Trends:Leonardo da Vinci Patterns - Revision history

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	Examination supports that Vitruvian Man was drawn to represent the fractional measures put forth by Vitruvius and is not based on the golden ratio. As discussed on the Great Pyramid page, however, irrational numbers like Phi can be closely approximated with integer fractions. So while Vitruvian Man may produce a very well proportioned human body, it seems unlikely that the human form would be based on a system of halfs, 4ths, 6ths, 7ths, 8ths and 10ths when we find constant rates of fractal expansion in the proportions of other living organisms. Other studies and approaches to measuring the human body express it just as well or better in golden ratio, which is better aligned to the growth relationships found in nature. See the Face, Body and Hand/Foot pages for illustrations.		Examination supports that Vitruvian Man was drawn to represent the fractional measures put forth by Vitruvius and is not based on the golden ratio. As discussed on the Great Pyramid page, however, irrational numbers like Phi can be closely approximated with integer fractions. So while Vitruvian Man may produce a very well proportioned human body, it seems unlikely that the human form would be based on a system of halfs, 4ths, 6ths, 7ths, 8ths and 10ths when we find constant rates of fractal expansion in the proportions of other living organisms. Other studies and approaches to measuring the human body express it just as well or better in golden ratio, which is better aligned to the growth relationships found in nature. See the Face, Body and Hand/Foot pages for illustrations.
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	[[File:6-Da-Vinci-The-Last-Supper-Table-.jpg\|frame\|300 px\|Center of table is a golden ratio to its sides\|link=https://www.enterpriseplus.tools/images/d/d9/6-Da-Vinci-The-Last-Supper-Table-.jpg\|center]]		[[File:6-Da-Vinci-The-Last-Supper-Table-.jpg\|frame\|300 px\|Center of table is a golden ratio to its sides\|link=https://www.enterpriseplus.tools/images/d/d9/6-Da-Vinci-The-Last-Supper-Table-.jpg\|center]]
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		+	=== Da Vinci’s Mona Lisa and the Golden Ratio ===
		+	One of Da Vinci’s most famous paintings is “La Jaconde,” the Mona Lisa. This painting was begun in about 1503 and work on it continued for years. It has similar composition to “Christ as Savior of the World.” The application of the Divine proportion in this painting is the most subject to interpretation and debate. Unlike “The Last Supper” and “The Annunciation,” the Mona Lisa has few straight lines or architectural elements to use as references points in making a determination. It’s possible to find golden ratios in the Mona Lisa, but they’re not as definitive. If you do a Google search for Mona Lisa golden ratio you’ll also find some very creative interpretations of golden ratios in the Mona Lisa. Many of these are not easily supported as representing Da Vinci’s intent because their starting points, position and size are somewhat arbitrary and inconsistent.
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		+	There are, however, observations that can be made about the Mona Lisa. The image on the left below shows that golden ratios from the sides of the canvas. This approach reveals no golden ratios from the canvas edges that align with key elements of the composition. There may still be golden ratios here though. The width of her face is very close to a golden ratio of the width of the canvas. This is illustrated by the yellow rectangle of the same dimensions. In the image on the right, we see that her eye is rather precisely aligned with the center of the canvas. Golden ratio lines from the center of the painting to the sides of the canvas align nicely with the width of her hair. There may also be golden ratios in the vertical dimensions of the painting. As with the painting of Christ above, the most prominent elements of the composition are her head, the garment neck line and her arm. These also show golden ratios in their positioning. So, while this is not as definitive as the straight lines of architectural elements in other paintings, a reasonable case can be made that the Mona Lisa also embodies intentional golden ratio proportions in its composition. Given Da Vinci’s prior usage, it would not be unusual or unexpected for him to have applied it here as well.
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		+	[[File:1-Da-Vinci-Mona-Lisa-Golden-Ratio.jpg\|frame\|300 px\|Golden ratios from sides of canvas\|link=https://www.enterpriseplus.tools/images/7/79/1-Da-Vinci-Mona-Lisa-Golden-Ratio.jpg\|center]]
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		+	[[File:2-Da-Vinci-Mona-Lisa-Golden-Ratio-from-Center.jpg\|frame\|300 px\|Golden ratios from center of canvas\|link=https://www.enterpriseplus.tools/images/0/04/2-Da-Vinci-Mona-Lisa-Golden-Ratio-from-Center.jpg\|center]]
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		+
		+	=== Analysis of Da Vinci’s Vitruvian Man ===
		+	Another of Da Vinci’s most famous works is that of the Vitruvian Man, created around 1490. The official title of the drawing is “Le proporzioni del corpo umano secondo Vitruvio,” or “The proportions of the human body according to Vitruvius.”
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		+	Wikipedia states,
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		+	''"The drawing is based on the correlations of ideal human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise De Architectura. Vitruvius described the human figure as being the principal source of proportion among the Classical orders of architecture. Vitruvius determined that the ideal body should be eight heads high. Leonardo’s drawing is traditionally named in honor of the architect. This image demonstrates the blend of art and science during the Renaissance and provides the perfect example of Leonardo’s deep understanding of proportion."''
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		+	The Wikipedia article describes how Vitruvio measured the entire human body in integer fractions of the height of a man. Examination of the Vitruvian man illustration shows that the guide lines drawn by Da Vinci on the body appear to be based on integer fractions of the height, which is also equal to its width. The illustration below shows the height/width divided into 4ths, 5ths, 8ths and 10ths. This aligns with the guide lines drawn horizontally at the collar bone, chest, genitals and knee. They align horizontally with the guide lines drawn at the wrist, elbow and shoulder.
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		+	Examination supports that Vitruvian Man was drawn to represent the fractional measures put forth by Vitruvius and is not based on the golden ratio. As discussed on the Great Pyramid page, however, irrational numbers like Phi can be closely approximated with integer fractions. So while Vitruvian Man may produce a very well proportioned human body, it seems unlikely that the human form would be based on a system of halfs, 4ths, 6ths, 7ths, 8ths and 10ths when we find constant rates of fractal expansion in the proportions of other living organisms. Other studies and approaches to measuring the human body express it just as well or better in golden ratio, which is better aligned to the growth relationships found in nature. See the Face, Body and Hand/Foot pages for illustrations.

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	[[File:6-Leonardo-da-Vinci-The-Annunciation-Uffizi-Landscape-Detail.jpg\|frame\|300 px\|The peaks of the mountains in relation to the top of the canvas are in golden ratio proportion\|link=https://www.enterpriseplus.tools/images/c/ca/6-Leonardo-da-Vinci-The-Annunciation-Uffizi-Landscape-Detail.jpg\|center]]		[[File:6-Leonardo-da-Vinci-The-Annunciation-Uffizi-Landscape-Detail.jpg\|frame\|300 px\|The peaks of the mountains in relation to the top of the canvas are in golden ratio proportion\|link=https://www.enterpriseplus.tools/images/c/ca/6-Leonardo-da-Vinci-The-Annunciation-Uffizi-Landscape-Detail.jpg\|center]]
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		+	=== Da Vinci’s “The Last Supper” has many clear examples of Divine proportions ===
		+	Perhaps one of the best illustrations of its use is in “The Last Supper,” painted between 1494 and 1498. Various design and architectural features show very clear golden ratios. Some believe that even the positions of the disciples around the table were placed in divine proportions to Jesus.
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		+	[[File:1-The Last Supper by Leonardo da Vinci.png\|frame\|300 px\|The Last Supper by Leonardo da Vinci\|link=https://www.enterpriseplus.tools/images/7/7b/1-The_Last_Supper_by_Leonardo_da_Vinci.png\|center]]
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		+	[[File:2-Da-Vinci-The-Last-Supper-Sheild-Center.jpg\|frame\|300 px\|Last Supper detail showing golden ratios\|link=https://www.enterpriseplus.tools/images/3/33/2-Da-Vinci-The-Last-Supper-Sheild-Center.jpg\|center]]
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		+	[[File:3-Da-Vinci-The-Last-Supper-Shield-Center-Markings.jpg\|frame\|300 px\|Markings on the shield are golden ratios of its width\|link=https://www.enterpriseplus.tools/images/6/62/3-Da-Vinci-The-Last-Supper-Shield-Center-Markings.jpg\|center]]
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		+	[[File:4-Da-Vinci-The-Last-Supper-Sheild-Right.jpg\|frame\|300 px\|Small shield is a golden ratio of the width of its enclosure\|link=https://www.enterpriseplus.tools/images/c/c9/4-Da-Vinci-The-Last-Supper-Sheild-Right.jpg\|center]]
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		+	[[File:5-Da-Vinci-The-Last-Supper-Table-Window.jpg\|frame\|300 px\|From table top to ceiling, Jesus is at the midpoint and the top of the windows is at the golden ratio\|link=https://www.enterpriseplus.tools/images/a/ab/5-Da-Vinci-The-Last-Supper-Table-Window.jpg\|center]]
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		+	[[File:6-Da-Vinci-The-Last-Supper-Table-.jpg\|frame\|300 px\|Center of table is a golden ratio to its sides\|link=https://www.enterpriseplus.tools/images/d/d9/6-Da-Vinci-The-Last-Supper-Table-.jpg\|center]]
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← Older revision	Revision as of 13:12, 8 June 2023
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	+	== Humans not superior to animal world ==
	+	Leonardo never challenged the Christian belief that human beings were made in the image of God, nor the classical notion that man’s proportions and symmetries (albeit a white, middle-aged, able-bodied, European man) were beautiful and worthy of imitation in architecture and art. But he also never claimed other living beings were less beautiful, soulless, or lacked intelligence.
	+
	+	When comparing animals and humans – which he did often – animals often came out looking better. In one of his notes, Leonardo wrote, “Man has much power of discourse, which for the most part is vain and false; animals have but little, but it is useful and true, and a small truth is better than a great lie.” He often pointed out how much more powerful animals’ senses were, how much faster, stronger, more efficient and capable they were of performing remarkable feats, such as flight.
	+
	+	And animals were not nearly as “bestial” to one another as humans could be. “King of the animals – as thou hast described him – I should rather say king of the beasts,” he wrote. Leonardo lamented how human stomachs have become “a sepulcher for all animals” and how “our life is made by the death of others.”
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	+	== Leonardo the vegetarian? ==
	+	This passage, along with other writing about humans as killing machines and their esophagi as animal cemeteries, as well as a few comments by his contemporaries, have led many to believe that Leonardo was a vegetarian.
	+
	+	There is a 1515/6 letter by the Italian explorer Andrea Corsali to Giuliano de’ Medici that – in discussing how the Gujarati of India won’t eat anything with blood or allow hurt to come to any animate thing – says they are “like our Leonardo da Vinci.” Corsali, however, did not know Leonardo well, and the sentence is ambiguous; it could just mean that Leonardo never hurt animals or wanted to see them hurt.
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	+	Artist and biographer Giorgio Vasari (1511-1574) noted that Leonardo was famed for buying caged birds and setting them free and Leonardo did, in fact, advocate for eating Nature’s abundant senplici (“simples”), a term which seems to imply plant-based recipes. He pondered why Nature had created a world in which animals ate each other, but concluded it was because life is compelled to reproduce and endure, and consequently, Nature needed a way to keep numbers down.
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	+	[[File:Leonardo was captivated by birds’ power of flight.png\|frame\|300 px\|Leonardo was captivated by birds’ power of flight. Leonardo da Vinci/Wikimedia Commons.\|link=https://www.enterpriseplus.tools/images/2/21/Leonardo_was_captivated_by_birds%E2%80%99_power_of_flight.png\|center]]
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	+
	+	Nowhere in his writing, however, did he speak of not eating meat. His grocery lists have meat on them, although it is possible he was purchasing it for members of his household: students, servants, guests, animals.
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	+	Whether he ate a totally meat-free diet or not is unclear, but his love for animals is unquestionable. He lived with animals on a farm as a child and they were ever-present in his studio – likely cats and dogs, insects, birds and reptiles (some alive, some deceased). Leonardo studied them, depicted them, wrote about them and built machines – even war machines – inspired by them.
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	+	[[File:Leonardo’s ‘Allegory of a Dog and an Eagle’.png\|frame\|300 px\|Leonardo’s ‘Allegory of a Dog and an Eagle.’ Leonardo da Vinci/Royal Collection Trust.\|link=https://www.enterpriseplus.tools/images/e/ee/Leonardo%E2%80%99s_%E2%80%98Allegory_of_a_Dog_and_an_Eagle%E2%80%99.png\|center]]

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 == Frequently Asked Questions ==
 '''What Are Patterns?'''
 Pattern in art is one of the principles of art and are motifs (consisting of shapes, lines, and forms) that are repeated in arrangements, sequences, and groupings, whether ordered horizontally, vertically, or diagonally, or more irregular and random. Patterns can create a sense of rhythm or lead to a main focal point.
 '''What Are the Types of Pattern in Art?'''
 There are so-called man-made patterns and natural patterns, and they can be geometric or organic. Some patterns can consist of lines, curls, spirals, animal shapes, zigzags, dots, arabesques, circles, and squares, among many others.
 '''What Are the Principles of Art?'''
 The principles of art are so-called organizational principles, in other words, they determine how art elements (line, color, form, texture, space, shape, and value) will be applied in a visual composition. The art principles are namely, balance, harmony, unity, scale, proportion, emphasis, variety, pattern, repetition, movement, and rhythm.

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	Emphasis = This stresses certain significant aspects of a visual composition.		Emphasis = This stresses certain significant aspects of a visual composition.

−	The elements of art, on the other hand, include seven main parts, namely, shape, form, line, texture, color, space, and value. These are also understood as the “building blocks” of a visual composition of a specific artist.

		+	The elements of art, on the other hand, include seven main parts, namely, shape, form, line, texture, color, space, and value. These are also understood as the “building blocks” of a visual composition of a specific artist.

	'''Art Elements and their Characteristics'''		'''Art Elements and their Characteristics'''

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 ''July 7, 2014 by Gary Meisner''
 Leonardo Da Vinci has long been associated with the golden ratio. This association was reinforced in popular culture in 2003 by Dan Brown’s best selling book “The Da Vinci Code.” The plot has pivotal clues involving the golden ratio and Fibonacci series. In 2006, the public awareness of the association grew when the book was turned into a movie starring veteran actor Tom Hanks. Da Vinci’s association with the golden ratio, known in his time as the Divine proportion, runs much longer and deeper.
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 == Leonardo da Vinci saw in animals the ‘image of the world’ ==
-'' April 12, 2019, Arielle Saiber, Professor of Romance Languages and Literatures, Bowdoin College''
+''April 12, 2019, Arielle Saiber, Professor of Romance Languages and Literatures, Bowdoin College''
 About six months ago I stopped eating meat. I was teaching a graduate course at UCLA that investigated how Italian Renaissance writers conveyed their concepts about the human through writing about the nonhuman – plants, animals, objects, angels, demons, gods and God. As weeks passed, I found myself becoming more and more attuned to the nonhuman entities all around me, more aware of their vibrant lives. Cutting flowers for a short-lived bouquet seemed wrong; chewing on animal flesh became flat out impossible.
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 ''“By the ancients man has been called the world in miniature; and certainly this name is well bestowed, because, inasmuch as man is composed of earth, water, air, and fire, his body resembles that of the earth; and as man has in him bones — the supports and framework of his flesh —, the world has its rocks — the supports of the earth; as man has in him a pool of blood in which the lungs rise and fall in breathing, so the body of the earth has its ocean tide which likewise rises and falls … ”''

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−	=== ~~Golden ratios / Divine proportions appear~~ in ~~Renaissance art in paintings~~ of ~~religious importance =~~==	+
		+	= Animals in Painting =
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		+	== Leonardo da Vinci saw in animals the ‘image of the world’ ==
		+
		+	'' April 12, 2019, Arielle Saiber, Professor of Romance Languages and Literatures, Bowdoin College''
		+
		+	About six months ago I stopped eating meat. I was teaching a graduate course at UCLA that investigated how Italian Renaissance writers conveyed their concepts about the human through writing about the nonhuman – plants, animals, objects, angels, demons, gods and God. As weeks passed, I found myself becoming more and more attuned to the nonhuman entities all around me, more aware of their vibrant lives. Cutting flowers for a short-lived bouquet seemed wrong; chewing on animal flesh became flat out impossible.
		+
		+	Leonardo da Vinci was one of the authors we were studying in the course. Out of the thousands of pages comprising his 25 documented codices, known collectively as his “Notebooks,” we read passages describing the natural world and its inhabitants, and some of his philosophical maxims, fables and riddles. In a striking passage that introduces his “Treatise on Water,” he wrote:
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		+	''“By the ancients man has been called the world in miniature; and certainly this name is well bestowed, because, inasmuch as man is composed of earth, water, air, and fire, his body resembles that of the earth; and as man has in him bones — the supports and framework of his flesh —, the world has its rocks — the supports of the earth; as man has in him a pool of blood in which the lungs rise and fall in breathing, so the body of the earth has its ocean tide which likewise rises and falls … ”''
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-[[File:1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|frame|300 px|Golden ratios based on width of painting canvas, using Florence Museum image. Note alignment of vertical walls and courtyard entry.|link=https://www.enterpriseplus.tools/images/d/d7/1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|center]]
+[[File:2-Leonardo-da-Vincis-The-Annunciation-Uffizi-Left-Center.jpg|frame|300 px|Golden ratios from left side to precise center of canvas, which aligns with the mountain peak. Note positioning of angle face and wings, as well as position of the one tree in the background that’s different from all the others.|link=https://www.enterpriseplus.tools/images/4/42/2-Leonardo-da-Vincis-The-Annunciation-Uffizi-Left-Center.jpg|center]]
-[[File:1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|frame|300 px|Golden ratios based on width of painting canvas, using Florence Museum image. Note alignment of vertical walls and courtyard entry.|link=https://www.enterpriseplus.tools/images/d/d7/1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|center]]
+[[File:3-Leonardo-da-Vincis-The-Annunciation-divine-proportion.jpg|frame|300 px|The Annunciation|link=https://www.enterpriseplus.tools/images/f/f2/3-Leonardo-da-Vincis-The-Annunciation-divine-proportion.jpg|center]]
-[[File:1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|frame|300 px|Golden ratios based on width of painting canvas, using Florence Museum image. Note alignment of vertical walls and courtyard entry.|link=https://www.enterpriseplus.tools/images/d/d7/1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|center]]
+[[File:4-Leonardo-da-Vincis-The-Annunciation-golden-ratio-entry.jpg|frame|300 px|Variation on this image shows divine proportion position of the entry to the courtyard|link=https://www.enterpriseplus.tools/images/5/5e/4-Leonardo-da-Vincis-The-Annunciation-golden-ratio-entry.jpg|center]]
-[[File:1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|frame|300 px|Golden ratios based on width of painting canvas, using Florence Museum image. Note alignment of vertical walls and courtyard entry.|link=https://www.enterpriseplus.tools/images/d/d7/1-Leonardo-da-Vincis-The-Annunciation-Uffizi-Right.jpg|center]]
+[[File:5-da-vinci-the-annunciation-table.jpg|frame|300 px|The ornamentation of the table is at the golden mean of its width|link=https://www.enterpriseplus.tools/images/0/06/5-da-vinci-the-annunciation-table.jpg|center]]
-[[File:5-de-divina-proportione-architecture-B.jpg|300 px|link=https://www.enterpriseplus.tools/images/0/06/5-de-divina-proportione-architecture-B.jpg|alt=|left]]
+[[File:6-Leonardo-da-Vinci-The-Annunciation-Uffizi-Landscape-Detail.jpg|frame|300 px|The peaks of the mountains in relation to the top of the canvas are in golden ratio proportion|link=https://www.enterpriseplus.tools/images/c/ca/6-Leonardo-da-Vinci-The-Annunciation-Uffizi-Landscape-Detail.jpg|center]]