Analysis of the work
The Characteristics of Sir Gawain and the Green Knight
Pentangle and Virgin Mary
Comparisons and contrasts with Beowulf
A. The Characteristics of Sir Gawain and the Green Knight
 As one of the most influential works in medieval English Literature, Sir Gawain and the Green Knight is a representative of medieval English Romance.  This genre, which appeared in Old French literature of the twelfth century, features in a tale of adventure in which the main figures are knights, kings, or distressed ladies, motivated by love, religious faith, or mere desire for adventure.  Medieval romance often refers to the narrative of chivalric adventure that are set in a distant time or place and involve elements of the supernatural; and romance heroes are usually of high birth, and the world of romance is a world in which magical transformations are always a possibility.  Compare this work with Beowulf (an epic), we can discover some differences.  For example, the epic reflects an heroic age, whereas the romance reflects a chivalric; the epic has weight and solidity, but the romance exhibits mystery and fantasy; the tragic seriousness of the epic is not matched in the lighter-hearted romance; the epic uses observes narrative unity while the structure of the romance is loose; love usually absent or of minor interest in the epic, is supreme in the romance; the epic uses the dramatic method of having the characters speak for themselves, whereas the reader of a romance remains conscious of a narrator (many ideas of the above passage are from A Handbook to Literature, edited by William Harmon and C. Hugh Holman).
 Sir Gawain and the Green Knight stresses the idea of a lesson in chivalry and knighthood.  Chivalry, often implies as a kind of polite, kind and unselfish behavior especially by men towards women, in Middle Ages refers to the set of rules and conventions which knights had to follow.  In this work, we can clearly discover that Sir Gawain in order to protect the king, takes part in the game the Green Knight offers at Christmas night.  However, we can also discover the irony when we read the work.  For example, on page 207, line 236-38:

  All the onlookers eyed [green knight], and edged nearer;
  And awaited in wonder what [green knight] would do.

From these lines we can see that the knights who should protect the king are scared by the green giant and none of them would confront with him.  Also from line 308-10, we can realize that the green knight also teases the knights who should protect the king:
When the court kept its counsel [green knight] coughed aloud,
  And cleared his throat coolly, the clearer to speak:
  “What, is this Arthur’s house,” said that horseman then, 
  “Whose fame is so fair in far realms and wide?
These lines show that the knighthood, which was so honored in Medieval culture, is somehow distorted and this kind of spirit is used as a kind of irony.
 In addition, in this work, we can see that “green” is a kind of dominant color.  Why Green Knight?  We often associate green with nature.  As a result, the sudden appearance of the green giant in the Christmas night seems to indicate the unexpected difficulty and challenge in human world.  And like what Grendel and the dragon in Beowulf, Green Knight seems to suggest the test given to human beings.  This test examines the loyalty of the knight his values of Christianity (chastity, honesty, fortitude and faithfulness). 
 This work is also a form of holiday tale. Holiday tales often narrate the celebration of harvest; however, the danger often happens during the crazy celebration.  The tales are usually covered with colorful adventure and marvels.  In Sir Gawain and the Green Knight, we can see the contrasts of inside and outside of the house.  Outside of the house is the bleak winter, while inside of the house is warm and everyone celebrates the victory from the battle. This celebration leads more challenge to the knights and there comes the green knight.  Furthermore, the darkness outside of the house also symbolizes the danger and the disorder in the world of human beings. 

B. Pentangle and Virgin Mary
The pentangle is a symbol of five virtues which knight should follow: generosity, fellowship, chastity, courtesy and pity.  In line 640, we see Gawain is said to be “faultless in his five senses and unfalling in his five fingers,” the requirement of natural perfection which is put on Knight actually is an ideal code posed on Knight’s behaviors.  Besides, Gawain’s shield also contains a portrait of Mary on the inside.  In this way, we see that Christian spirit is one part of so called “knighthood.”  In other words, the elements of Knighthood should be not only loyalty to his lord but also devotion to Christ.  The depiction of the pentangle occurs when Sir Gawain is preparing to gear up for his quest for the Green Knight.  Gawain’s gear is described in great detail, including its color, making and finery (which is on page 214 to 215).  His armor is meant to serve as a means to protecting his physical being; it is distinctly secular in its abilities.  Meanwhile, the shied with pentangle and portrait of Mary serves as spiritual values to keep Gawain’s spiritual purity.  However, the armor which is put on Gawain’s body and the shield Gawain holds create a conflict between secular ideas and high religious values.  In part I and Part II, we see Gawain still can stand on his own field as being a knight, like in the line: “As to his word must true / And in speech most courteous knight”, but then as the plot develops, Gawain finally fails to keep his honesty since he lies to the master of castle.  Actually, we can find a meaningful passage in page 220.  Sir Gawain removes both his shield and gear, and wears materialistic wrought clothing.  In other words, as he removes his shield and gear, the material and physical desire now is unconsciously taking over the high religious values and the code of knighthood.  This hints us that Gawain is going to step into secular garb while removing gear and shield.  Furthermore, we can take a look at how Gawain describes the master’s lady.  We skip the beginning part of this description, we just move to the line 968-69, “more toothsome, to his taste.”  This obviously is not a proper way for Gawain to view a wife of a lord as “toothsome” who is giving him safe harbor for the next several nights, especially he is renowned as the Virgin Mary’s Knight.
Through Gawain’s quest, we see Gawain’s personal growing up and rebirth.  However, as he struggles, we see the virtues which pentangle and portrait of Mary tries to contain are filled with difficulty for a knight to carry out. 
C. Comparisons and contrasts with Beowulf
    Beowulf is written in old English and it is an epic. Sir Gawain and the Green Knight was written in medieval English and it is a chivalric poem. Therefore, they represent two different types of hero, epic hero and chivalric hero.
Common
A. The Virtues:
No mater Beowulf or Sir Gawain, they both possess the qualities of valor, military, prowess, loyalty, generosity, and skills in battle and honor. They both are very brave and courageous to fight the giant or monster. They are loyal to their king or lord. Beside, the honorable code is also important to them. They never fight with a foe that is weaker. They want a fair fight.
B. The journey of quest
They both have a journey of quest. Beowulf travels to Hrothgar’s court to battle Grendel and his mother. Sir Gawain travels through the land for a year in search of the Green Knight and find Bercilak’s castle. They pass through all difficulties to gain triumph. It is symbolic. As a hero, they must pass all kinds of difficulties and defeat all enemies to win the final triumph.
C. A feudal court
  The social background of both works is under the Feudalism and hierarchy. The higher-class people who owned the warriors and knights to help them controlled the society. Like the Beowulf and Sir Gawain, they are the knights of their lord and they have to be loyal to their lord. By helping their lords to gain lands and fame, they gain fame and fortune. 
D. Insurmountable odds
    They both face and stand up to the insurmountable odds, the great challenges: Beowulf and the dragon, sir Gawain and the Green Knight, and the dragon and the Green Knight are represented the huge and supernatural power.
Differences:
A. Purpose of fighting
In Beowulf, the idea of the hero is as a savior. He must fight for the survival of his people and tribe. The epic hero fights only when the circumstances requires. They do not just fight for fighting. In Sir Gawain, he fights not only for his people but also for his ideals. Tribe and people are not his only reasons to fight. Besides, the chivalric hero sets out to find a test which he can prove himself by fighting. The reasons for chivalric hero to fight are more than epic hero. 
B. The tone
The tone in Beowulf is very solemn and gloomy. The poem begins and ends with a funeral whereas the tone in Sir Gawain and the Green Knight is merrier and happier, which begins and ends with a celebration. The world of Sir Gawain seems magical and merry, whereas the world of Beowulf is mythical and serious. 
C. Divine and Humanistic
    In Beowulf, the hero is a great person who is semi-divine, larger than human and people are attracted by his valor, courage and so on. However, in Sir Gawain, the chivalric knight must know temperance, courtesy, a reverence for women and courtly skills. It is not enough if he only performs well on the battle field. He must present at court. The chivalric hero is more humanistic. Like a human being, they are also selfish, fearful, temptable and so on. This is very different from the epic hero.