![]() The distances between line markers on the drawing are in good coincidence with the above description, as shown in from below the knee to the root of the penis is a quarter of the height of a man.from below the foot to below the knee is a quarter of the height of a man.the root of the penis is at half the height of a man.the length of the hand is one-tenth of the height of a man.the distance from the elbow to the armpit is one-eighth of the height of a man.the distance from the elbow to the tip of the hand is a quarter of the height of a man.from the breasts to the top of the head is a quarter of the height of a man.the maximum width of the shoulders is a quarter of the height of a man.from above the chest to the hairline is one-seventh of the height of a man.from above the chest to the top of the head is one-sixth of the height of a man.In the texts on the lower section of “Vitruvian Man”, Lines, segments, dots and scale drawn by da Vinci (red). There are four points marking the edges of two lines, AA′ and BB′ in Those markers and scale are superimposed as red lines in Lines marking the proportions about human body are drawn in “Vitruvian Man”, and there is a kind of a scale below the figure. Lines drawn by da Vinci (red) and a circle going through the top vertex of the 45°-rotated square (blue). It indicates that da Vinci really intended to introduce those additional conditions. Since the allowable range for the radius of the circle becomes much more restricted by the conditions (iii) and (iv), The circumference touches the fingertips at the height of the top of the head. ![]() The circumference touches the soles of the man standing upright The circle drawn by da Vinci has following additional properties, which may not have been described by Vitruvius, Then the conditions (i) and (ii) cannot fully determine the position and radius of the circle. However, the best position of the navel will be ambiguous,Īnd the circumference that touches fingertips and feet will depend on the angles of the arms and legs from the trunk of the body. The circumference should touch both fingertips and feet. However, no trace to support this assumption is found in the drawing.Įven if the result of this model shows good fit to the observed data, it is still difficult to justify the assumption.īy the way, the circle described by Vitruvius should satisfy the following conditons, (2 1/2 + 1) / 4 = 0.604, which is certainly closer to the measured value 0.606 ∼ 0.609 than the golden ratio 0.618. In this case, the radius of the sphere should have the value ] that the circle goes through the top vertex of the 45°-rotated square, as shown in Geometrical construction of the Vitruvian Man by Leonardo da Vinci Square and circle drawn by da Vinci (red) and a circle with the radus of golden ratio (blue) The radius of the circle drawn by da Vinci was not intended to be the golden ratio. It looks impossible to achieve the situation that the fingertip touches both the square and the golden-ratio circle When the “golden-ratio circle” is in contact with the base line of the square, the upper part of the circle should necessarily be located closely to the upper vertices of the square. The circle calculated with the golden ratio (0.618). However, such a condition could never be satisfied with The fingertip touches both the red circle and square drawn by da Vinci, when it is located at the hight of the top of the head. , where the square and circle drawn by da Vinci (red) and the circle calculated with the golden ratio (blue) are superimposed. ![]() The discrepancy in the “golden-ratio model” is more pronounced in The ratio was estimated at 0.606 ∼ 0.609, which is significantly smaller than the golden ratio 0.618. The image after the normalization is shown in The author has evaluated the radius of the circle for a normalized image, obtained by slight modification, where the figure intended to be square by da Vinci was adjusted to be square by linearly mapping the image with Adobe Photoshop. The “Vitruvian Man”, which is said to be drawn by To the side length of the square (= the height of a man) in The golden ratio is the proportion given by the numerical value: “Vitruvian Man” by Leonardo da Vinci and the golden ratio It is concluded that the ratio of the radius of the circle to the side length of the square was intended to be 137 / 225 = 0.6088 ![]() The drawing scheme of “Vitruvian Man” by Leonardo da Vinci has been analyzed. “Vitruvian Man” by Leonardo da Vinci and the Golden Ratio
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