Latest news with #GoldenRatio
Yahoo
4 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
India Today
07-07-2025
- Health
- India Today
Why do some faces appear more attractive than others? Science has the answer
Ever noticed how, in a crowd, some faces instantly grab your attention? It's not just makeup, lighting, or Instagram filters. While beauty is deeply personal and culturally shaped, scientists say that our brains are hardwired to find certain proportions, patterns, and symmetries more attractive. And at the heart of it lies a number that's been called "divine"-1.618, also known as the Golden ancient mathematical principle has fascinated artists, architects, and now even plastic surgeons. But can something as mysterious as beauty really boil down to geometry? Let's break it GOLDEN RATIO: A QUICK REFRESHER Phi, pronounced "Fye," equals approximately ratio appears repeatedly in nature spirals of seashells, sunflower seed patterns, and yes, even the human face. A face is said to be closer to "ideal beauty" when the:Length of the face divided by its width 1.6Distance between the eyes and mouth, eyes and eyebrows, etc., reflect this ratioIt's no surprise then, that faces perceived as attractive often reflect this harmonious STUDIES THAT BACK IT UP1. The London University StudyIn 2009, researchers at Royal Free and University College Medical School in London studied facial attractiveness using measurements and symmetry. They found that faces adhering more closely to the Golden Ratio were consistently rated more attractive by participants.2. University of Toronto, 2006Another study, published in the journal Vision Research, revealed that people's brains process symmetrical faces more quickly and positively-suggesting we're neurologically inclined to prefer them.3. Dr. Stephen Marquardt's Beauty MaskA maxillofacial surgeon, Dr. Marquardt created a "beauty mask" using the Golden Ratio to demonstrate ideal facial proportions. He tested this across ethnicities and cultures, and found that universally admired faces-from Angelina Jolie to classical sculptures-fit the pattern remarkably well. SYMMETRY: NATURE 'S SHORTCUT TO BEAUTY? While no human face is perfectly symmetrical, those with near symmetry are more likely to be perceived as attractive. That's because symmetry may act as a visual shorthand for genetic health and biological fitness.A 1997 study published in Proceedings of the Royal Society B found that people with more symmetrical faces reported fewer illnesses, linking facial symmetry with perceived and actual IS ALSO CULTURAL (AND EVOLVING)advertisementOf course, mathematical ratios aren't the whole story. Cultural ideals of beauty shift over time-from the curvier figures of the Renaissance to today's diverse beauty standards that celebrate individuality, scars, freckles, and unconventional in East Asia, large eyes and pale skin have historically been considered beautiful, while in parts of Africa and the Middle East, facial tattoos or fuller features are admired. Even in the West, imperfections can become iconic. Think Benedict Cumberbatch's asymmetrical face or Cindy Crawford's mole. What they "lack" in symmetry, they more than make up for in character, charisma, and confidence-which, many argue, are just as IS BEAUTY REALLY IN THE EYE OF THE BEHOLDER?In part, yes. But studies show that our brains are programmed to respond positively to certain mathematical and biological cues. Symmetry and the Golden Ratio offer a glimpse into the science of why we're drawn to some faces more than others-but that's only half the other half? It's shaped by culture, emotion, memory, and connection.- Ends
Mint
16-06-2025
- Business
- Mint
Stocks to buy for short term: From Swiggy to Biocon— Jigar Patel of Anand Rathi suggests 3 stock picks
Stocks to buy for the short term: Frontline indices, the Sensex and the Nifty 50, ended lower last week on profit booking amid heightened tensions between Israel and Iran, persisting concerns over US tariffs and stretched valuations. The Indian stock market may remain volatile this week, tracking news flows surrounding Israel and Iran and ahead of the US Fed policy decision on June 18. On the technical front, the Nifty 50 is now below 24,750, and experts see key support for the index at 24,450. "The index ended last week with over a 1 per cent loss. Notably, the reversal occurred precisely near the 161.8 per cent Golden Ratio extension, reinforcing it as a strong resistance. A break below 24,450 could extend the fall toward 24,000," said Jigar S. Patel, Senior Manager of Equity Research at Anand Rathi Share and Stock Brokers. "Traders are advised to stay cautious, avoid aggressive longs, and use relief rallies to lighten positions unless fresh momentum emerges. 25,200–25,300 is the key resistance zone, while 24,450–24,000 is the key support," Patel said. Jigar Patel recommends buying shares of Swiggy, Biocon and Route Mobile for the next two to three weeks. Swiggy recently broke out of a falling channel and touched ₹ 376, indicating bullish momentum. Over the past five sessions, it has seen mild correction but found support at the monthly R3 Camarilla pivot. Notably, the stock had consolidated between R3 and S3 pivots from March to May, a setup that often precedes strong directional moves. This technical structure suggests potential for further upside. "Consider long positions in the ₹ 355–345 zone, targeting ₹ 390. Maintain a stop loss at ₹ 330 on a daily closing basis," said Patel. Swiggy stock technical chart Biocon recently broke out of a consolidation zone between ₹ 330–345 and is now trading well above it, signalling renewed strength. On the monthly floor pivot, an inside value relationship between May and June (R1–S1) suggests potential for an explosive move. The breakout was supported by a volume surge and a breach of the short-term falling trendline, reinforcing bullish sentiment. Additionally, RSI held steady in the 40–50 range during consolidation and now hovers around 65. "Go long in the ₹ 356–350 range, targeting ₹ 390. Maintain a stop loss at ₹ 335 on a daily closing basis," Patel said. Biocon stock technical chart Recently, Route Mobile broke out after nearly a month of consolidation, accompanied by a significant surge in volume, indicating strong accumulation. What makes this consolidation phase notable is that it occurred within the R3–S3 zone of the monthly Camarilla pivots, establishing an Inside Value relationship. This setup forms when the current month's pivots are nested within the previous month's range, often signalling a potential breakout with strong directional bias. Adding to the bullish case, the daily RSI has consistently held above the 60 level and is now positioned at 71, reflecting strengthening momentum. "We recommend a buying opportunity in the ₹ 1,090-1,060 zone, with a target price of ₹ 1,220. Maintain a stop loss at ₹ 1,000 on a daily closing basis," said Patel. Route Mobile stock technical chart Read all market-related news here Read more stories by Nishant Kumar Disclaimer: This story is for educational purposes only. The views and recommendations above are those of individual analysts or broking companies, not Mint. We advise investors to check with certified experts before making any investment decisions, as market conditions can change rapidly, and circumstances may vary.
Scottish Sun
26-05-2025
- Entertainment
- Scottish Sun
Kate Moss fans stunned as supermodel ‘spotted at BBC Radio One's Big Weekend' – but all is not what it seems
KATE Moss fans were stunned when the supermodel was 'spotted at BBC Radio One's Big Weekend' - but all was not what it seems. Some of the biggest names in music headed to Sefton Park for the weekend, including Mel C, Tom Grennan, Lola Young and Natasha Bedingfield. 4 Kate Moss fans were stunned as supermodel 'spotted at BBC Radio One's Big Weekend' – but all is not what it seems Credit: Instagram 4 Super model Kate Moss at the first day of the Glastonbury Music Festival in 2005 Credit: WireImage - Getty But fans were even more dazzled by a famous celebrity that appeared in the crowd. Dressed in a black t-shirt, denim cut offs and cowboy boots - fans were convinced supermodel Kate Moss had turned up to enjoy the festival vibe. However, things were not as they seemed because the stunning beauty was in fact the lovely Denise Ohnona. Denise, 44, works as a lookalike for Kate Moss, who recently was found to have the most physically perfect face, according to the Golden Ratio theory. But even though, Denise uses her own name on TikTok which categorically states "I am not Kate Moss" - fans still couldn't believe it. After seeing Denise's post which showed her dancing at the festival, fans were still left baffled. "Wait is this not Kate Mosse!!" exclaimed one fan. "I refuse to believe this isn't Kate Moss !!" added another. One confused fan said: "The comments are saying that this isn't Kate Moss so I've watched the video 5 times and I'm absolutely baffled! "If this isn't Kate Moss, then who the hell is it and is she cashing in on this skill?!" Kate Moss is officially the most beautiful of all supermodels, according to science Denise explained: "I work as a lookalike but never get rich from it. I'm not actually Kate so don't get paid like Kate for jobs." But still fans were confused - despite being on Denise's actual account. "It is Kate Moss isn't it?" asked another. To which Denise once again replied: "No it's me." But the comments kept on coming with many still questioning if the video was really of the supermodel. "Wait is this Kate Moss?! I'm convinced it is" said another fan. And another cheekily suggested: "Maybe this is why we all think Kate Moss looks amazing for her age. "We've all just been spotting Denise out and about." Despite having worked as a lookalike for the glamorous supermodel since 2017, Denise has admitted she still struggles with self-esteem. The blonde beauty told Fabulous: 'For me, it is so so flattering that I even get to be a lookalike for Kate Moss. 'Personally I've never thought I was beautiful. I didn't like how I looked different. 'I had wide set eyes and still to this day I don't think I'm beautiful.' Meanwhile, Kate, 51, used to be a regular at Glastonbury— but her daughter Lila, 22, is now taking centre stage as the family representative. Lila has admitted that she raids her supermodel mum's wardrobe — to find outfits to wear at Glastonbury Festival. Kate was last seen attending Glastonbury back in 2023 when she was pictured watching Primal Scream from the side of the Pyramid Stage. 4 Denise on the runway during the Marine Serre Womenswear Fall/Winter 2024-2025 show as part of Paris Fashion Week Credit: Getty
Mint
19-05-2025
- Business
- Mint
Stocks to buy for short term: From Cyient to Tata Tech— Jigar Patel of Anand Rathi suggests 3 stock picks
Stocks to buy for short term: Easing geopolitical tensions, foreign capital inflow and better-than-expected Q4 earnings kept the Indian stock market up last week. The benchmark Nifty 50 rose over 4 per cent for the week ended May 16, reclaiming the 25,000 mark. On Monday, however, the index traded lacklustre in the morning session. Around 10:30 AM, it was 14 points up at 25,034. Jigar S. Patel, Senior Manager of Equity Research at Anand Rathi Share and Stock Brokers, pointed out that since the April 2025 low of 21,800, the Nifty 50 has surged nearly 3,300 points with minimal retracement — a strong uptrend powered by renewed FII inflows and calming global cues. Patel further said that on the technical front, a bullish golden crossover has been confirmed on the daily chart, where the 50-DEMA has crossed above the 200-DEMA — a long-term positive signal. However, Patel emphasised that such crossovers often see brief mean reversions before the larger trend resumes. He said currently, both moving averages lie between 23,500 and 23,800 — levels that may be retested if the market cools off. "The Nifty 50 is now testing the 161.8 per cent Fibonacci extension of the previous move — a classic golden ratio that could act as near-term resistance. With this, we expect 25,300 to act as an immediate hurdle. A failure to sustain above this level may trigger some profit-booking," said Patel. "On the downside, support is seen in the 24,800–24,500 zone. Traders are advised to tighten stop losses, avoid aggressive longs at current levels, and look for opportunities on dips to enter fresh positions," Patel said. Jigar Patel recommends buying shares of Cyient, Tata Technologies and JSW Energy for the next two to three weeks. Cyient is approaching a significant technical inflection point, where a convergence of multiple technical factors suggests a potential trend reversal. One of the most critical signals is the alignment with a 34-week time cycle—a key Fibonacci number often associated with major turning points in harmonic trading. This temporal synchronisation adds weight to the possibility of a directional change. Supporting this, Fibonacci ratio analysis of two corrective price legs—one falling 32.18 per cent (A to B) and the other 49.43 per cent (C to D)—reveals a compelling harmonic relationship. The ratio of 49.43/32.18 yields 1.536, which is close to the Golden Ratio of 1.618, while the inverse yields 0.651, approximating the key 0.618 level—both central to harmonic analysis. Further reinforcing this view is the price symmetry: the absolute drop from A to B is ₹ 778.75, while the drop from C to D is ₹ 1059.55, giving ratios of approximately 1.36 and 0.734, closely matching √1.618 (1.27) and √0.618 (0.786), respectively. These findings indicate a structurally sensitive zone where the price may stabilise or reverse. On the daily chart, the stock has completed a bullish inverse head and shoulders pattern and confirmed a breakout—a classic reversal signal in technical analysis. "Considering this strong confluence of time, price, and pattern structure, a long position is advisable in the ₹ 1,280– ₹ 1,300 range, targeting ₹ 1,600, with a stop loss at ₹ 1,150. The setup offers an attractive risk-reward ratio, underpinned by solid harmonic and structural evidence," said Patel. Cyient stock technical chart Tata Technologies is approaching a critical technical juncture marked by the confluence of key time cycles and Fibonacci ratios, suggesting a potential trend reversal. The ongoing setup aligns with a 35–36-week time cycle, which is closely related to the Fibonacci number 34—a level often linked to cyclical market turning points. Analysing the corrective structure, the stock witnessed a 30 per cent drop from point A to B, followed by a steeper 47.45 per cent correction from C to D. The ratio of these moves stands at 1.58, nearly matching the Golden Ratio (1.618), while the inverse, 0.632, closely approximates its reciprocal (0.618). Examining price symmetry, the decline from A to B amounted to ₹ 416.60, while the C–D leg corrected by ₹ 539, yielding a ratio of around 1.27, equivalent to the square root of 1.618. This move also aligns with the 0.786 retracement level, which is the square root of 0.618, enhancing the harmonic confluence. 'Given this strong technical setup, a long position is recommended in the ₹ 735– ₹ 750 zone, with an upside target of ₹ 825 and a stop loss at ₹ 695 on a daily closing basis,' said Patel. Tata Technologies stock technical chart JSW Energy has recently formed multiple bottoms in the ₹ 420– ₹ 460 range, indicating a strong support zone. This area also aligns with the 61.8 per cent Fibonacci retracement of the entire rally from February 2023 to September 2024, adding technical significance. Additionally, a bullish divergence is visible on the daily RSI, and the stock has broken a prevailing bear trendline, reinforcing the potential for upward momentum. "Based on this confluence of signals, a long position is recommended in the ₹ 500– ₹ 505 zone. The upside target is ₹ 575, with a stop loss placed below ₹ 475 on a daily closing basis to manage risk effectively," said Patel. JSW Energy stock technical chart Read all market-related news here Read more stories by Nishant Kumar Disclaimer: This story is for educational purposes only. The views and recommendations above are those of individual analysts or broking companies, not Mint. We advise investors to check with certified experts before making any investment decisions, as market conditions can change rapidly, and circumstances may vary.
