Latest news with #Vitruvius
Yahoo
2 days ago
- Science
- Yahoo
Hidden Detail in Crotch Solves 500-Year-Old Leonardo Da Vinci Mystery
Leonardo da Vinci, the famous Italian polymath who painted the Mona Lisa, had a sophisticated geometric understanding way ahead of his time. To draw the Vitruvian Man in 1490 – an illustration of the 'ideal' human body – the Renaissance man may have relied on a mathematical ratio not formally established until the 19th century. It's one of the most iconic images of all time, and yet for more than 500 years, no one could figure out why da Vinci chose such specific proportions for the arms and legs. A London dentist thinks he's solved the mystery at last. Related: Rory Mac Sweeney has found a crucial hidden detail, tucked in the Vitruvian Man's crotch: an equilateral triangle that he thinks may explain "one of the most analyzed yet cryptic works in art history." The Vitruvian Man is partly inspired by the writings of Roman architect Vitruvius, who argued that the perfect human body should fit inside a circle and square. Da Vinci's drawing uses a square to precisely contain a 'cruciform pose', with arms outstretched and legs in. The circle, meanwhile, encompasses a posture where the arms are raised and the legs are spread. A popular explanation is that da Vinci chose the Vitruvian Man's proportions based on the Golden Ratio Theory, but the measurements don't quite match up. According to Mac Sweeney, "the solution to this geometric mystery has been hiding in plain sight". "If you open your legs… and raise your hands enough that your extended fingers touch the line of the top of your head… the space between the legs will be an equilateral triangle," da Vinci wrote in his notes for the Vitruvian Man. When Mac Sweeney did the math on this triangle, he found that the spread of the man's feet and the height of his navel created a ratio of around 1.64 to 1.65. That's very close to the tetrahedral ratio of 1.633 – a uniquely balanced geometric form, officially established in 1917. The ratio is used to establish the optimum way to pack spheres. If four spheres are connected as closely as possible into a pyramid shape, for instance, then the height to base ratio from their centers will be 1.633. Perhaps Mac Sweeney recognized the significance of that number because of a similar triangular principle used in dentistry. Imagined on the human jaw, Bonwill's triangle dictates the optimal positioning for jaw function, used since 1864. Its ratio is also 1.633. Mac Sweeney doesn't think that's a coincidence. Similar to minerals, crystals, and other biological packing systems found in nature, Mac Sweeney thinks the human jaw naturally organizes around tetrahedral geometries, which maximize mechanical efficiency. If the tetrahedral ratio is repeated around our bodies, Mac Sweeney thinks that is because "human anatomy has evolved according to geometric principles that govern optimal spatial organization throughout the universe." If Mac Sweeney is right, Da Vinci may have stumbled across a universal principle while drawing the Vitruvian Man. "The same geometric relationships that appear in optimal crystal structures, biological architectures, and Fuller's coordinate systems seem to be encoded in human proportions," writes Mac Sweeney, "suggesting that Leonardo intuited fundamental truths about the mathematical nature of reality itself." Whether other scientists agree with Mac Sweeney remains to be seen, but the fact that da Vinci mentioned the equilateral triangle in his notes suggests that what lies between the Vitruvian man's legs is important. The study was published in the Journal of Mathematics and the Arts. Related News Neanderthal 'Swiss Army Knife' Discovered in Belgian Cave 'Classic' Hymn Deciphered From Ancient Babylonian Library Ancient Neanderthal 'Fat Factory' Reveals How Advanced They Really Were Solve the daily Crossword
Spectator
04-06-2025
- General
- Spectator
The Romans wouldn't have put up with Thames Water
It is embarrassing to compare Thames Water's efforts even to the Greeks, let alone the Romans. Most Greek cities got their water from public fountains fed by springs. Doctors new to a district examined the supply to determine likely ailments (one spring was said to make your teeth fall out). A few towns had piped supplies: Athens had one, and Greek Pergamum (in Turkey), from a source 20 miles away. An inscription there ordered wardens to ensure 'fountains are clean and pipes supplying them allow the free flow of water'. But the Romans were the great water engineers, spreading comfort and luxury thereby far down the social scale. Initially they were privately funded benefactions (not 'serious' enough for the state: this changed under the empire). The first (ten-mile) aqueduct – a water-leat, running along the ground and through tunnels – was commissioned in Rome in 312 bc. In the 4th C ad Rome had 11 aqueducts totalling 320 miles in length, the longest stretching for 56 miles, to serve 154 public lavatories, 1,352 water points and 46 brothels. They daily brought into Rome some 1.2 million cubic yards of water, about 25 gallons per inhabitant, per day. Why so much? Because it was needed in the noble cause of human pleasure: the Romans' 856 public baths, their universal means of social relaxation. Plebs and emperors alike used them (though they disgusted Marcus Aurelius – all 'oil, sweat, filth and greasy water'). The rich who had water piped into their homes provided a useful source of revenue. The Roman architect Vitruvius gives rules for checking its cleanliness at source: are the inhabitants there strong, without physical distortions or inflamed eyes? Does the water leave traces when sprinkled over certain alloy vessels? When boiled in a copper pan, does it leave a sludge? Will it cook vegetables quickly? Is it clear, from an untainted source? Vitruvius knew that lead pipes were unhealthy ('observe the lead workers' pallid complexion') but lead poisoning did not cause the fall of the Roman Empire.
Wall Street Journal
08-05-2025
- Automotive
- Wall Street Journal
The Twisted Design Logic of Kia's K4 Sedan
As the Roman architect Vitruvius once observed, everything should look like something. I'm paraphrasing. Upon seeing the new-for-2025 Kia K4 sedan, your eye will be instantly drawn to the incongruent triangles of glass, window masking, molding and metal trim (the quarterlight), extending the car's glass section (greenhouse) into the fastback-style roof buttresses. Note how the rear door handles are hidden in smaller triangle shapes that are built into the rear window frames.
Forbes
21-04-2025
- Business
- Forbes
Lessons From (Re)Building A Security Company From Scratch
Christofer Hoff is the Chief Secure Technology Officer of LastPass. getty I've always admired the Roman architect Vitruvius, who once said that if you're going to build something, it ought to be beautiful, strong and useful. After spending the past two and a half years building the software and platform engineering teams, as well as a new security organization, at LastPass, I've come to truly understand how right he was. I joined LastPass in 2022 as its chief secure technology officer (CSTO)—combining security and technology into one role—an opportunity I couldn't resist. The business was taking the first of many steps to spin out from its parent company and form a stand-alone company. A whole new executive team of industry veterans was at the helm, setting out to deliver on the promise of tackling the decades-long, ever-complex challenge of passwords—making them more secure and more convenient for people and organizations. This was my opportunity to integrate security by design, not just into the company's operations but throughout the entire product development life cycle. I would work alongside the leaders we had assembled to build something beautiful, strong and useful from the ground up. Three months after I joined LastPass, the company was the target of a sequenced set of two security attacks that spanned multiple months and threatened to derail everything we were working toward. But in the end, it didn't. In fact, the security incident acted as an accelerant for the people, process, technology, controls and infrastructure initiatives we already had planned to build while establishing a new company from scratch. In reflecting on this experience, I hope to offer something relatable in its honesty, strong in its lessons and useful to anyone tasked with rebuilding—not just systems, but trust. Here is how you can do it. From day one, I knew that security couldn't be a checklist—it had to be a blueprint. If you want to drive innovation while keeping trust intact, security, privacy and engineering must be tightly coupled. It's important to consciously embed security into every phase of decision-making and build the right teams around it—architecture, threat intel, governance, detection and response. We did it intentionally and with buy-in from across the company, leveraging the outcomes of decades of experience to understand where security can be a differentiator and become a business-enabler. As an example, and something unique among password manager providers, we built a dedicated threat intelligence team. With backgrounds in counterterrorism and financial services, this team monitors threats, delivers actionable insights and automates threat response to help protect our customers, data and company. It's not just a line of defense—it's a proactive, strategic asset that keeps us a step ahead. That's what it means to design with security at the core. Security and engineering won't click together on their own. You need to define how they'll collaborate—and then back it up with process, structure and, most importantly, the right people. We hired brilliant engineers from world-class companies and combined them with our existing team. The mix gave us a rare advantage: experience, new ways of working and belief in the mission. Hiring great people is step one. Step two is giving them the space, clarity and support to do their best work—especially under pressure. As a leader, your job is to make sure they know you trust them and to give them the resources they need to succeed. We built an entirely new development infrastructure in months because the team believed they could. And they were right. Transparency was our prerogative, and that's why we documented how we made LastPass secure. We have a trust center where we reflect, and we've also created a publicly available compliance center for close to real-time monitoring of LastPass systems and access to the latest certifications. We didn't just rebuild the platform; we reimagined it through the lens of the customer's experience. What did users need? Where were the friction points? What would make them feel safe, confident and in control? That's what drives decisions—from introducing stronger password recovery options and implementing secure sharing to strengthening master password protections and encrypting sensitive data fields. Through hackathons, we've started to integrate new features and functions like AI into our platforms. Under pressure, perfection is a luxury. Progress is a necessity. There were days when we moved fast because we had no other choice. But every sprint, every decision, every hard call got us closer. You need to be flexible, decisive and focused on what matters most—especially when time and attention are scarce resources. I'll never forget the conversations I had with dozens of CISOs from our customer base—internalizing their concerns and their wishes for the new LastPass. The first time a CISO asked me, 'How are you doing?', I was moved to tears. Imagine possessing such empathy and grace. This—the security and experience of the people behind our product—was our raison d'être, fueling us through every 20-hour workday. So here is my advice: Talk to your customers. Listen. Internalize what they're worried about. Let it shape your work. Then build something worthy of their trust. That's what we did. We started with a mission, built a blueprint for success and responded to adversity with momentum through our people, empowered and enabled by the support of our leadership. We've seized a once-in-a-lifetime opportunity. We have built something beautiful, strong and useful—and so can you. Forbes Technology Council is an invitation-only community for world-class CIOs, CTOs and technology executives. Do I qualify?
