A vitally important triangle, hidden in plain sight in Leonardo da Vinci’s Vitruvian Man, has been revealed and explained, more than half a millennium after the Renaissance genius drew it.
Is there an Irish angle to this, you ask? Yes there is: it was dentist from west Cork who found it. Sometimes these things write themselves.
Rory MacSweeney, who practices in London but comes originally from Dunmanway, explained his discovery and the relevance of the tooth trade in an article published in the Journal of Mathematics and the Arts. It goes something like this: everyone knows the famous Da Vinci drawing situates a man within a circle and a square and shows ideal proportions.
But there was a third shape hiding in the drawing – an equilateral triangle created by the man’s legs, and mentioned by Da Vinci himself. This shape has gone largely ignored by scholars, but MacSweeney says it was no accident and adds insight to our understanding of the drawing’s meaning.
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It’s the same shape – stay with us here – as the triangle between the corners of the jaw and the place the teeth meet. Hence the dentist angle. It also happens to also be the ratio you see in superstrong crystals and other things in nature. Da Vinci, ever the engineer, found an “architectural common denominator”, MacSweeney told Overheard.
MacSweeney’s interest comes back to the question of evolution. Very few other animals have crooked teeth like humans do – “something went wrong”, he said, and he’s interested in the maths of how we evolved.
“Humans have evolved over various iterations,” he said. “We’ve tried out various versions of bipedalism. We reached a point when we’re fully erect – it’s when you reach the 1.633 ratio.”
“It’s not just that we’re the only humans to survive. There’s an X factor with homosapiens. We’re hugely successful, more dominant than anything else in nature.”
The ratio isn’t just an ideal, from an engineering perspective – “it’s a destination”, the optimal situation our evolution has worked towards.
Curiously, MacSweeney points out, the Vitruvian Man as drawn could spin on an X, Y or Z axis – which is to say, after a fashion, that he can breakdance.
Plugged into high places
It is easier for a camel to pass through the eye of a needle than for a rich man to enter the kingdom of God, as someone once said. But it looks like it can be done: Dundalk electrical appliance mogul Martin Naughton, the owner of Glen Dimplex, has been awarded the Order of St Gregory the Great, adding a Papal knighthood to his British KBE and his French Legion d’Honneur.
The industrialist was recognised alongside his wife Carmel for their philanthropy in education and the arts, including scholarships and supports for university students at home and abroad. The conferral was one of the last acts of Pope Francis, “who himself studied in Ireland at one point and for whom peace and education were especially close to his heart”, said John McCaffrey, president of the Association of Papal Orders in Ireland.
The Naughtons join the starry ranks of the knighthood alongside British Tory-turned-Reform politician Ann Widdecombe, Argentinian caudillo Juan Perón and Australian-American media magnate Rupert Murdoch. They are among about 60 Irish people who currently hold one of the five orders.
Such honours were perhaps more prominent in Irish life in the past, with names such as Hume, Hillery and Lemass adorned by holy acronyms. The tenor John McCormack had three papal knighthoods as well as being a count. But the Naughtons should be warned: Fine Gael TD Oliver J Flanagan’s efforts to style himself Sir Oliver after receiving the honour in 1978 prompted consternation from the government – which considered doing so potentially unconstitutional – and the Church itself, which confirmed that the “sir” stuff is more of a British thing anyway.
RTÉ retires Conor McGregor
Another blow to Conor McGregor in the High Court this week as the decorated-but-dormant UFC star was forced into retirement by the state broadcaster. In broadcasts and online, RTÉ News referred prominently to him as a “former MMA fighter”.
McGregor is appealing the High Court’s finding that he is civilly liable for the rape of Nikita Hand. The 36-year-old hasn’t fought since 2021, when he was stopped by Dustin Poirier at UFC 264. A comeback in the summer of 2024 was cancelled due to a training camp toe injury.
After some talk of a 2025 return, UFC head honcho Dana White said in May that he wouldn’t be fighting for him “any time soon”, and with the High Court appeal and an apparent desire to run for president occupying McGregor’s time, there are no independent extravaganzas in the books either.
But if there was an announcement that he is formally retired, we missed it. Perhaps RTÉ simply saw the writing on the wall. It’s unlikely he would have given them the scoop: he once described them as “robbing, lying, fake hypocrites”, “robbers of the Irish public” and even “ooh laa laa heads” (snobs) in an online rant.
Golf diplomacy
Whoever inherits the Áras will have a neighbour who’s also new to the area: Edward S Walsh, United States ambassador to Ireland. The businessman and member of the Trump Bedminster golf club in New Jersey presented his credentials to the Irish Government this week, introducing himself to the Irish public with a video.
What did we learn? He’s Irish-American, like every ambassador since Lyndon Johnson sent a polo-playing second cousin of Winston Churchill’s. His roots are in Clare. He doesn’t read phonetic renderings of the phrase “go raibh maith agat” especially well, although that will come with practice. And he likes golf.
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In fact, he tells us in the video that “as a lifelong golfer, I’ve learned a lot about fairness, diligence and building relationships, values that I will bring with me into this position”.
It will be interesting to see which aspects of golf help him keep the Irish-US relationship special while the two nations go in opposite directions on Israel.
“Ireland, while often a valuable US partner, is on a hateful, anti-Semitic path that will only lead to self-inflicted economic suffering,” the Senate Foreign Relations Committee chairman Jim Risch threatened on social media website X this week in the wake of coverage of the Government’s Occupied Territories Bill.
“If this legislation is implemented, America will have to seriously reconsider its deep and ongoing economic ties.”
Ambassador Walsh might have dreamt of cherishing Irish links, so to speak, but he faces a period in the rough first.
