logo
Hidden Detail in Crotch Solves 500-Year-Old Leonardo Da Vinci Mystery

Hidden Detail in Crotch Solves 500-Year-Old Leonardo Da Vinci Mystery

Yahoo5 days ago
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
Orange background

Try Our AI Features

Explore what Daily8 AI can do for you:

Comments

No comments yet...

Related Articles

Long COVID Gene Variants: A Step Toward a Diagnostic Test?
Long COVID Gene Variants: A Step Toward a Diagnostic Test?

Medscape

time11 minutes ago

  • Medscape

Long COVID Gene Variants: A Step Toward a Diagnostic Test?

A large-scale global study has identified genetic variants that are risk factors for long COVID, a discovery that helps researchers better understand the biological systems involving the disease and one small, early step toward the elusive goal of developing a long COVID diagnostic test. International researchers with the Long COVID Host Genetics Initiative used data from 33 independent studies and 19 countries across North America, Europe, the Middle East, and Asia to analyze the genomes of nearly 16,000 patients with long COVID, representing populations from six genetic ancestries. Nearly 1.9 million controls were included in the genome-wide association study, a research method that scans complete sets of DNA to identify genetic variations associated with a specific trait or disease. Genetic variants found in the FOXP4 gene had a statistically significant risk linked to long COVID, the study, published in Nature Genetics , found. The FOXP4 gene is known to impact lung function, and its expression levels were higher in those with long COVID than in controls. In addition, the risk variants had a consistent effect across different ancestries. The researchers also found a causal relationship between a SARS-CoV-2 infection and long COVID and an additional causal risk between infections severe enough to require hospitalization and long COVID. Researchers also analyzed possible connections between variants associated with long COVID and those linked to other diseases and conditions. Scientists said the overall findings provided evidence that was consistent with long COVID research that suggests both individual genetic variants and environmental risk factors contribute to disease risk. The findings also provide genetic proof linking abnormal lung physiology and the development of long COVID, the authors concluded; however, they noted that long COVID symptoms are not only limited to lung function and may include fatigue and cognitive dysfunction as well. The study's co-author, Hanna Ollila, PhD, with the Institute for Molecular Medicine Finland, University of Helsinki, Helsinki, Finland, underscored that the newly discovered genetic variants were not predictive for clinical tests or personal disease risk. 'The findings from our study, and from genome-wide association studies in general, tell about biological mechanisms behind a disease. This can then help to understand the disease better. For example, is it a disease neuronal, immune, metabolic, and so on?' said Ollila, who is also a researcher with the Department of Anesthesia and Center for Genomic Medicine at Massachusetts General Hospital, Boston. There are still many steps between these types of discoveries and the development of a diagnostic test, she explained, since these types of genetic variants do not function like high-impact variants such as the BRCA mutations in breast cancer. 'In other words, they do not strongly predict whether someone will develop long COVID at the individual level,' Ollila said. 'Instead, they highlight the biological systems involved in the disease. In this case, our findings point to immune pathways related to lung function.' Ollila explained that genetics can guide diagnostic development by pointing to underlying mechanisms, which may then help identify biomarkers in blood or other tissues. These biomarkers could eventually contribute to diagnostic tools, but it is a process that takes time and collaboration and often depends on progress across several fields of research including imaging and clinical phenotyping. Researchers hope that when larger sample sizes become available for bigger studies, the analyses and understanding of the correlations will become more precise, bringing more understanding and clarity on genetic risk factors, biological mechanisms, and biomarkers that could someday help with disease diagnosis. 'We are likely still several years away, and possibly even a decade or more, from having a clinically useful diagnostic test based on genetic or biological markers for long COVID,' said Ollila. 'That said, progress is accelerating thanks to the growing number of well-characterized cohorts and international collaborations. While these genetic findings are not yet ready for clinical application, they are an important step toward understanding long COVID, its relationship with other diseases, and the disease mechanisms that modulate risk for long COVID.'

COVID-19 Made Our Brains Age Faster
COVID-19 Made Our Brains Age Faster

Yahoo

time2 hours ago

  • Yahoo

COVID-19 Made Our Brains Age Faster

Credit - Yuichiro Chino—Getty Images COVID-19 is leaving all kinds of legacies on our health, both on our bodies and our brains. In a study published July 22 in Nature Communications, researchers report that living through the pandemic aged our brains—whether or not you were infected with COVID-19. To investigate COVID-19's impact on the brain, researchers looked at brain scans from 1,000 people during and before the pandemic. They compared these to brain scans from other people taken during "normal" times as a model for typical brain aging. Led by Ali-Reza Mohammadi-Nejad from the University of Nottingham School of Medicine in the U.K., the researchers looked at measures like brain function, gray and white matter volume, a person's cognitive skills, and their chronological age. Gray matter is critical for memory, emotions, and movement, while white matter is essential for helping nerves transmit electrical signals. The pandemic-era brains aged about 5.5 months faster compared to the brains of those studied before the pandemic. The accelerated aging was documented in people who had COVID-19 infections as well as those who didn't, which strongly suggests that pandemic-related factors other than biological or virus-driven ones—like high stress—were also at work. In fact, the changes in gray and white matter were similar in people who were and were not infected. 'This finding was interesting and rather unexpected,' says Mohammadi-Nejad. Other studies have already shown that the COVID-19 virus can change the brain for the worse, but "we found that participants who simply lived through the pandemic period, regardless of infection, also showed signs of slightly accelerated brain aging. This highlights that the broader experience of the pandemic—including disruptions to daily life, stress, reduced social interactions, reduced activity, etc.,—may have had a measurable impact on brain health.' Read More: What to Know About the New COVID-19 Variant XFG The impact of the pandemic seemed to be greater in certain groups—notably men, the elderly, and people with more compromised health, lower educational status and income, or unstable housing. People with less stable employment had an average of five months of additional brain aging compared to those with higher employment status, while poorer health added about four months of increased brain age compared to better health. However, only people infected with COVID-19 showed drops in cognitive skills. But the fact that those who weren't infected during the pandemic also showed accelerated aging reflects the need to acknowledge the broader health effects of the pandemic beyond the obvious physical metrics on which doctors tend to focus. 'Brain health can be influenced by everyday life activities, and major societal disruptions—like those experienced during the pandemic—can leave a mark even in healthy individuals,' Mohammadi-Nejad says. 'This adds to our understanding of public health by reinforcing the importance of considering mental, cognitive, and social well-being alongside traditional physical health indicators during future crisis-response planning.' While the study did not explore specific ways to address brain aging, he says that strategies known to maintain brain health, such as a healthy diet, exercise, adequate sleep, and social and cognitive interactions are important, especially in the context of stressful circumstances such as a pandemic. 'Whether these can reverse the specific changes we observed remains to be studied,' he says. Contact us at letters@ Solve the daily Crossword

How Myeloma Plays Hide and Seek With CAR T Cells
How Myeloma Plays Hide and Seek With CAR T Cells

Medscape

time3 hours ago

  • Medscape

How Myeloma Plays Hide and Seek With CAR T Cells

TOPLINE: G protein-coupled receptor, class C, group 5, member D (GPRC5D) loss after chimeric antigen receptor (CAR) T-cell therapy in multiple myeloma (MM) occurs through biallelic genetic inactivation and hypermethylation-driven epigenetic silencing. Among 10 patients who relapsed, eight showed GPRC5D loss, while two had mixed expression. METHODOLOGY: Researchers conducted whole-genome sequencing (WGS) and whole-genome bisulfite sequencing (WGBS) analysis on MM samples from 10 patients who relapsed after GPRC5D CAR T-cell therapy. Analysis included CD138+ MM cells isolated from bone marrow samples with purity exceeding 80%, with tumor samples sequenced at 100× coverage and matched normal samples at 30× coverage. Investigators performed targeted bisulfite sequencing to evaluate methylation status of GPRC5D regulatory regions across seven MM cell lines, with library construction and sequencing conducted by specialized institutes. Patient characteristics included median age of 57.5 years (range, 44-66 years), equal gender distribution, and 90% having high-risk cytogenetic abnormalities. TAKEAWAY: Genetic alterations were identified in three cases: one with homozygous deletion in GPRC5D gene, another with biallelic loss in regulatory regions, and a third with homozygous deletions in both TNFRSF17 and GPRC5D after sequential anti-B-cell maturation antigen and anti-GPRC5D CAR T-cell therapies. Multiple hypermethylation sites were present in transcriptional regulatory elements of GPRC5D gene in five posttreatment MM samples, with no genetic changes detected at GPRC5D locus in seven cases. GPRC5D expression showed inverse correlation with methylation levels in regulatory regions of MM cell lines, with azacitidine treatment inducing GPRC5D messenger RNA and protein expression in hypermethylated MM cell lines. All 10 patients achieved complete response or better as best response with median time to best response of 2.5 months (range, 0.5-15.3 months), though median time to disease progression was 15.9 months (range, 3.0-26.5 months). IN PRACTICE: 'Our findings highlight that biallelic genetic inactivation and hypermethylation-driven epigenetic silencing are key mechanisms contributing to GPRC5D loss and treatment resistance,' wrote the authors of the study. SOURCE: The study was led by Mingshan Niu, Blood Diseases Institute, Xuzhou Medical University in Xuzhou, China. It was published online in Blood. LIMITATIONS: According to the authors, the structural variant deletions on chromosomes may be missed by 100× WGS in patients with a clone size less than 20%. The limit of detection for quantitative polymerase chain reaction ranged from 16 to 50 copies per reaction, indicating sensitivity limitations of these detection methods. Additionally, genetic alterations in the GPRC5D locus could either be acquired after CAR T-cell therapy or selected from preexisting clones, necessitating more sensitive detection methods for dynamic monitoring. DISCLOSURES: The research received support from the National Natural Science Foundation of China (82270181) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (21KJA320005). The authors reported having no relevant conflicts of interest. This article was created using several editorial tools, including AI, as part of the process. Human editors reviewed this content before publication.

DOWNLOAD THE APP

Get Started Now: Download the App

Ready to dive into a world of global content with local flavor? Download Daily8 app today from your preferred app store and start exploring.
app-storeplay-store