Introduction
This is filler text for my personal engagement paragraph, where I will be writing about the wonderful game of chess and how it interests me. I will talk about my past history and interactions with chess and why I chose the knight’s tour as my topic for math exploration. I won’t include too much research or calculations here but it should help my case. I will now copy and paste the paragraph I just wrote to make it look longer. This is filler text for my personal engagement paragraph, where I will be writing about the wonderful game of chess and how it interests me. I will talk about my past history and interactions with chess and why I chose the knight’s tour as my topic for math exploration. I won’t include too much research or
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One can go about constructing a knight’s tour in many possible ways, they usually always fall into two categories: algorithms1 and Heuristics2.
[1] Algorithms
The first algorithm is one of brute force, appropriately named the brute force algorithm, it involves the use of a computer to place the knight at a random or given square and then test for open possibilities for the knight to move in its iconic “L” shape pattern. It will iterate the board until a solution is reached, even with current technology it is extremely impractical on larger boards.
The second algorithm is one that is referred to as divide and conquer, the board is divided into smaller rectangles and the knight’s tour is constructed on those, then the ending square on one rectangle leads to the beginning on another, connecting rectangles making it extremely easy to solve large
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In this case, when parts of a term are equal to zero, the entire term is equal to zero, because anything multiplied by zero is zero; for example, if a = 0, then a(x-r_1 )(x-r_2 )=0. The same applies to (x-r_1 ) and (x-r_2 ). With this in consideration, it is trivial to determine which n x n boards do not have any edges in its knight graph. (n-2)=0 and (n-1) = 0 if one of these equations is true, the edges in the knight graph will be zero, further simplified by solving for n (2 or 1) which are the solutions for the n x n knight graph which contain zero edges also known as the roots of the parabola.
Explanation of table: for the knight graph on a n x n board n has a relationship with the number of edges and vertices in its graph. The vertex relation is relatively simple as it is the area of the square, n x n, or n2, shown by the second column in the table. The number of edges the graph has is a more difficult relation as it is an exponential one, represented by f(n) = 4(n - 2)(n – 1) and the third column or by the parabola
In Sir Gawain and The Green Knight, our main character is faced with a challenge. A
Once you see the Medieval Times Knight battle you will have a whole new appreciation for knights; a castle garden. It all started with the stairs. When it was time for the show to begin my family and I went to the grand staircase. Once we got there two trumpet players dressed in baggy pants and shirts started playing. Their trumpets were unusually long with banners on them. One banner had a lion's head on it and the other had a shield. The trumpet players played the most crisp and majestic sound I have ever heard. The sound rang through the castle and all of the crowds fell silent.
Before knights were created, the defense on the borders were low. Europe was being invaded from the north, east, south, and west. Knights were meant to protect their king and their land. The “invasions of the Magyars from the east, Muslims from the south, and Vikings from the north
In this medieval race to no place, valiant knight upon courageous knight attempt to haul the
Knights were a type of soldier established in the middle ages, sworn to protect the nobility. They followed the rules of chivalry, rode the best horses, bared the finest arms and weaponry, and were highly respected. A strong need for protection of the nobility brought knighthood to be and chivalry to order. True knights are far and few now, by the end of the 16th century knighthood was over. Real knights fought hand-to-hand, before guns and gun-powder, heavily armored and ready for battle. Finding a true knight might seem hard now, but true knights exist, they just don’t look the same.
The tales of Sir Gawain and the Green Knight and Lanval offer their readers insight into a common knightly quandary. Gawain and Lanval are both faced with challenges that threaten their ability to protect, uphold, and affirm their very knightliness. The two knights repeatedly see several knightly traits--- each invaluable to the essence of a knight--- brought into conflict. While the knights are glorified in their respective texts, they are faced with impossible dilemmas; in each story, both reader and knight are confronted with the reality that knightly perfection is unattainable: concessions must be made--- bits and pieces of their honor must be sacrificed.
The idea of chivalry encompasses the virtues of truth, honor, courage, kindness, loyalty, and valor. Combining this and many other benevolent traits make the ideal knight. Being a knight means something more than just armor, weaponry, and a good horse. It is about a code. This code of a knight is what sets him apart from the rest of the world, defining him and the beliefs he alone stands for. A knight is bounded by honor and valor usually to his king, his country, and his god.
and his noble knights of the Round Table, by Sir Thomas Malory, a book that
Harbison, Robert. "Knights: In History and Legend." Library Journal 134.20 (2009): 119. Academic Search Premier. EBSCO. Web. 20 Mar. 2011.
The first step in Campbell's hero cycle is "the call." This is when the hero of the story is drawn into some type of journey, challenge, or adventure. In Sir Gawain and the Green Knight, this step occurs after the Green Knight enters the castle and requests a challenge, and no one but King Arthur will accept it. Then, Sir Gawain says, "I beseech you uncle, to grant me a kindness. Let this contest be mine. Gentle lord, give me permission to leave this table and stand in your place there" (Ponsor 127). Gawain believes that he is the least brave knight in the court and should take the blame if he fails so that it does not rest on the court since it is such a foolish challenge in the first place. So Arthur grants him his request and wishes him good luck. The second phase of the hero cycle is called "crossing the threshold." This is when the hero crosses his ordinary, everyday world and enters the dark, unknown area where his challenge awaits him. This happens when the story states, "Gawain walked, ax in hand, to the Green Knight, who had been waiting patiently" (Ponsor 127). Gawain then faces his first challenge with the Green Knight.
“Sir Gawain and the Green knight” is a romantic Middle English poem written in the fourteenth century by an unknown author. This poem is a fairy-tale like story that gives its readers a glimpse into the social class system of Medieval England. This literary work opens with the famous King Arthur, a local bishop, and King Arthur’s knights enjoying a royal feast at Camelot during the Christmas season. This poem provides an accurate depiction of the feudal system of the middle ages. Within this tale are individuals representing the “pyramid of power” that symbolizes the social class system of Medieval England. This top of the pyramid group consists of royalty, clergy and noble knights.
A mysterious knight shows up at the king’s castle and calls himself the Green Knight. The Green Knight then challenges one to play a game which he challenges the king to strike him with his axe if he will take a return hit in a year and a day. Sir Gawain steps forward to accept the challenge for his uncle King Arthur when nobody else in the castle would. He took the King’s role in the game to protect him from the Green Knight. He must learn to accept his responsibility as a knight, in accepting his fate.
The chivalric ideas and knightly behavior are themes portrayed throughout Medieval literature within many different ways. The typical Knight is known to stand up for what is truly believed in. They are meant to fight and remain loyal to their king. The mockery of Monty Python shows each Knight to show a faint type of personality toward the normal beliefs. Instead of showing strength and skill, they act very afraid and childish. Each story provides different examples of how chivalric ideas were valued during this time period. Honor, bravery, and loyalty are chivalric ideas emphasized all through Monty Python, Sir Gawain and The Green Knight, and Morte D’ Arthur.
There are two ways you could be a knight in the medieval period you were either born into it or you showed bravery and prowess on the battlefield. If you were born into power you would be sent off to learn how to be a page at the age of 8. Then by the age of 13 were called a squire they were taught how to be a better knight. Knights had a lot of tournaments all the time they jousted, shot bow and arrows, and had hand to hand combat. Knights even had a code of conduct which was also called the code of chivalry. The code of conduct or chivalry told you what your goal and what you had to do to be a good knight. Knights were expected to do a lot around the castles and what not. A knight was expected to protect those less or lesser rank than himself and to hold to the highest standards of combat and knowledge in religion, writing, music, and leadership. A knight was very closely related to their horse. They had a lot training in them horses and hours working with them. A knight had to have years and year of training before they called be called a knight. Their armor was very expensive to produce. They had to be brave and fearless in battle to be able to be a knight. Knights also did some hunting and they had to put some hour into everything they honestly did. Being a knight meant you have a job and you better go get or done or you were severely punished. A knight didn't just stand for having power it meant you
In the Knight, the reader is given the picture of a Middle English nobleman. He has fought in many wars, but is careful not to boast about his conquests. Clearly, the Knight is the most admired of the pilgrims, and not coincidentally, he tells his tale first.