Giotto’s Circle

*author’s note: the following is intended to read as an introduction for an imaginative text of an imaginative class — “Math Appreciation”

Imagine, if you will, a scenario in which you must have your bedroom designed by any artist of your choosing. What might you do to begin? What might assist in your decision making? Would you have someone instantly in mind? Or, perhaps you would hold some type of contest in which the best and brightest would compete for the opportunity to paint, decorate, and design your new room. If this latter design were the case, how would it be judged? Would you choose the most colorful? Would you choose the artist that seemed to best relate to your image or identity? Or, might you look specifically at the various submissions assessing their merit: determining who is the most skilled artist? If this last measure were to be the case, would you ever assume the winning submission could be a drawing of a circle? No more, no less. The only thing that exists on the winning artists submitted page is a hand drawn circle. Would you declare them the winner?

This is precisely what Pope Boniface VIII did (late in thirteenth century), when he needed painting commissioned for his church, St. Peter’s. Pope Boniface VIII sent a courier all over Italy in search of the finest artist: someone worthy of such commissioned work. As the story goes, the courier reached the artist Giotto di Bondone asking if he would like to submit work to be judged by Pope Boniface VIII. Giotto accepted the offer and submitted a drawing that (Giotto believed), proved greatly his talent. The courier, upon viewing the drawing, insisted that Giotto was a fool (or at least playing the courier for one). Why did the courier think this of Giotto’s drawing? Simply because all Giotto submitted was a circle: a red circle drawn freehand: a perfect red circle drawn freehand. This perfect circle (though a joke to the courier), won Pope Boniface VIII’s favor, and Giotto was chosen to complete the commissioned work for St. Peter’s church.

So, why on Earth does this matter? How is it relevant? Why is it being discussed in a mathematics textbook? I believe the better question may be, why isn’t this (and various other stories), discussed more often in mathematics textbooks? You see, the only way one can understand the importance of this story is if one understands an extremely simple shape: a circle. No, I don’t mean one must know what a circle is, I mean one must understand what it is. Where did circles come from? What do they mean? Is it simply a symbol representing “zero” or perhaps the English letter “O”? Well this can’t be the case if the observation of circles has occurred on our planet since the dawn of humankind (consider a full moon or the invention of the wheel). In fact, it may surprise you to know that circles are not simply an aspect of what you may know as geometry, but, in fact, helped create the study of geometry! (Euclidian geometry, to be precise.)

Again, I ask, why does this matter? Allow me to answer this question with another question: do you find this story of Giotto and circles interesting? Has it given you a new perception regarding the depth of mathematics? Well, why shouldn’t this be the case? We study the history of time, America, various other countries, our language, so why not study the great historical depths of mathematics? I believe this absence of depth and inquiry within the current standards of taught mathematics has done our society a disservice. If paintings can be appreciated, as well as poetry, as well as a delicious 5 star meal, so can the Fibonacci sequence. So can pi. So can the method of exhaustion. This brings us to the here and now. This brings us to Mathematics Appreciation.

In order to begin this appreciation we must discover mathematics in a new lens: a humanities lens. Consider mathematics not merely a study of numbers and formulas you are given and encouraged to repeat, but instead, view mathematics as a language that surpasses all boundaries of time and place.

View mathematics as the quest for truth.