Hidden Detail in Crotch Solves 500-Year-Old Leonardo Da Vinci Mystery
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
Hashtags
Try Our AI Features
Explore what Daily8 AI can do for you:
Comments
No comments yet...
Related Articles
Yahoo
an hour ago
- Yahoo
Thousands of cancer cases could be prevented with more breast removal surgeries
Thousands of breast cancer cases could potentially be prevented if more women were offered 'risk reducing' breast removal surgery, a study suggests. Breast removal surgery, also known as a mastectomy, is offered to treat breast cancer in some women. It can also be offered to women who are deemed to be high risk of the disease to prevent them from getting it in the first place. A study has found that if more women were given preventative mastectomies, then about 6,500 cases of breast cancer could be prevented each year. Risk-reducing mastectomies (RRM) are currently only offered to women with the BRCA1, BRCA2, PALB2 genes, experts said. But the new analysis suggests that some women with other genes linked to a higher risk of breast cancer – including ATM, CHEK2, RAD51C, RAD51D – who may also be at higher risk due to a number of other factors may benefit from RRM if they are assessed as having a high risk of disease. These other factors can include a family history of breast cancer, the number of children they have had, whether or not they breast fed and mammogram density. Women in the UK have an 11% chance of developing breast cancer across their lifetime. Medics can calculate a woman's risk of breast cancer using tools which combine the effect of various risk factors. This is your breast check reminder! Learn the signs and symptoms of breast — Breast Cancer Now (@BreastCancerNow) May 6, 2025 Researchers from Queen Mary University of London and the London School of Hygiene and Tropical Medicine (LSHTM) found that if health officials could identify all women aged 30 to 55 who have a 35% or higher risk of breast cancer, and they all went on to have RRM, then an estimated 6,538 breast cancer cases could be prevented in the UK each year. This is the equivalent of around 11% of the 59,000 women in the UK who are diagnosed with breast cancer each year. The academics point out that women who have one of the other genes linked to breast cancer, who may be at high risk of disease, could potentially be found by a mechanism called 'cascade testing' – where genetic tests are offered to family members of women who have been found to have these different genes linked to breast cancer. The economic evaluation study, published in the journal JAMA Oncology, concludes: 'Undergoing RRM appears cost-effective for women at 30-55 years with a lifetime BC-risk 35% (or more). 'The results could have significant clinical implications to expand access to RRM beyond BRCA1/BRCA2/PALB2 pathogenic variant carriers.' Corresponding author on the paper, Professor Ranjit Manchanda, professor of gynaecological oncology at Queen Mary and consultant gynaecological oncologist, said: 'We for the first time define the risk at which we should offer RRM. 'Our results could have significant clinical implications to expand access to mastectomy beyond those patients with known genetic susceptibility in high penetrance genes- BRCA1/ BRCA2/ PALB2 – who are traditionally offered this. 'This could potentially prevent can potentially prevent (around) 6500 breast cancer cases annually in UK women. 'We recommend that more research is carried out to evaluate the acceptability, uptake, and long-term outcomes of RRM among this group'. Dr Rosa Legood, associate professor in health economics at LSHTM, added: 'Undergoing RRM is cost-effective for women (aged) 30 to 55-years with a lifetime breast cancer risk of 35% or more. 'These results can support additional management options for personalised breast cancer risk prediction enabling more women at increased risk to access prevention.' Women deemed to be at high risk of breast cancer can also be offered regular screening and medication. Louise Grimsdell, Breast Cancer Now senior clinical nurse specialist, said: 'While this modelling provides valuable insights into the cost-effectiveness of risk-reducing mastectomy for women with a high risk of developing breast cancer, each individual must be offered all risk-management options that are suitable for them. 'Choosing to have risk-reducing surgery is a complex and deeply personal decision that comes with emotional and physical implications. 'So, it's vital women can consider all their options, including screening and risk-reducing medications, and are supported by their clinician to make an informed decision that's right for them. 'It's also crucial that the unacceptably long waits that far too many women who chose risk-reducing surgery are facing are urgently tackled.'
Yahoo
2 hours ago
- Yahoo
New study reaches landmark conclusion about impact of wind turbines on human health: 'Not a cause-and-effect relationship'
New study reaches landmark conclusion about impact of wind turbines on human health: 'Not a cause-and-effect relationship' A new peer-reviewed study from researchers at Poland's Adam Mickiewicz University has found no evidence that wind turbine noise causes mental harm, putting to rest a persistent and unsubstantiated claim that clean energy projects may be harming our health. Medical Xpress reported that the study measured brainwave activity in 45 university students exposed to different sounds — including traffic, wind turbines, and silence — without revealing the sources. Participants described the turbine noise as white noise and did not report it as any more stressful than city traffic. The researchers also found no measurable differences in brain activity, nor any signs of psychological harm, across the various sound environments. "Although these results cannot be generalized, they support the concept that the interlinkage between exposure to wind turbine noise and human cognitive functioning is not a cause-and-effect relationship," the authors wrote in the study, published in the journal Humanities and Social Sciences Communications. While they acknowledged that their research is not definitive on long-term exposure, they concluded that "wind turbine syndrome" — the conspiracy theory suggesting these sounds cause cancer or mental illness — has no scientific basis. This is reassuring news for consumers and communities. Wind turbines are among the most cost-effective sources of clean energy and can offer great economic and health benefits. They reduce dependence on dirty energy sources like oil and gas, helping to curb rising health risks tied to air pollution. They can also help stabilize public energy grids and lower utility costs for homeowners. Plus, by reducing the amount of heat-trapping air pollution the energy industry generates, we're working toward a safer, cleaner future for all of us. Studies like this help cut through misinformation that could dampen public reception to clean power sources. "This interpretation is compatible with previous findings showing social contexts, such as socialization and misinformation, as a moderator of the interlinkage between wind turbine noise and human functioning," the study authors wrote. A discussion on Reddit shared similar viewpoints on the topic. "Colleague of mine [used] to do community engagement," one commenter said. "Received lots of calls about how the wind turbines were making people in the area sick. She had to tell them that the newly built turbines hadn't actually been switched on yet. Not saying some people weren't having a reaction though as the mind can be a powerful tool (look up the Nocebo effect)." Do you worry about air pollution in your town? All the time Often Only sometimes Never Click your choice to see results and speak your mind. Join our free newsletter for weekly updates on the latest innovations improving our lives and shaping our future, and don't miss this cool list of easy ways to help yourself while helping the planet. Solve the daily Crossword
Fast Company
3 hours ago
- Fast Company
The time of day could impact your job interview
You landed a job interview: You've researched the company, reread the job listing, and practiced your talking points. But have you considered the importance of choosing the right time of day to interview? According to new research, when you interview might impact how well you do. In a study analyzing the timing and performance of Italian students in oral interviews—which are required to pass many classes at Italian universities—researchers found that the time of day had a big impact on students' likelihood of success. Researchers believe the study could shed light on successes and failures in other high-pressure situations, like job interviews. Researchers utilized a University of Messina database of interview-style exam results from October 2018 to February 2020. Data from more than 100,000 exams revealed that the rate of students who passed followed a bell curve that peaked between 11 a.m. and 1 p.m. and was much lower in the early morning and late afternoon. The research was inspired by a study that found judges are more lenient in their sentencing at the beginning of the court session or after meal breaks, says Carmelo Vicario, a neuroscientist at the University of Messina and lead author of the new study. After seeing the data on judicial rulings, Vicario says he was interested in discovering whether the same principle might apply to other fields, including education. 'This was, of course, a completely different field,' Vicario tells Fast Company. 'But we found this similarity.' Since the study analyzes existing data, rather than data from controlled trials, Vicario says he isn't able to confirm exactly why the middle of the day seems to be when students are most successful. Still, the researchers have a number of theories. For starters, since younger people tend to be night owls and older people tend to prefer the morning, the middle of the day might help mitigate the clash between these 'chronotypes,' or biological rhythms that impact how alert people are throughout the day. Between 11 a.m. and 1 p.m. could be a middle ground when both students and their professors are in their prime. This same mismatch between chronotypes could contribute to the difference in interview success during the hiring process for young workers being interviewed by more senior employees, adding to the bias that an estimated 36% have against Gen Z candidates, according to a recent ResumeBuilder survey. More than 80 genes regulate the circadian rhythms behind different chronotypes, and people consistently operating outside the hours that work with their circadian rhythm can experience issues with productivity, as well as health problems and work-related anxiety. To help overcome bias related to the time of day, experts have a few tips that can be applied to everything from exams to job interviews and beyond, such as offering flexible meeting hours and scheduling collaboration when both parties have high energy levels. 'By recognizing biological differences in how and when people work best—and making room for that diversity—leaders can reduce hidden bias, unlock untapped potential, and build more productive and inclusive teams,' Camilla Kring, a researcher who studies applied chronology, wrote in a recent article for Fast Company. Still, authors of the new study note that more research is needed to determine whether mismatched chronotypes are the hidden force behind varying interview success. 'Even this is a speculative interpretation,' Vicario says, noting his hope that this work will inspire future research that helps to pin down exactly why interviews in the middle of the day tend to go better. Vicario also hopes people will consider researching the impact of timing on decision-making in other high-pressure situations. 'When there's a kind of pressure, the influence of the time of the day can be stronger compared to when you have a large amount of time to evaluate the details of the situation,' Vicario says. 'Being aware [of timing's impact] can make decisions fairer.'
