https://www.sciencealert.com/hidden-detail-in-crotch-solves-a-500-year-old-leonardo-da-vinci-mystery
Vitruvian Man.
(Leonardo da Vinci/Wikimedia Commons/Public Domain)
To draw the Vitruvian Man in 1490 – an illustration of the 'ideal' human body – the Renaissance artist 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 decipher why da Vinci chose such specific proportions for the arms and legs.
As revealed in a paper published this year, a London dentist thinks he's solved the mystery at last.
Rory Mac Sweeney 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.
Vitruvian Man.
(Leonardo da Vinci/Wikimedia Commons/Public Domain)
To draw the Vitruvian Man in 1490 – an illustration of the 'ideal' human body – the Renaissance artist 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 decipher why da Vinci chose such specific proportions for the arms and legs.
As revealed in a paper published this year, a London dentist thinks he's solved the mystery at last.
Rory Mac Sweeney 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.
(Upscaled version of image from Mac Sweeney, J. Math. Arts, 2025)
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.
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.
(Mac Sweeney, J. Math. Arts, 2025)
Perhaps Mac Sweeney recognized the significance of that number because of a similar triangular principle used in dentistry since 1864.
Imagined on the human jaw, the Bonwill triangle dictates the optimal position for its function. Its ratio is also 1.633.
Mac Sweeney doesn't think that's a coincidence.
Perhaps Mac Sweeney recognized the significance of that number because of a similar triangular principle used in dentistry since 1864.
Imagined on the human jaw, the Bonwill triangle dictates the optimal position for its function. Its ratio is also 1.633.
Mac Sweeney doesn't think that's a coincidence.
(Mac Sweeney, J. Math. Arts, 2025)
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.
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 birth of modern Man
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