When I heard that my flatmate Julia was heading off to spend a week in Rome, I devised a cunning plan. I got my son McHaggis to hide in her suitcase with instructions to find interesting mathematical sites when he got to the Italian capital. This brilliant idea was inspired by my other flatmate Graeme, who has been writing a series of articles on Sosauce about ‘mathematical tourism‘, and by Marcus du Sautoy, who is currently designing a mathematical walking tour of London. Surely in Rome, one of the oldest capitals in the world, there would be a hoard of mathematical treasures to explore?

On a first flick through the guide book, the pickings actually seemed pretty slim. The only thing that caught my eye was the Pantheon, which is the best-preserved of the ancient buildings in Rome. It was built in 27BC by Marcus Agrippa, and rebuilt in the subsequent couple of centuries because of some unfortunate fires. The word *Pantheon* means ‘all the gods’, and the giant dome was intended to symbolise the dome of the heavens. Giant indeed it is: its span of 43.2m made it the largest in the world until 1420, and it still remains the world’s largest unreinforced concrete dome. It is perfectly hemispherical, and more interestingly, the height from the floor to the apex is exactly 43.2m, meaning that the interior fits perfectly into a cube. At the top of the dome is a circular aperture nearly 9m in diameter, which surely could have been used as a sort of sundial if the architect had thought about it a bit.

So, some interesting dimensions there, but nothing to really get the mathematical tastebuds juicing. Then one day I got a message back from McHaggis, saying that he was in the Vatican City and was very excited by two discoveries.

The first, and main one, was that the plaza in front of St Peter’s Basilica is designed as a perfect ellipse, with fountains at the two focus points, and a giant obelisk in the centre. In fact (according to Wikipedia) there was originally just the obelisk and one fountain outside the basilica, and the architect (Gian Lorenzo Bernini) had to decide what shape to make the plaza. He originally thought of having a rectangle (but it would have necessitated demolition of some buildings) and then having a trapezoid (but it would have made the front façade of the church look too wide). So in the end he decided to build an ellipse, with the curving arms symbolising the welcoming arms of the Catholic church. Of course, he then had to build another fountain to sit at the other focus point, which he did just five years before he died.

In contrast to the under-used central hole of the Pantheon, people did realise the time-keeping uses of the central obelisk of the plaza. In 1817 they built a circle of stones around the obelisk that could be used to tell the time of day.

The second thing that McHaggis noticed was that inside St Peter’s Basilica (a very beautiful church, and one of the most important sacred sites for Christians) there was a clock with only 6 numbers!

Mathematicians love using clocks with only a few numbers on them, although usually they prefer clocks with prime numbers of numbers on them. They call it doing *modular arithmetic*: for example, on this clock 1+4=5 (like normal) but 2+5 = 1 (if you don’t believe me, count 5 numbers around from the number two!). If you’ve only got a few numbers to worry about, it makes the whole business of mathematics a lot easier to deal with. And mathematicians are nothing if not lazy, as I think was mentioned in a previous post. So, yes, this clock was very exciting. 🙂

As a thanks to McHaggis for exploring Rome for me, I’ve agreed to put a photo of him up to prove that he was really in Rome. Here’s him on the foot of (what was) a giant statue of Constantine the Great.

You go, son.