic being performed by those within the mortal world, and it is magic that affects the mind, instilling great temptation in the men. Another example is in the land of the lotus-eaters, where the men fall asleep against their will by eating the lotus flowers (Odyssey, book 9), yet another example of magic that indeed affects the mind. Odysseus and his crew travel to the land of the dead by performing certain magical rites (Odyssey, book 11), once again using magic for nonphysical means, in this case to figure out how to make their journey lead them home. One of the most famous female practitioners of magic, Circe, is found in the Odyssey, and she uses magic to transform men into animals, and Odysseus himself uses a substance, moly, to avoid transformation (Odyssey, book 10). This type of magic, though it seems physical in nature, affects the being of these men, and in that sense is a mental force. However, not all of the magic is found in the distant, exotic lands of Odysseus voyage. On Telemachus initial journey in the poem, he is in Menelaus court discussing his father and Helen gives the characters a magical drug to wash away their sadness, named nepenthe (Odyssey, book 4). This is yet another case of magic affecting the mind in the Odyssey.All of these examples point out two things first, that the Odyssey is focused on cunning and the mind, and second, that the magical practice found throughout the poem are all related to this same area. It is undeniable that these two are linked, especially since the few situations in which strength prevails in the Odyssey are somehow connected back to the gods. For example, when the souls of the suitors go to the underworld after Odysseus defeats them, the ghosts of Odysseus heroic comrades all make reference to how the Gods have fated Odysseus victory (Odyssey, book 24). Additionally, when Odysseus figh ts the suitors kin, it is said in the poem that the Gods have fated Odysseus victory (Odyssey, book 24). Anytime that strength prevails, it is referred to somehow as part of the Gods plan, and even Poseidons superior strength prevailing in sending Odysseus all over the seas can be thought of in this same sense.Therefore it can be said that the Odyssey contains a great deal of magic practice, which contributes to its focus on the importance of cunning and the mind. As such, it shows that humans and the mortal world itself are in control of issues of the mind. This is in direct contrast with the Iliad, which focuses a great deal on strength and physical aspects of the world; as a result its utter lack of magical practices represents the idea that humans do not have control of the physical world and that it is under the powers of the Gods. The rift between the Iliad and Odyssey shows the belief that the physical world is the dominion of the Gods and that the mental world is under t he control of mortals. Magical practices are key in distinguishing this important message in the works of Homer, since their presence helps indicate what was believed to be under the control of mortals themselves. Through analysis of magic, we are able to recognize that this was a belief of that time period, and that it is a clear theme in Homeric Epic.

How to Format PHP Text

So youve gone through the PHP  tutorials  or are new to PHP in general, and you can make some nifty things in PHP, but they all look like plain text. How do you jazz them up? Formatting PHP text isnt done with PHP; its done with HTML. You can do this in two ways. You can add HTML inside the PHP code or you can add the PHP code inside the HTML. Either way, the file must be saved as a .php or another file type that is allowed to execute PHP on your server. Changing PHP Text Color Using HTML Inside PHP For example, to change the PHP text color to red. Hello World!; ? In this case, the hex color number #ff0000 sets the PHP text that follows it to red. The number could be replaced by other  hex color numbers for other colors. Notice the HTML code is located inside the echo.   Changing PHP Text Color Using  PHP Inside HTML The same effect is achieved with the following code, which uses PHP inside HTML. In the second example, a single line of PHP is inserted inside the HTML. Although here it is only a line to make the text red in this example, it could be inside a fully formatted HTML page to get any look you want. Types of Formatting Available in HTML It is easy to make text formatting changes to PHP text inside HTML. Although many of these formatting commands have been suspended in Cascading Style Sheets, they all still work in HTML. Some of the text formatting commands that can be used include: Bold - Italic -      Underline -  Strike-out -   or  Small -  Font size -   , replace the ? with a number from 1 to 7, 1 being the smallestCenter text -   A complete list of text formatting tags is available.

Essay on William Blake as a Critic of His Time - 838 Words

William Blake as a Critic of His Time Blake took an active role in exposing the corruption taking place in his society. Prime targets of his criticisms were the institutions that remained silent in the faces of injustice. Blake stands agains the institutions that allow human oppression. Three of his poems from Songs of Experience present his views on the matter: The Chimney Sweeper, The Garden of Love, and London. In The Chimney Sweeper, Blake takes his stand against the the calamities brought upon children by those supposed to protect him. Innocence comes to an end for the child when he is exposed to the horrors of sweeping chimneys . His sadness can be felt when he says : They clothed me in the clothes of†¦show more content†¦Man wants to be close to God : I went to the Garden of Love (Blake, 1) as he used to be when little: Where I used to play in the green (Blake, 4) but, finds the church standing in his way: A Chapel was built in the midst (Blake, 3). Blake sees the church as an obstacle between men and God: And the gates of this Chapel were shut/ And Thou shalt not writ over the door (Blake, 5-6). Blake gives emphasis to the word Thou shalt not to indicate once more how oppressive the church is. He attacks the Priests because, instead of offering Gods comfort as they were meant to do, they become like judges or police officers telling men what they can or cannot do:: And Priests in black gowns were walking their rounds/ And binding with briars my joys and desires (Blake, 11- 12). Blake asks society to take a second look at the way the church treats them and to realize that God cannot found among oppressionists. London is yet another one of Blakes poems used to expose the suffering of men. He speaks of the streets and the river as being bound to give a sense of mens predicament: I wander thro each charterd street/Near where the charterd Thames does flow (Blake, 1-2) . 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Dynamic Range

Question: Discuss about the Dynamic Range. Answer: Dynamic range is a way of describing a range of light intensities from darkest shadows to brightest highlighted parts. (Diaz 2014). Dynamic range gives the ratio between maximum and minimum light that can be measured; white and black respectively. It is determined by EV-Exposure Value. In photography, some scenes may have a wide dynamic range (ratio between maximum and maximum light) while other have narrow have narrower exposure value. (McCollough 2008, p.152). Changes in the size of dynamic range can cause an image taken to be either very gray or very black and white. This is because dynamic range operates more on weaker noise and acts less on the strong echoes. (McCollough 2008, p.160). This is attributed to the fact that weak echoes give reflectors that are small and reveal texture and noise that has no diagnostic value. The wider the dynamic range of the imaging machine, the more information it will capture. On the other hand, the narrower the dynamic range the lesser information captured by the imaging machine used. However, the contrast of the two images taken will differ. (Marcus 2015).The more the information captured by a camera, the lesser the contrast between the features of the image. (Marcus 2015).That means that the wider the dynamic range the lesser the contrast of the image while the narrower the image the sharper the contrast of the image features captured. (Upstate Medical University 2014). Wider dynamic Range (Upstate Medical University 2014). Narrower dynamic Range (Upstate Medical University 2014). Reference Diaz, R 2014, An introduction to High Dynamic Range HDR and its Support within H.265/HEVC Standard Extension, viewed 6th April 2017, https://www.google.com/url?sa=trct=jq=esrc=ssource=webcd=1cad=rjauact=8ved=0ahUKEwiA4sSVzZTTAhUcR48KHc1PCdoQFggbMAAurl=https%3A%2F%2Fwww.slideshare.net%2Fxinhxinhqua_678%2Fhigh-dynamic-range-an-introductionusg=AFQjCNG2SrjXci6brlWCAYqAFHifSvpMcAsig2=BMg6EF_gZYgokslg-l-djwbvm=bv.152174688,d.c2I Marcus. H 2015, Dynamic Range in Photography: How to capture all the tones in a Scene, Techradar, viewed 6th April 2017, https://www.techradar.com/how-to/photography-video-capture/cameras/dynamic-range-in-photography-how-to-capture-all-the-tones-in-a-scene-1320985 McCollough, F 2008. Complete Guide to High Dynamic Range Digital Photography, Pixiq, New York. Upstate Medical University 2014, Effects of Changing X-ray Tube Voltage, viewed 7th April 2017, https://www.upstate.edu/radiology/education/rsna/radiography/kvp.php

Special Military Force Shayetet Essay Sample free essay sample

SHAYETET 13 is the elect naval ranger unit of the Israeli Navy. The unit is considered one of the primary Particular Forces units of the Israel Defense Forces. S’13 specializes in sea-to-land incursions. counter-terrorism. sabotage. nautical intelligence assemblage. nautical surety deliverance. and get oning. The unit has taken portion in about all of Israel’s major wars. every bit good as other actions. The unit is one of the most close in the Israeli military. Shayetet 13 is a seasoned Israeli particular forces unit. It was formed in 1948 by Yohai Ben-Nun with work forces drawn from the ranks of the Palyam. the naval subdivision of the Haganah. The being of S’13 was merely made populace in 1960. Shayetet 13 is divided into three specialised company-sized units: * Foraies: Particular Reconnaissance and Direct Action missions on land. Maritime Counter-Terrorism and Hostage Rescues. * Underwater: Underwater Attacks and Sabotage. Hydrographic ( Beach ) Reconnaissan ce. and Beachhead Reconnaissance and Security. * Above H2O: Surface Attacks. We will write a custom essay sample on Special Military Force Shayetet Essay Sample or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page Sea Transportation of units to and from mark countries. TrainingThe preparation of Shayetet 13 recruits lasts 20 months. and is considered one of the toughest classs in the IDF. The preparation phases consist of: * Selection procedure: A choice cantonment to enroll for the unit is held twice a twelvemonth. Cadets are put through physically and mentally ambitious trials. This stage stresses psychological stamina. and tests recruits in their ability to take and run under emphasis and fright. * Six months of basic and advanced foot preparation with the Nahal Brigade. * Preparation stage: this stage lasts for three months and consists of advanced foot and arms developing. parachute preparation. basic elements of maritime warfare. operation of little vass. long swims. forced Marches. and destructions. * Four hebdomads of advanced preparation in combat diving. During this class. plebes learn the rudimentss of combat diving. and how to get by with state of affairss such as cold. darkness. clouded H2O. and how to last bad submerged state of affairss. * Dedicated stage: This stage of preparation stopping points about a twelvemonth and includes preparation in advanced diving techniques with close-circuit systems. submerged destruction. sea-to-land incursions via plunging. ships. pigboats. and jumping into the sea. During their preparation. plebes train extensively in Krav Maga. a hand-to-hand combat system which is Israel’s national soldierly art. Weapons USED * AK-47* M4 carbine* M203 grenade launcher* Negev machine gun* Tavor assault rifle* Glock handguns* Limpet mines* Zodiac RHIB boats* Morena RHIB boats* Snunit fast onslaught trade OPERATIONS PERFORMEDThe major operations performed by SHAYETET 13 are:* 1982 Lebanon War* Operation Moses* Second Intifada* 2006 Lebanon War* Syria 2008* Operation Cast Lead* Francop Affair* Victoria Affair

Queen Elizabeth Grammar School Essays

Queen Elizabeth Grammar School Essays Queen Elizabeth Grammar School Essay Queen Elizabeth Grammar School Essay The Towers of Hanoi is an ancient mathematical game. The aim of this coursework is to try to identify patterns and rules associated with the game and explain them in mathematical terms. The definitions and rules are: Rules: * There are only three positions a disc can be placed. Poles A, B or C. * A disc can only go on top of a larger one. (I.e. Disc A can only go on top of Discs B and C, but Disc B cannot go on top of disc A) * The object of the game is to get all the discs to move from pole A to pole B of C in the least number of moves. * Only one disc may be moved at a time. Finding Formula A Number Of Discs Least Number Of Moves Previous term (Doubled) 1 1 2 3 2 3 7 6 4 15 14 5 31 30 6 63 62 7 127 126 8 255 254 From looking at the table it is quite clear that there is a pattern linking the number of discs and the least number of moves. It is clear that there is an element of doubling involved, as the least number of moves nearly doubles each time. When I add the extra column see above, it is clear that there is a doubling element involved. When I look again, I can see that the pattern is the previous term doubled plus 1. This can be expressed mathematically as: Un = 2(Un-1) +1 This can be shown in: 1. For 1 disc, it takes 1 move to move disc A from pole 1 to pole 3; 2. For 2 discs, it takes 3 moves: 2(Un-1) +1 = 2(1) + 1 = 3 3. For 3 discs, it takes 7 moves: 2(Un-1) +1= 2(3) + 1 = 7 4. For 4 discs, it takes 15 moves: 2(Un-1) +1= 2(7) + 1 = 15 5. For 5 discs, it takes 31 moves: 2(Un-1) +1= 2(15) + 1 = 31 To understand how this works, coding is needed to see how a disc moves individually. Coding should show me the patterns involved and then I should be able to justify my formula based on this. Coding is on the next page. Coding Number of Discs: 2 3 4 5 Disc Moving: A A A A B B B B A A A A C C C A A A B B B A A A D D A A B B A A C C A A B B A A E A B A C A B A D A B A C A B A From my coding it is now clearer why that formula is that particular formula. It can be seen that there is symmetry involved in each pattern. The symmetry is always about the name of the bottom disc. I.e. with 3 discs the symmetry is about disc C and this is the bottom disc From the coding, I can also see that the pattern of moves for 2 discs is present in the beginning of 3 discs, 4 discs etc. The pattern for 3 discs is also in the pattern for 4 discs and so on. This is can therefore be explained as: In n number of discs where n is greater than 2, the first three moves will always be ABA. This is because the n-1 discs pattern is included in the n pattern. We have (Un-1), because we take into account the previous terms pattern when making the next tower. We have the 2 term because this pattern is repeated twice, firstly to deconstruct the tower and then to rebuild the tower on top of the bottom disc. We have the +1 term because this is where the bottom disc moves from Pole A to Poles B or C. This can be demonstrated when we move three tiles. ABA This is the move pattern for 2 tiles (Un-1). This allows C to be able to move. C This is when the bottom tile moves and we therefore get the +1 from. ABA This is where the doubling element comes in as well as the n-1 discs moves pattern. This is where the tower is rebuilt on top of disc C. So overall, we get the formula: 2(Un-1) +1 There are limitations to this however. Un-1 has to be an integer because we cannot have 3.5 moves. Un-1 has to also be equal to or greater than 0 and has to be an integer because the formula wouldnt work as the result would be negative and we cannot have a negative number of moves. Formula B Finding the formula that shows how many times a certain disc moves From formula A I now have a basis on which to work. Given a certain number of discs I need to be able to say how many times a desired disc moves. Firstly, I need to analyze my results from the coding. Disc: Disc A Disc B Disc C Disc D Disc E Disc F Total Number of times each disc moves: 3 Discs 4 2 1 7 4 Discs 8 4 2 1 15 5 Discs 16 8 4 2 1 31 6 Discs 32 16 8 4 2 1 63 We can also once again see a pattern here. There is a doubling, well halving element involved depending on which way you look at it. The table above shows how many times a certain disc moves. Whenever a new disc is added to the sequence, such as in Disc 4, the number of moves for Disc A doubles. I.e. As you go down the table the number of moves for each disc doubles. When I look at the results, I notice that they are all from the 2n pattern. Therefore I can come up with the relationship for the number of times each disc moving being: Number of times a certain disc moves = 2n-d with d being the disc number. So in Disc A, the number for d would be 1, as this is the first disc. Disc B would be 2 etc. In the series for 6 discs, the terms would be Disc A: 2n-d = 26-1 = 32 Disc B: 2n-d = 26-2 = 16 Disc C: 2n-d = 26-3 = 8 Disc D: 2n-d = 26-4 = 4 Disc E: 2n-d = 26-5 = 2 Disc F: 2n-d = 26-6 = 1 This therefore works. Now I have to prove that this works. We can see that Disc B always moves half as many times as Disc A. If we do 2n we get how many times Disc A Moves always. If we do 2n-2 we get how many times disc B moves always. This is because as we take more away from 2n we get smaller and smaller until it ultimately converges to 0. Taking 1 away from this halves the number of moves; whereas taking 2 away quarters the number of moves. Disc B always moves less times than Disc A because of the recurring pattern. A has to move more times, because it has to keep going on top of the larger tiles as the rules state. A has more options to move than B because it is smaller. There are limitations to this however, because we cannot have d being greater than n because the formula would not work. It wouldnt work because we cannot have half of a move or a quarter of a move. We cannot also have n being less than 1 because of the same principal. The number of moves and the disc number have to also be an integer because we cannot have Disc A moving 3.5 times. The Link The series above is a geometric series. I know this because the difference is different each time. The general way to write a geometric series is: General: a + ar + ar2 + ar3 + arn-1 The terms: a is the starting number in the sequence. I will use a 6 tiled sequence so my starting number from the table will be 32 as this is the number of times disc A moves. Ratio r This is the amount that a is multiplied to get the next term. So 32 is multiplied by 0.5 to get 16. Our sequence is: S= 32 + 16 + 8 4 +2 +1 To get the sum of a geometric sequence, we need to multiply by the common ratio (0.5) S = a + ar + ar2 + ar3 + + arn-1 rS = a + ar + ar2 + ar3 + +arn-1+ arn S-rS = a arn This can be expressed as S(1-r) = a(1-rn) Divide this by 1-r gives: a(1-rn) S= 1-r Before I can use this information however, I need to determine a formula to get a. I can use the formula I discovered above but just modify it slightly. To get a the formula is: 2n-1 as this is the formula for Disc A always. So the formula above instead of being 2n-d could have also been 2n-1 for the same principals. With n being the disc number you are trying to find. Disc 50 would be 249 and disc 3 would always be 22 and so on. Therefore I can now substitute in my values in a pile of 6 discs to get the formula that links formula A and B. To determine the ratio we have to just see how much the sequence is decreasing each time. 32 + 16+ 8 + 4 + 2 + 1 To get the next term suing the general geometric sequence rule, it says that we have to multiply 32 by a constant. a ar. So: a ar is the same as ar divided by a. 16 = 0.5. This is the ratio. 32 Therefore for the sum of my geometric series, the formula should be: a(1-rn) S= 1-r S = 25(1-0.56) 0.5 S= 31.5 = 63 0.5 Therefore the sum of a 6 termed series is 63. This can be proved by getting the formula for the previous term. S = 24(1-0.55) = 31 0.5 According to my earlier formula (Un = 2(Un-1) +1) when I substitute in I should get the answer 63. 2 x 31 + 1 = 63. This works because of the algebra of the general geometric sequences: S = a + ar +ar2 This is the rule for each term in the sequence: arn-1 or 2n-d I then multiplied by the common ratio (r) rS = ar + ar2 + ar3 This is the rule: arn Then I subtracted the sequence multiplied by the common ratio from the first sequence. This gave: S-rS = a arn = a(1-rn) Therefore S=a(1-rn) (1-r)) Limitations are: S has to be greater than 0 and has to be an integer a has to be positive and an integer r has to be an integer and greater than 0 Extension Work: Finding which pole the pile will be built upon. I have noticed from my work that when I had 3 discs on my pile, disc C landed on where I put disc A to start off with which was on Pole C. When I had 4 discs however, I noticed that the pile finished on where I did not place tile A which was Pole B. This can therefore be expressed as: If the number of discs in the pile to start with is even then the bottom disc will land where you place Disc A to start off with. If the number of discs in the pile is odd however, then the bottom disc in the pile will finish up on the pole where you did not place Disk A. Therefore where you put Disc A can be considered crucial to where you want your pile to land Overview: If I have 25 discs in my pile, I can expect there to be: 33554431 moves involved in the series. Disc A will move 16777216 times; whereas disc y will move only once. The Pile will end up on the pole where you place disc A, so if I leave it on pole B to start with, the pile will end up on Pole B. According to the monks in Hanoi, the world will end in over 500 Million Years. The problems with my investigation: I have realized that there are only 26 letters in the alphabet. With my system of labeling, it is impractical for me to label each disc A, B C etc because I will run out of letters. I will either have to name the poles ABC or call each disc past 26, A1 etc.

Business law case Study Example | Topics and Well Written Essays - 500 words

Business law - Case Study Example Imperial could find itself with a sudden, severe decrease in its cash flow. It might also have to layoff employees and have equipment sit idle. Simply put, litigation, regardless of the outcome could do irreparable damage to both parties. In this case negotiation would be the appropriate form of alternative dispute resolution to pursue. The two parties need to sit down face-to-face. They need to lay out there understanding of the ambiguous clause in the contract, seek common ground, and perhaps by consent share any costs or losses involved in their differing interpretations of the clause. If negotiation proves fruitless they should move to mediation. Then an objective and disinterested third party could assist them in understanding one anothers position and finding a middle ground. (Marsh, 2008) Due to the complexity of the case collaborative law would be the best approach. The case, too complex for a jury, might also be too complex for a mediator or arbitrator, regardless of their qualifications and experience. Therefore, the parties would be wise to sit down together, with their lawyers accompanying them, and work towards an agreement in camera with trained lawyers, able to understand the complexity of the case. If they were to negotiate in good faith, in this private environment with expert legal advice they stand the best chance of resolving the dispute in a fair manner that also takes account of the legal complexities of the situation. Collaborative law would also ensure that the case never ended up in court. Collaborative law is â€Å"cost effective and discrete†, and with trade secrets involved that is precisely what each party needs. (Newitt, â€Å"Shot before dawn†) It is an unusual proposal for a business dispute, but most appropriate in this instance. In this case it is plain that Empire Corporation wishes to avoid a court case There is the danger of disadvantageous precedent being set if the case does go to trial. Also, the company may find