The Measure of an Athlete: Mathematical Proportion in Greek Sculpture

MA Cities graduate David Archbold (2015/ 16) wrote a highly successful thesis on mathematical proportions in the work of the Greek sculptor Polykleitos. Here he shares some thoughts on his research:


A body of research

My thesis was about the mathematical principles behind the athletic sculptures produced by the ancient Greek sculptor Polykleitos. The thesis was formed around two research questions. Firstly, as the original sculptures no longer exist, do the sculptural copies represent the same figures as the originals, and secondly, is the mathematical system used by Polykleitos evident in the Roman sculptural copies of his athletes?  Investigating this involved building up Polykleitos’ notion of the ideal athletic figure, while also authenticating the sculptural copies as representations of athletes. It also involved whether the examination a mathematical system proposed by Richard Tobin was the one used by Polykleitos, and the examination of the measurements of the sculptural copies. The cross-examination of these measurements and the mathematical system prove the existence of an underlying maintenance of the mathematical principles used by Polykleitos.

Building up contacts

Although there is a lavish amount of material written about Greek and Roman sculpture, there is a dearth of mathematical research around Polykleitos’ athletes and even less around their Roman copies. As my thesis concerned itself with measurements, a lot of my time was spent trying to accumulate as much information as possible. In researching the sculptures of Polykleitos’ athletes, I formed a list of museums which held particularly significant sculptural copies. I contacted each of these museums in an attempt to compile the measurements of the sculptures. This put me in touch with some established art historians in the area of Greek and Roman sculpture. These connections significantly impacted my thesis research. Each of the museums have only documented the total height of the marble and not the figure itself, while some also have documented the length of the head. My contact with these museums made it possible for new measurements to be taken. One person I was in contact with was able to measure a sculpture in the Szczecin National Museum ( my behalf, following the method outlined in my thesis. Furthermore, two of the contacts offered to assist me in my work if I were to visit their museums. The first of these was Dr. Ian Jenkins of the British Museum (british museum)and the second was d.ssa. Eleonora Ferrazza of the Vatican Museums.


Out in the field

After the thesis proposal presentation, at the beginning of the second semester at UCD, I had a better understanding of what exactly it was I wanted to research and write about. In February I went to London to measure three of the sculptures in the Greek and Roman Collection in the British Museum. Then later in the semester I applied for the Thomas Dammann Award (, which funds traveling for research. Fortunately, I was awarded the funding and was able to travel to Greece and Italy in May to undertake further research. Through my supervisor, Lynda Mulvin, I got in contact with the Irish Institute of Hellenic Studies at Athens ( I became a member of the Institute and boarded in their facilities when I was in Athens. I also got to travel around Greece for a short while, which allowed me to visit Argos, the birth place of Polykleitos. I then travelled to Rome, where I got the chance to explore several museums which house sculpture copies of Polykleitos’ athletes. Most importantly, I got the chance to measure three sculptures in the Vatican Museums’ Collection. Lastly, I took a short trip to Naples as its archaeological museum houses the most documented sculptural copy of Polykleitos’ Doryphoros.



The most difficult part about the research was trying to accumulate enough relevant information on the measurements of the sculptures. In the vast majority of cases no measurements were taken of the figures and the few that do exist often vary. Luckily I had the chance to produce my own measurements on which the bulk of my research is based. I also emailed Scan the World (scan the world), which is an online collection of three-dimensional scans of sculptures. As it was not possible for me to measure all of the relevant sculptural copies, through Scan the World I was able to measure three-dimensional scans in their place.

Writing up

It was not until late May that I had compiled my measurements and developed my research to a satisfactory stage, albeit with very little writing done. The initial draft was due at the end of June, which meant I spent the whole month of June writing. I found the draft to be the most helpful part of understanding my topic, as it formed a base structure from which the eventual thesis grew. My research continued well into July as things began to click and I began to really fine tune the focus of my research. Ultimately, I had to stop researching in August as I could easily have kept developing the topic. However, at that stage, knowing I had a solid structure and a substantial amount of research, my focus turned to presenting that research in the best way I could.

My research was focused on two questions although in researching my topic many different paths of enquiry presented themselves most of which I had to completely ignore.  In writing the thesis I felt there was always more I could say. I found that the most challenging part of writing was making sure that the reader could clearly follow my line of reasoning throughout.  While my structure remained the same from draft to completion, I spent a lot of time moving things around. This was when a second reader was of huge benefit.

Doryphoros Braccio Nuovo Vatican Museums (3).pngSome final thoughts

The topic I chose for my MA thesis grew out of my undergraduate dissertation, which looked at the head to body ratio of Polykleitan sculpture types. This topic has significantly evolved from that stage. The one piece of advice I would give to a student embarking on the MA thesis is to research and write about what interests you, regardless of the artistic connection and then see how it can be applied in an art historical context. I was lucky enough to combine my interest in mathematics with art history and, as a result, this topic is one that I intend to research further.

David Archbold, October 2016


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