Regular Polygons

I have been wondering about spaces used in combat sports, almost all of which are formed by regular polygons: from the circle of sumo, to the square of boxing, to the octagon of mixed martial arts.

Regular polygons: circle, square, octagon

The circle is known in many cultures as the perfect shape or form: all lines of force radiate perfectly from the centre of the circle to its perimeter. In gladiatorial sports contested within a circle (which also include freestyle and Greco-Roman wrestling and various forms of animal combat) motion is continually assured by the degrees of freedom that this geometrical form allows; even when against the perimeter boundary there is plenty of room to maneuver.

The square competition area in organized boxing has existed at least since the institution of the London Prize Ring rules in 1743. Why the square (ironically referred to as a ring) instead of the circle for boxing? Is it because of the strong linear references characteristic of architectural forms in the modern age?

(As an aside, the circular area of competition in Greco-Roman and freestyle wrestling is inscribed on a square mat, which is then rolled up into a cylindrical form for storage. Similarly, the circular sumo dohyo is inscribed on a raised square platform, which presumably is meant to honour the historical traditions of the sport while fitting into the rational rectilinear spaces of modern Japanese arenas. Was this always the case for spectatorship of sumo?)

With the square, we cannot make the same claims to maneuverability mentioned earlier, despite its perfect symmetry on all axes that bisect the centre point. Lines of force are fairly constrained along horizontal and vertical dimensions, which leaves dead spots of motion in the corners — the last thing a boxer wants to do is get trapped in a corner with no line of flight to escape. This is not to say there is a dead spot in action; to the contrary, the constraint on motion often yields to a violent increase in action.

As for the octagon of mixed martial arts, it seems to exist primarily as a form of differentiation from other combat sports that serves an important role in the brand strategy of the Ultimate Fighting Championship organization. But beyond this pragmatic association, the octagon seems to offer us, by way of superficial observation, a hybrid of the two spaces mentioned already. Geometrically, this makes sense to us: a circle is nothing more than a regular polygon with an infinite number of sides, so the fact that the octagon doubles the number of sides of the square suggests that it will be more like the circle in the way it structures movement possibilities within.

Interior AnglesWe notice the difference particularly in the corners of each polygon: the interior angle of a boxing ring (black line) measures 90 degrees, while the interior angle of a mixed martial arts octagon (red line) measures 135 degrees, giving combatants in the latter space 45 more degrees of freedom to maneuver should they become trapped in a corner. What does this mean in terms of practical consequences? It suggests a competition with more mobility, more movement, and more action.

But we must qualify this last term: what do we mean by "action"?

In the glory days of prizefight boxing last century, action often meant a flurry of punch combinations being rained down on a boxer trapped against the ropes or in the corner; large, lumbering, powerful boxers, relics of the industrial age. Action today, by contrast, is far more about speed, with the goal being to sacrifice as little of the earlier gains made in power as possible. Thus, the newfound mobility offered by the octagon creates new kinds of strategic challenges as part of the action. How does one engage an opponent without sacrificing too much power in the more open space at the middle area of the octagon, or when retreat by the opponent is more easily possible, particularly in a lateral sense?

Comments

4 responses to Regular Polygons

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  1. Chris Doyle says:

    An issue discussed often in sport shows such as Off The Record is the increase in the popularity of mixed martial arts, as well as the decrease in the popularity of boxing. Often, the majority of the guests on the show conclude that the shift in popularity will be short term, noting reasons such as boxing not having a highly popular figure to draw audiences at the present time (eg. Mike Tyson). However, perhaps the shift in popularity is related to the different types of action which each sport exhibit, due in large part to the shapes of the rings. Boxing seems to have not yet been able to adapt to the new type of action (speed and mobility) which draws spectators to sport today. Rather, boxing still employs the type of action which drew spectators to the sport over a century ago. Perhaps a change of the sport is in order. Since the variables which define action in today's world vary from those of last century, perhaps boxing should consider adapting the octagon shaped ring, which has worked quite successfully in mixed martial arts. Although I highly doubt this type of radical change would occur in a sport with as rich a history as boxing has, it would be interesting to see the effects that altering the shape of the ring would have on the strategies which the boxers employ, as well as the popularity of the sport.

  2. David Allison says:

    It seems the shape of the fighting arena can dramatically influence the style of the fight. A circular ring may lead to a more defensive style as each opponent has more room to maneuver and can easily retreat when being acted on by the opposition. A square or octagon shape on the other hand may lead to a more offensive match as it becomes more difficult to maneuver away from an attack. This may explain why most combat sports in Western society use square or octagon rings. Most valued sports in Western culture are those which stress the importance of offense. For example, fans watch basketball games to see high flying dunks, and high scoring athletes. In some professional sport leagues such as the NHL, modifications are made in order to insure higher scoring games (ie. no two line passes, increased holding calls). Low scoring sporting events that focus more on defensive aspects such as soccer are generally not valued as much in Western Society. As sport has developed into a multi billion dollar industry throughout the Western World, it is not surprising that sporting events are designed or modified to cater to the interests of the general public.

  3. Jessica Foster says:

    It is evident that throughout the years the structure of the area in which a fight takes place has an impact on the fight itself. Strictly for the use of entertainment, a circular area is suggested to have the greatest peripheral ability for the fans attending the fight. Also, with a circular area fighters are left with the opportunity to escape their opponent. This is due to the fact that a circular shape does not allow for corners that the fighter may become trapped in, as that of a square does. Using a circular fighting area suggests a faster paced fight as offensive and defensive strategies are frequently evident. With the use of a square shaped area comers more frequent defensive strategies, as being cornered can lead to the destruction of an opponent. Therefore, as displayed today with the new era of fighting, known as Ultimate Fighting (UFC), the shape of an octagon is a key element for maximal "action" within the sport of fighting. As stated in the article, the octagon exhibits corners but not to the extent of the square, which leaves the opponent to be able to manoeuvre out of a defensive position. In conclusion, I think that the shape of the fighting area does play a significant role for the "action" involved in a fight.

  4. David Tertula says:

    As time passes we discover new and innovative ways to change old sports. Boxing and UFC fighting have their respective technicalities, but changing the area in which the individuals fight could drastically influence strategy. The circular ring allows fighters (sumo wrestlers) the ability to circle each other while always staying the same distance from the edge; in sumo wrestling the circular ring is historic as mentioned but allows for the competitors to use great amounts of power as they are usually large men. The practicality behind this is that sumo wrestling is a points fight where individuals are awarded points for pushing their competitor out of the ring; given this idea, the ability for a sumo wrestler to easily dodge an opponent due to the circular ring can be very advantageous because the other man will have to much inertia to counter and can easily be forced out of the ring. The boxing rings do allow for opponents to be cornered but this adds excitement as fighters usually throw a flurry of punches while cornered. The square shape of the ring has evolved into boxing strategy as the boxers are trained to keep moving and circling their opponent to avoid being cornered. As for the octagon in the UFC, it seems to be the most aggressive shape because of the multiple angles and due to the fact that the fighters are contained in a ‘cage’. The fighters in the UFC use the 5-6 foot high walls of cage in their strategy as fighters can pin their opponent against the cage, or fighters can use it as leverage against an opponent. This is not possible in a circular ring as there aren’t any physical barriers, and does not happen in boxing because the boxers are told to get off of the ropes. So not specifically based on the shape of these fighting surfaces but the boundaries which outline the shapes is very important as well. But to make an obvious statement, the shape of the fighting parameter has a direct effect on training and strategy for the fighters and the event in its entirety. Sumo wrestling is not popular in North America as it lacks ethnic significance here. Boxing has always been a large spectator sport as heavyweight bouts draw crowds of millions but the speed of the event is usually in the upper body movement. The UFC incorporates a large scale of fighting styles and is appealing to fans who like non-stop action. The UFC is exciting to watch and is becoming an increasingly popular phenomenon as its fan base is increasing due to the appeal of the sport and the speed and training etc that is involved.