Body proportions
While there is significant variation in anatomical proportions between people, there are many references to body proportions that are intended to be canonical, either in art, measurement, or medicine.
In measurement, body proportions are often used to relate two or more measurements based on the body. A cubit, for instance, is supposed to be six palms. While convenient, these ratios may not reflect the physiognomic variation of the individuals using them.
Similarly, in art, body proportions are the study of relation of human or animal body parts to each other and to the whole. These ratios are used in veristic depictions of the figure, and also become part of an aesthetic canon within a culture.
Basics of human proportions
It is important in figure drawing to draw the human figure in proportion. Though there are subtle differences between individuals, human proportions fit within a fairly standard range, though artists have historically tried to create idealised standards, which have varied considerably over different periods and regions. In modern figure drawing, the basic unit of measurement is the 'head', which is the distance from the top of the head to the chin. This unit of measurement is reasonably standard, and has long been used by artists to establish the proportions of the human figure. Ancient Egyptian art used a canon of proportion based on the "fist", measured across the knuckles, with 18 fists from the ground to the hairline on the forehead. This was already established by the Narmer Palette from about the 31st century BC, and remained in use until at least the conquest by Alexander the Great some 3,000 years later.[1]
The proportions used in figure drawing are:[citation needed]
- An average person, is generally 7-and-a-half heads tall (including the head).
- An ideal figure, used when aiming for an impression of nobility or grace, is drawn at 8 heads tall.
- A heroic figure, used in the heroic for the depiction of gods and superheroes, is eight-and-a-half heads tall. Most of the additional length comes from a bigger chest and longer legs.
Western ideal
Leg-to-body ratio
A study using Polish participants by Sorokowski found 5% longer legs than an individual used as a reference was considered most attractive.[5] The study concluded this preference might stem from the influence of leggy runway models.[6] The Sorokowski study was criticized for using a picture of the same person with digitally altered leg lengths which Marco Bertamini felt were unrealistic.[7]
Another study using British and American participants, found "mid-ranging" leg-to-body ratios to be most ideal.[8]
A study by Swami et al. of American men and women showed a preference for men with legs as long as the rest of their body and women with 40% longer legs than the rest of their body[9] The researcher concluded that this preference might be influenced by American culture where long leg women are portrayed as more attractive.[9] The Swami et al. study was criticized for using a picture of the same person with digitally altered leg lengths which Marco Bertamini felt were unrealistic.[7] Bertamini also criticized the Swami study for only changing the leg length while keeping the arm length constant.[7] Bertamini's own study which used stick figures mirrored Swami's study, however, by finding a preference for leggier women.[7]
Muscle men and thin women
A 1999 study found that "the (action) figures have grown much more muscular over time, with many contemporary figures far exceeding the muscularity of even the largest human bodybuilders," reflecting an American cultural ideal of a super muscular man.[10] Also, female dolls reflect the cultural ideal of thinness in women.[10]
Japanese ideal
Japanese ideals for body proportions differ from Western ideals. The most prominent example of this is moe, characteristics of which include large eyes, small noses, tall irises[clarification needed], thin limbs, large heads, and neotenized faces.[11] Manga characters are usually sized to be 5.7 to 6.5 heads tall.[11][12][13] Another example of the Japanese ideal is the concept of the gracilized man: in contemporary Japanese society, bishōnen, literally "beautiful boys", are "delicate", "svelte" and "beautiful" males who are drawn to appeal to "adolescent girls".[14]
Leonardo da Vinci
Leonardo da Vinci believed that the ideal human proportions were governed by the harmonious proportions that he believed governed the universe[15] such that the ideal man would fit cleanly into a circle as in his famed "Vitruvian man" drawing.[15]
Examples of Body Proportions Referenced in Art and Architecture
Proportion is the relation between elements and a whole. Historically that relation has valued symmetry. “Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. Without symmetry and proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members as in the case of those of a well shaped man. —Vitruvius,[1] The Ten Books of Architecture (III, Ch. 1)” A Fibonacci spiral, created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling shown above – see golden spiral A tiling with squares whose sides are successive Fibonacci numbers in length
In architecture the whole is not just a building but the set and setting of the site. The things that make a building and its site "well shaped" include the orientation of the site and the buildings on it to the features of the grounds on which it is situated. Light, shade, wind, elevation, choice of materials, all should relate to a standard and say what is it that makes it what it is, and what is it that makes it not something else.
Vitruvus thought of proportion as ordered, especially architecturally in terms of unit fractions[2] such as those used in the Greek Orders of Architecture.[3]
Pythagorus
Going back to the Pythagoreans there is an idea that proportions should be related to standards and that the more general and formulaic the standards the better. This idea that there should be beauty and elegance evidenced by a skillful composition of well understood elements underlies mathematics in general and in a sense all the architectural modulors of design as well.
Body Proportions as Standards of Measure
The classical standards are a series of paired opposites designed to expand the dimensional constraints of the harmony and proportion. In the Greek ideal Vitruvus addresses they are similarity, difference, motion, rest, number, sequence and consequence.
These are incorporated in good architectural design as philosophical categorization; what similarity is of the essence that makes it what it is, and what difference is it that makes it not something else? Is the size of a column or an arch related just to the structural load it bears or more broadly to the presence and purpose of the space itself?
The standard of motion originally referred to encompassing change but has now been expanded to buildings whose kinetic mechanisms may actually determine change depend upon harmonies of wind, humidity, temperature, sound, light, time of day or night, and previous cycles of change.
The stability victim of inflicted madness is questionable architectural standard of the universal set of proportions references the totality of the built environment so that even as it changes it does so in an ongoing and continuous process that can be measured, weighed, and judged as to its orderly harmony. Scribes had been using unit fractions for their calculations at least since the time of the Egyptian Mathematical Leather Roll and Rhind Mathematical Papyrus[4] in Egypt and the Epic of Gilgamesh[5] in Mesopotamia.
Inscription Grids
One example of symmetry might be found in the inscription grids[6] of the Egyptians which were based on parts of the body and their symmetrical relation to each other, fingers, palms, hands, feet, cubits, etc.; Multiples of body proportions would be found in the arrangements of fields and in the buildings people lived in.[7]
A cubit could be divided into fingers, palms, hands and so could a foot, or a multiple of a foot. Special units related to feet as the hypotenuse of a 3/4/5 triangle with one side a foot were named remen and introduced into the proportional system very early on. Curves were also defined in a similar manner and used by architects in their design of arches and other building elements.
Precursors to the Greek Orders of Architecture
Generally for the Egyptians, Greeks, and Romans the goal of a proportional system began with inscription grids based on body measures and was from there extended to include agricultural and architectural standards such as similarity, and difference, geographical proportions with a sense of motion, as fast, slow or at rest as covering a given distance in a given time according to certain expectations of a proper relation between number and sequence taken all together to produce as a consequence a well ordered sense of symmetry, coherence and harmony, especially among the elements of a building, property or realm.
These proportional elements were used by the Persians, Greeks, Phoenicians and Romans, in laying out cities, stadiums, roads, processional ways, public buildings, ports, various areas for crops and grazing beasts of burden, so as to arrange the city as well as the building to be well proportioned,[8][9]
Egyptian Orders of Architecture
Going back in time the same logic applied to the Pyramids of Egypt, the Hanging Gardens of Babylon, the Mortuary Temple of Hatshepset, the Temple of Solomon, the Treasury of Athens, the Parthenon, and the Cathedrals and Mosques and Corporate Towers.
Greek Orders of Architecture
The frieze and architrave vary from 3/4:1/2 in the Doric style to 5/8:5/8 in the Ionic and Corinthian styles. Capitals are 1/2 in all styles except Corinthian which is 3/4. The shaft width is always 5/6 at the top. Column shaft heights are Tuscan 7, Doric 8, Ionic 9 and Corinthian 10. Column bases are always 1/2. In the Pedestal, caps are always 1/4, dies are 8/6 and bases are 3/4. In the quarter of the column entasis, Tuscan styles are 9/4, Doric are 10/4, Ionic are 11/4 and Corinthian columns are 12/4.
Having established the column proportions we move on to its arcade which may be regular with a single element at a spacing of 33⁄4 D, coupled with two elements at 11⁄3 D spaced 5 D, or alternating at 33⁄4 spaced 61⁄4 D. Variations include adding a series of arches between column cap and entablature in the Renaissance style Arcade. Exterior door widths W, have trim 1/5 W for exterior doors and 1/6 W for interior doors. Door heights a re 1 D less than column heights. Anciently if a door is two cubits or between 36" and 42" wide, then its trim is between a fist and a span in width. Proportioned vs dimensioned modules
The Greek classical orders are all proportioned rather than dimensioned or measured modules and this is because the earliest modules were not based on body parts and their spans (fingers, palms, hands, feet, remen, cubits, ells, yards, paces and fathoms, which became standardized for bricks and boards before the time of the Greeks) but rather column diameters and the widths of arcades and fenestrations.
Typically one set of column diameter modules used for casework and architectural moldings by the Egyptians, Romans and English is based on the proportions of the palm and the finger, while another less delicate module used for door and window trim, tile work, and roofing in Mesopotamia and Greece is based on the proportions of the hand and the thumb. Board modules tend to round down for planing and finishing while masonry tends to round down for mortar. Fabric, carpet and rugs tend to be manufactured in feet, yards and ells.
Palladian or Greek Revival Architecture
In Palladian or Greek Revival architecture as in Jeffersonian architecture, modern modular dimensional systems based on the golden ratio and other pleasing proportional and dimensional relationships begin to influence the design as with the modules of the volute. One interface between proportion and dimension is the Egyptian inscription grid. Grid coordinates can be used for things like unit rise and run. Architectural practice has often used proportional systems to generate or constrain the forms considered suitable for inclusion in a building. In almost every building tradition there is a system of mathematical relations which governs the relationships between aspects of the design. These systems of proportion are often quite simple; whole number ratios or incommensurable ratios (such as the vesica piscis or the golden ratio)which were determined using geometrical methods.
Sacred proportions
Among the Cistercians, Gothic, Renaissance, Egyptian, Semitic, Babylonian, Arab, Greek and Roman traditions; the human harmonic proportions, geocommensurate earth measures and cosmological/astronomical proportions and orientations, were combined as a sense of what was right and proper in sacred geometry (the vesica piscis), pentagram, golden ratio, and small whole-number ratios were all applied using the ratios of body measures as part of the practice of architectural design.
In the design of European cathedrals the necessary engineering to keep the structures from falling down gradually began to take precedence over or at least to have an influence on aesthetic proportions. Other concerns were symbolic astronomical references such as the towers of the Sun and Moon at Chartres and references to the various astrological and alchemical relationships being discovered by the natural philosophers and sages of the renaissance.
Body Measures used in Agriculture, Commerce and Navigation
Body measures of feet and paces extended to agricultural measures of yards and rods eventually extended still further to stadia and minutes of march. The Egyptian Aroura or thousand, Greek mia chilios, Roman Mille passus, became the Myle of medieval western Europe. West of the Rhine palm based Roman feet or pes measured Roman archs and architecture while East of the Maine hand based Greek feet or pous mia chillioi influenced eastern Europe with its Gothic arches and architecture. In Frankfurt, Germany which once separated Havover from Bavaria on a north south axis and West Prussia from East Prussia along the line of the Rhine foot measures of 285 mm and a meille of 1/16 degree are common whereas to the East its 308.4 mm and 1/15 meille and to the west 296 mm and sometimes to the south near Austria and the Danube 1/10 meille. Today in the Western hemisphere the foot is longer than the foote because of the researches of Galileo, Gabriel Mouton, Newton and others into the period of a seconds pendulum.
Body Measures as the basis of Proportional Systems
One aspect of proportional systems is to make them as universally applicable as possible, not just to one application but as a universal ideal statement of the proper proportions. There is a relationship between length and width and height; between length and area and between area and volume. Doors and windows are fenestrated. Fenestration is important so that the negative area of openings has a relation to the area of walls. Plans are reflected in sections and elevations. Themes are developed which spin off and relate to but expand upon the themes found in other buildings. Often there is a symbolic sacred geometry which goes outside the proportions of the building to relate to the observations of the beauty of nature and its proportions in time and space and the elements of natural philosophy.
Pleasing proportions - Body Measures as providing as sense of Human or Municipal Scale
Architects observe that buildings which scale down to dimensions humans can relate to and scale up through distances humans can travel as a procession of revelations which may sometimes invoke closure, or glimpses of views that go beyond any encompassing framework and thus suggest to the observer that there is something more besides, invoking wonder and awe draw people in.
Thomas Jefferson wrote of how the substantive scale of public buildings made a statement of government stability and gave a nation consequence. The Casinos of Las Vegas and the underwater hotels of Dubai are all competing to be the tallest, the biggest, the brightest, the most exciting to get international trade to come there and do business. In other words the modern business ethos is to be out of proportion, overscaling all the competition.
Part of the practice of feng shui is a proportional system based on the double tatami mat. Feng Shui also includes within it the ideas of cosmic orientation and ordering, as do most systems of "Sacred Proportions". Harmony and proportion as sacred geometry
Sacred geometry has the same arrangement of elements found in compositions of music and nature at its finest incorporating light and shadow, sound and silence, texture and smoothness, mass and airy lightness, as in a forest glade where the leaves move gently on the wind or a sparkle of metal catches the eye as a ripple of water on a pond.
The architectural foot as a reference to the human body was incorporated in architectural standards in Mesopotamia, Egypt, Greece, Rome and Europe. Common multiples of a foot in buildings tend to be decimal or octal and this affects the modulars used in building materials. Elsewhere, it is a multiple of the palm, hand, or finger that is the primary referent. Feet were usually divided into palms or hands, multiples of which were also remen and cubits.
The first known foot referenced as a standard was from Sumer, where a rod at the feet of a statue of Gudea of Lagash from around 2575 BC is divided into a foot and other units. Egyptian foot units have the same length as Mesopotamian foot units, but are divided into palms rather than hands converting the proportional divisions from sexagesimal to septenary units. In both cases feet are further subdivided into digits.
In Ancient Greece, there are several different foot standards generally referred to in the literature as short, median and long, which give rise to the different architectural styles known as Ionic and Doric in discussions of the classical orders of architecture. The Roman foot or pes is divided into digitus, uncia and palmus, which are incorporated into the Corinthian style.
Some of the earliest records of the use of the foot come from the Persian Gulf bordered by India (Meluhha), Pakistan, Balochistan, Oman (Makkan), Iran, Iraq, Kuwait, Bahrain (Dilmun), the United Arab Emirates and Saudi Arabia where in Persian architecture it is a sub division of the Great circle of the earth into 360 degrees. In Egypt, one degree was 10 Itrw or River journeys. In Greece a degree was 60 Mia chillioi or thousands and comprised 600 stadia, with one stadion divided into 600 pous or feet. In Rome a degree was 75 Mille Passus or 1000 passus. Thus the degree division was 111 km and the stadion 185 m. One nautical mile was 10 stadia or 6000 feet. The incorporation of proportions which relate the building to the earth it stands on are called sacred geometry.
Vitruvus
Vitruvus described as the principal source of proportion among the orders of proportion of the human figure. . Da Vinci Vitruve Luc Viatour.jpg
According to Leonardo's notes in the accompanying text, written in mirror writing, it was made as a study of the proportions of the (male) human body as described in a treatise by the Ancient Roman architect Vitruvi\us, who wrote that in the human body
a palm is the width of four fingers or three inches a foot is the width of four palms and is 36 fingers or 12 inches a cubit is the width of six palms a man's height is four cubits and 24 palms a pace is four cubits or five feet the length of a man's outspread arms is equal to his height the distance from the hairline to the bottom of the chin is one-tenth of a man's height the distance from the top of the head to the bottom of the chin is one-eighth of a man's height the maximum width of the shoulders is a quarter of a man's height the distance from the elbow to the tip of the hand is one-fifth of a man's height the distance from the elbow to the armpit is one-eighth of a man's height the length of the hand is one-tenth of a man's height the distance from the bottom of the chin to the nose is one-third of the length of the head the distance from the hairline to the eyebrows is one-third of the length of the face the length of the ear is one-third of the length of the face
Leonardo is clearly illustrating Vitruvius' De architectura 3.1.3 which reads
"The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square."
Though he was certainly aware of the work of Pythagoras, it does not appear that he took the harmonic divisions of the octave as being relevant to the disposition of form, preferring simpler whole-number ratios to describe proportions. However, beyond the writings of Vitruvius, it seems likely that the ancient Greeks and Romans would occasionally use proportions derived from the golden ratio (most famously, in the Parthenon of Athens), and the Pythagorean divisions of the octave. These are found in the Rhynd papyrus 16. Care should be taken in reading too much into this, however, while simple geometric transformations can quite readily produce these proportions, the Egyptian were quite good at expressing arithmetic and geometric series as unit fractions. While, it is possible that the originators of the design may not have been aware of the particular proportions they were generating as they worked, it's more likely that the methods of construction using diagonals and curves would have taught them something.
The Biblical proportions of Solomons temple caught the attention of both architects and scientists, who from a very early time began incorporating them into the architecture of cathedrals and other sacred geometry.
Regarding the Pythagorean divisions of the octave mentioned above, these are a set of whole number ratios (based on core ratios of 1:2 (octave), 2:3 (fifth) and 3:4 (fourth)) which form the Pythagorean tuning. These proportions were thought to have a recognisable harmonic significance, regardless of whether they were perceived visually or auditorially, reflecting the Pythagorean idea that all things were numbers. Renaissance orders
The Renaissance tried to extract and codify the system of proportions in the orders as used by the ancients, believing that with analysis a mathematically absolute ideal of beauty would emerge. Brunelleschi in particular studied interactions of perspective with the perception of proportion (as understood by the ancients). This focus on the perception of harmony was somewhat of a break from the Pythagorean ideal of numbers controlling all things.
Leonardo da Vinci's Vitruvian Man is an example of a Renaissance codification of the Vitruvian view of the proportions of man. Divina proportione took the idea of the golden ratio and introduced it to the Renaissance architects. Both Palladio and Alberti produced proportional systems for classically based architecture.
Alberti's system was based on the Pythagorean divisions of the octave. It grouped the small whole-number proportions into 3 groups, short (1:1, 2:3, 3:4), medium (1:2, 4:9, 9:16) and long (1:3, 3:8, 1:4).
Palladio's system was based on similar proportions with the addition of the square root of 2 into the mix. 1:1, 1:1.414..., 3:4, 2:3, 3:5.[10]
The work of de Chambray, Desgodetz and Perrault [11] eventually demonstrated that classical buildings had reference to standards of proportion that came directly from the original sense of the word geometry, the measure of the earth and its division into degrees, miles, stadia, cords, rods, paces, yards, feet, hands, palms and fingers Le modulor
Based on apparently arbitrary proportions of an "ideal man" (possibly Le Corbusier himself) combined with the golden ratio and Vitruvian Man, Le Modulor was never popularly adopted among architects, but the system's graphic of the stylised man with one upraised arm is widely recognised and powerful. Anti-Modernists (Langhein, 2005) claim the modulor is not well suited to introduce proportion and pattern into architecture, to improve its form qualities (gestalt pragnance) and introduce shape grammar in design in building. However, through its application in the design of some of the last century's most beautifully proportioned and harmonic buildings (Le Corbusier: Architect of the Twentieth Century, Kenneth Frampton, 2002) Le Corbusier's work strongly disputes this.
The plastic number
The plastic number is of interest primarily for its method of genesis. Its creator, Hans van der Laan, performed experiments on human subjects to attempt to discover the limits of human beings ability to perceive relationships between objects. From these discovered limits he extrapolated a system of proportions (the particular set he chose are quite close to the Pythagorean divisions of the octave). The range of scales over which the plastic number is considered functional is limited, so it is possible to construct a set of all proportional forms within it. The plastic number has not been widely adopted by practicing architects.
Design using proportion
Design by the use of architectural proportion differs from space planning using benchmarks for the sizes of spaces. In modern architecture proportions are of little interest so long as there is enough room for a given function in a given space. Many Cad programs use blocks or objects which have the modulor sizes manufacturers have determined best suit their production. These differ depending on whether the materials have structural constraints or are designed for a particulor function. For example: Pre built cabinets generally have standard dimensions based on a 3" modulor. The spacing of joists for modulor 8' plywood is based on even divisions of a sheet. Ceiling tiles are generally based on a 2'x2' modulor and floor tiles a 1'x1' modular.
What would be different if they were based on on non modulor architectual proportions such as those found in the Greek Orders of Architecture and Medieval cathedrals is more dependence of curves and sections of curves that have harmonic relationships with other elements and break down to a human scale.Rktect 15:17, 16 July 2007 (UTC)
Remen as a Proportion to other units
The proportion of foot to remen can be either 4:5 making it the hypotenuse or 3:4 making it the side of a right triangle. If the remen is the hypotenuse of a 3:4:5 triangle then the foot is one side and the quarter another so the proportions are 3:4 quarter to foot, 4:5 foot to remen and 3:5 quarter to Remen. The quarter is 1/4 yard. The foot is 1/3 yard. The remen is
The remen may also be the side of a square whose diagonal is a cubit The proportion of remen to cubit is 4:5
- The proportion of palm to remen is 1:5
- The proportion of hand to remen is 1:4
- The proportion of palm to foot is 1:4
- The proportion of hand to foot is 1:3
The table below demonstrates a harmonious system of proportion much like the musical scales, with fourths and fifths, and other scales based on geometric divisions, diameters, circumferences, diagonals, powers, and series coordinated with the canons of architectural proportion, Pi, phi and other constants..
In Mesopotamia and Egypt the Remen could be divided into different proportions as a similar triangle with sides as fingers, palms, or hands. The Egyptians thought of the Remen as proportionate to the cubit or mh foot and palm.
They used it as the diagonal of a unit rise or run like a modern framing square. Their relatedseked gives a slope. Its convenient to think of remen as intermediate to both large and small scale elements.
Even before the Greeks like Solon, Herodotus, Pythagorus, Plato, Ptolomy, Aristotle, Eratosthenes, and the Romans like Vitruvius, there seems to be a concept that all things should be related to one another proportionally.
Its not certain whether the ideas of proportionality begin with studies of the elements of the body as they relate to scaling architecture to the needs of humans, or the divisions of urban planning laying out cities and fields to the needs of surveyors.
In all cultures the canons of proportion are proportional to reproducable standards.
In ancient cultures the standards are divisions of a degree of the earths circumference into mia chillioi, mille passus, and stadia.
Stadia, are used to lay out city blocks, roads, large public buildings and fields
Fields are divided into acres using as their sides, furlongs, perches, cords, rods, fathoms, paces, yards, cubits, and remen which are proportional to miles and stadia
Buildings are divided into feet, hands, palms and fingers, which are also systematized to the sides of agricultural units.
Inside buildings the elements of the architectural design follow the canons of proportion of the the inscription grids based on body measures and the orders of architectural components.
In manufacturing the same unit fraction proportions are systematized to the length and width of boards, cloth and manufactured goods.
The unit fractions used are generally the best sexigesimal factors, three quarters, halves, 3rds, fourths, fifths, sixths, sevenths, eighths, tenths, unidecimals, sixteenths and their inverses used as a doubling system
Body Measures, Remen and Unit Fractions viewed as Harmonious or Symmetrical in Architectural proportions
Greek Remen generally have long, median and short forms with their sides related geometrically as arithmetric or geometric series based on hands and feet.
- The Egyptian bd is 300 mm and its remen is 375 mm. the proportion is 1:1.25
- The Ionian pous and Roman pes are a short foot measuring 296 mm their remen is 370 mm
- the Old English foot is 3 hands (15 digits of 20.32 mm) = 304.8 mm and its remen is 381 mm
- The Modern English foot is 12 inches of 25.4 mm = 304.8 mm and its remen is 381 mm (15")
- The Attic pous measures 308.4 mm its remen is 385.5
- The Athenian pous measures 316 mm and is considered of median length its remen is 395 mm
- Long pous are actually Remen (4 hands) and pygons
- See cubit for the discussion of the choice of division into hands or palms
- See the table below for proportions relative to other ancient Mediterranean units
Roman Remen generally have long, and short forms with their sides related geometrically as arithmetric or geometric series based on fingers palms and feet.
By Roman times the Remen is standardized as the diagonal of a 3:4:5 triangle with one side a palmus and another a pes. The Remen and similar forms of sacred geometry formed the basis of the later system of Roman architectural proportions as described by Vitruvius.
Generally the sexagesimal (base-six) or decimal (base-ten) multiples have Mesopotamian origins while the septenary (base-seven) multiples have Egyptian origins.
| Unit | Finger | Culture | Metric | Palm | Hand | Foot | Remen | Pace | Fathom |
|---|---|---|---|---|---|---|---|---|---|
| (1 ŝuŝi | 1 (little finger) | Mesop | 14.49 mm | .2 | 0.067 | 0.05 | |||
| 1 ŝushi | 1 (ring finger) | Mesop | 16.67 mm | .2 | 0.67 | 0.05 | |||
| 1 shushi | 1 (ring finger) | Mesop | 17 mm | .2 | 0.67 | 0.05 | |||
| 1 digitus | 1 (long finger) | Roman | 18.5 mm | .25 | 0.0625 | 0.04 | |||
| 1 dj | 1 (long finger) | Egyptian | 18.75 mm | .25 | 0.0625 | 0.04 | |||
| 1 daktylos | 1 (index finger) | Greek | 19.275 mm | .2 | 0.067 | 0.04 | |||
| 1 uban | 1 (index finger) | Mesop | .2 | .2 | 0.067 | 0.04 | |||
| 1 finger | 1 (index finger) | Old English | 20.32 mm | .2 | 0.067 | 0.045 | |||
| 1 inch | (thumb) | English | 25.4 mm | 0.083 | .067 | ||||
| 1 uncia | (thumb or inch) | Roman | 24.7 mm | .25 | 0.083 | .067 | |||
| 1 condylos | 2 (daktylos) | Greek | 38.55 mm | .5 | 2 | .1 | |||
| 1 palaiste, palm | 4 (daktylos) | Greek | 77.1 mm | 1 | 0.25 | .2 | |||
| 1 palaistos, hand | 5 (daktylos) | Greek | 96.375 mm | 1 | 0.333 | .25 | |||
| 1 hand | 5 (fingers) | English | 101.6mm | 1 | 0.333 | .25 | |||
| 1 dichas, | 8 (daktylos) | Greek | 154.2 mm | 2 | 0.5 | .4 | |||
| 1 spithame | 12 (daktylos) | Greek | 231.3 mm | 3 | .75 | .6 | |||
| 1 pous, foot of 4 palms | 16 (daktylos) | Ionian Greek | 296 mm | 4 | 1 | .8 | |||
| 1 pes, foot | 16 (digitus) | Roman | 296.4 mm | 4 | 1 | .8 | |||
| 1 uban, foot | 15 (uban) | Mesop | 300 mm | 3 | 1 | .75 | |||
| 1 bd, foot | 16 (dj) | Egyptian | 300 mm | 4 | 1 | .8 | |||
| 1 foote(3 hands) | 15 (fingers) | Old English | 304.8 mm | 3 | 1 | .75 | |||
| 1 foot, (12 inches) | 16 (inches) | English | 308.4 mm | 3 | 1 | .75 | |||
| 1 pous, foot of 4 palms | 16 (daktylos) | Attic Greek | 308.4 mm | 4 | 1 | .8 | |||
| 1 pous, foot of 3 hands | 15 (daktylos) | Athenian Greek | 316 mm | 4 | 1 | .8 | |||
| 1 pygon, remen | 20 (daktylos) | Greek | 385.5 mm | 5 | 1.25 | 1.25 | 1 | ||
| 1 pechya, cubit | 24 (daktylos) | Greek | 462.6 mm | 6 | 1.5 | 1.1 | |||
| 1 cubit of 17.6" 6 palms | 25 (fingers) | Egyptian | 450 mm | 6 | 1.5 | 1.3 | |||
| 1 cubit of 19.2" 5 hands | 25 (fingers) | English | 480 mm | 5 | 1.62 | 1.3 | |||
| 1 mh royal cubit | 28 (dj) | Egyptian | 525 mm | 7 | 2.33 | 1.4 | |||
| 1 bema | 40 (daktylos) | Greek | 771 mm | 10 | 2.5 | 2 | |||
| 1 yard | 48 (finger) | English | 975.36 mm | 12 | 3 | 2.4 | |||
| 1 xylon | 72 (daktylos) | Greek | 1.3878 m | 18 | 4.55 | 3.64 | |||
| 1 passus pace | 80 (digitus) | Roman | 1.542 m | 20 | 5 | 4 | 1 | ||
| 1 orguia | 96 (daktylos) | Greek | 1.8504 m | 24 | 6 | 5 | 1 | ||
| 1 akaina | 160 (daktylos) | Greek | 3.084 m | 40 | 10 | 8 | 2 | ||
| 1 English rod | 264 (fingers) | English | 5.365 m | 66 | 16.5 | 13.2 | 1 | ||
| 1 hayt | 280 (dj) | Egyptian | 5.397 m | 70 | 17.5 | 14 | 3 | ||
| 1 perch | 1,056 (fingers) | English | 20.3544 m | 264 | 66 | 53.4 | 11 | ||
| 1 plethron | 1,600 (daktylos) | Greek | 30.84 m | 400 | 100 | 80 | 20 | ||
| 1 actus | 1,920 (digitus) | Roman | 37.008 m | 480 | 120 | 96 | 24 | 20 | |
| khet side of 100 royal cubits | 2,800 (dj) | Egyptian | 53.97 m | 700 | 175 | 140 | 35 | ||
| iku side | 3,600 (ŝushi) | Mesop | 60m | 720 | 240 | 180 | 48 | 40 | |
| acre side | 3,333 (daktylos) | English | 64.359 m | 835 | 208.71 | 168.9 | |||
| 1 stade of Eratosthenes | 8,400 (dj) | Egyptian | 157.5 m | 2100 | 525 | 420 | 84 | 70 | |
| 1 stade | 8,100 (shushi) | Persian | 162 m | 2700 | 900 | 525 | 85 | ||
| 1 minute | 9,600 (daktylos) | Egyptian | 180 m | 2400 | 600 | 480 | 96 | 80 | |
| 1 stadion 600 pous | 9,600 (daktylos) | Greek | 185 m | 2400 | 600 | 480 | 96 | 80 | |
| 1 stadium625 pes | 9,600 (daktylos) | Roman | 185 m | 2400 | 625 | 500 | 100 | ||
| 1 furlong 625 pes | 10,000 (digitus) | Roman | 185.0 m | 2640 | 660 | 528 | 132 | 88 | |
| 1 furlong 600 pous | 9900 (daktylos) | English | 185.0 m | 1980 | 660 | 528 | 132 | 88 | |
| 1 Olympic Stadion 600 pous | 10,000 (daktylos) | Greek | 192.8 m | 2500 | 625 | 500 | 100 | ||
| 1 furlong 625 fote | 10,000(fingers) | Old English | 203.2 m | 2500 | 635 | 500 | 100 | ||
| 1 stade | 11,520 (daktylos) | Persian | 222 m | 2880 | 720 | 576 | 144 | 120 | |
| 1 cable | 11,520 (daktylos) | English | 222 m | 2880 | 720 | 576 | 144 | 120 | |
| 1 furlong 660 feet | 10,560 (inches) | English | 268.2 m | 2640 | 660 | 528 | 132 | 110 | |
| 1 diaulos | 19,200 (daktylos) | Greek | 370 m | 4800 | 1,200 | 960 | 192 | 160 | |
| 1 English myle | 75,000(fingers) | Old English | 1.524 km | 15000 | 5,000 | 4000 | 800 | ||
| 1 mia chilioi | 80,000 (daktylos) | Greek | 1.628352 km | 20,000 | 5,000 | 1000 | |||
| 1 mile | 84,480 (fingers) | English | 1.628352 km | 21,120 | 5,280 | 4224 | 1056 | 880 | |
| 1 dolichos | 115,200 (daktylos) | Greek | 2.22 km | 28,800 | 7,200 | 5760 | 4800 | ||
| 1 stadia of Xenophon | 280,000 (daktylos) | Greek | 5.397 km | 70,000 | 17,500 | 1400 | 3500 | ||
| 1/10 degree | 560,000 (daktylos) | Greek | 10.797 km | 140,000 | 35,000 | 2800 | 7000 | ||
| 1 schϓnus | 576,000 (daktylos)Z | Greek | 11.1 km | 144,000 | 36,000 | 288000 | 28800 | 24000 | |
| 1 stathmos | 1,280,000 (daktylos) | Greek | 24.672 km | 320,000 | 80,000 | 64000 | 16000 | ||
| 1 degree | 5,760,000 (digitus) | Roman | 111 km | 1,440,000 | 360,000 | 288000 | 72000 | 60000 |
- 1 daktulos (pl. daktuloi), digit
- = 1/16 pous
- 1 condulos
- = 1/8 pous
- 1 palaiste, palm
- = ¼ pous
- 1 dikhas
- = ½ pous
- 1 spithame, span
- = ¾ pous
- 1 pous (pl. podes), foot
- ≈ 316 mm, said to be 3/5 Egyptian royal cubit. There are variations, from 296 mm (Ionic) to 326 mm (Doric)
- 1 pugon, Homeric cubit
- = 1¼ podes
- 1 pechua, cubit
- = 1½ podes ≈ 47.4 cm
- 1 bema, pace
- = 2½ podes
- 1 khulon
- = 4½ podes
- 1 orguia, fathom
- = 6 podes
- 1 akaina
- = 10 podes
- 1 plethron (pl. plethra)
- = 100 podes, a cord measure
- 1 stadion (pl. stadia)
- = 6 plethra = 600 podes ≈ 185.4 m
- 1 diaulos (pl. diauloi)
- = 2 stadia, only used for the Olympic footrace introduced in 724 BC
- 1 dolikhos
- = 6 or 12 diauloi. Only used for the Olympic foot race introduced in 720 BC
- 1 parasanges
- = 30 stadia ≈ 5.5 km. Persian measure used by Xenophon, for instance
- 1 skhoinos (pl. skhoinoi, lit. "reefs")
- = 60 stadia ≈ 11.1 km (usually), based on Egyptian river measure iter or atur, for variants see there
- 1 stathmos
- ≈ 25 km, one day's journey. May have been variable, dependent on terrain
For variant, the stadion at Olympia measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as short as 157.5 m up to 222 m, but it is usually stated as 185 m.
The Greek root stadios means 'to have standing'. Stadions are used to measure the sides of fields.
In the time of Herodotus, the standard Attic stadion used for distance measure is 600 pous of 308.4 mm equal to 185 m. so that 600 stadia equal one degree and are combined at 8 to a mia chilioi or thousand which measures the boustredon or path of yoked oxen as a distance of a thousand orguia, taken as one orguia wide which defines an aroura or thousand of land and at 10 agros or chains equal to one nautical mile of 1850 m.
Several centuries later, Marinus and Ptolemy used 500 stadia to a degree, but their stadia were composed of 600 Remen of 370 mm and measured 222 m, so the measuRement of the degree was the same.
The same is also true for Eratosthenes, who used 700 stadia of 157.5 m or 300 Egyptian royal cubits to a degree, and for Aristotle, Posidonius, and Archimedes, whose stadia likewise measured the same degree.
The 1771 Encyclopædia Britannica mentions a measure named acæna which was a rod ten (Greek) feet long used in measuring land.
Additional images
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-
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Human body proportions change with age
Bibliography
- Gottfried Bammes: Studien zur Gestalt des Menschen. Verlag Otto Maier GmbH, Ravensburg 1990, ISBN 3-473-48341-9.
See also
References
- ^ Smith, W. Stevenson, and Simpson, William Kelly. The Art and Architecture of Ancient Egypt, pp. 12-13 and note 17, 3rd edn. 1998, Yale University Press (Penguin/Yale History of Art), ISBN 0300077475
- ^ Pallett, PM; Link, S; Lee, K (2010). "New "Golden" Ratios for Facial Beauty". Vision research. 50 (2): 149–54. doi:10.1016/j.visres.2009.11.003. PMC 2814183. PMID 19896961.
- ^ Prokopakis, EP; Vlastos, IM; Picavet, VA; Nolst Trenite, G; Thomas, R; Cingi, C; Hellings, PW (2013). "The golden ratio in facial symmetry". Rhinology. 51 (1): 18–21. doi:10.4193/Rhino12.111. PMID 23441307.
- ^ Fiona Macrae (27 December 2009). "Skin deep: Beautiful faces have Miss Average proportions". Daily Mail. Retrieved 2011-07-31.
All were head shots of the same person with different distances from eyes to mouth or between the eyes. She was at her most attractive when the space between her pupils was just under half, or 46 per cent, of the width of her face from ear to ear. The other perfect dimension was when the distance between her eyes and mouth was just over a third, or 36 per cent, of the overall length of her face from hairline to chin. ...
{{cite news}}: Italic or bold markup not allowed in:|publisher=(help) - ^ Sorokowski P., Pawlowski B. (Jan. 3, 2008). "Adaptive preferences for leg length in a potential partner". Evolution and Human Behavior. Vol. 29. pp. 86–91. Retrieved 2010-03-29.
{{cite news}}: Check date values in:|date=(help) - ^ Sorokowski, P. (2010). Attractiveness of Legs Length in Poland and Great Britain. In Human Ecology. 31(3):148
- ^ a b c d Bertamini, M. (2009). THE EFFECT OF LEG LENGTH ON PERCEIVED ATTRACTIVENESS OF SIMPLIFIED STIMULI. In Social, Evolutionary, and Cultural Psychology. 3(3).
- ^ Frederick, D. A. et al. (2010). The influence of leg-to-body ratio (LBR) on judgments of female physical attractiveness: Assessments of computer-generated images varying in LBR In Body Image. 7(1):51-55
- ^ a b Swami, V. et al. (2006). The leg-to-body ratio as a human aesthetic criterion. In Body Image. 3.
- ^ a b Pope, Harrison (1998-05-26). "Evolving Ideals of Male Body Image as Seen Through Action Toys". International Journal of Eating Disorders. 26 (1). John Wiley & Sons, Inc.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^ a b 電撃萌王 Special May 1, 2006, No. 127 Vol.11 No.8, Media, p. 104 ~ 105
- ^ Crilley, M. Manga Body Proportions. Youtube. Accessed May 2, 2011, from http://www.youtube.com/watch?v=dFuFwpGfbYU&
- ^ Crilley, M. How To Draw Manga Female Body Proportions (Talia from "Brody's Ghost"). Youtube. Accessed May 2, 2011, from http://www.youtube.com/watch?v=_VtBuFYvsW8&
- ^ Buckley (2002). Encyclopedia of Contemporary Japanese Culture. Taylor & Francis. pp. 188, 522, 553. ISBN 0-415-14344-6.
- ^ a b "Universal Leonardo: Leonardo Da Vinci Online › Essays." Universal Leonardo: Leonardo Da Vinci Online › Welcome to Universal Leonardo. Web. 22 Apr. 2010. <http://www.universalleonardo.org/essays.php?id=563>.
External links
- Attention: This template ({{cite pmid}}) is deprecated. To cite the publication identified by PMID 3828410, please use {{cite journal}} with
|pmid=3828410instead. - Alley, Thomas R. (Feb 1983). "Growth-Produced Changes in Body Shape and Size as Determinants of Perceived Age and Adult Caregiving". Child Development. 54 (1): 241–248. doi:10.2307/1129882. JSTOR 1129882.
- Pittenger, John B. (1990). "Body proportions as information for age and cuteness: Animals in illustrated children's books". Perception & Psychophysics. 48 (2): 124–30. doi:10.3758/BF03207078. PMID 2385485.
- Changing body proportions during growth
Leonardo da Vinci
Leonardo da Vinci believed that the ideal human proportions were governed by the harmonious proportions that he believed governed the universe[1] such that the ideal man would fit cleanly into a circle as in his famed "Vitruvian man" drawing.[1]
Additional images
-
-
-
Human body proportions change with age
Bibliography
- Gottfried Bammes: Studien zur Gestalt des Menschen. Verlag Otto Maier GmbH, Ravensburg 1990, ISBN 3-473-48341-9.
See also
References
- ^ a b "Universal Leonardo: Leonardo Da Vinci Online › Essays." Universal Leonardo: Leonardo Da Vinci Online › Welcome to Universal Leonardo. Web. 22 Apr. 2010. <http://www.universalleonardo.org/essays.php?id=563>.
External links
- Attention: This template ({{cite pmid}}) is deprecated. To cite the publication identified by PMID 3828410, please use {{cite journal}} with
|pmid=3828410instead. - Alley, Thomas R. (Feb 1983). "Growth-Produced Changes in Body Shape and Size as Determinants of Perceived Age and Adult Caregiving". Child Development. 54 (1): 241–248. doi:10.2307/1129882. JSTOR 1129882.
- Pittenger, John B. (1990). "Body proportions as information for age and cuteness: Animals in illustrated children's books". Perception & Psychophysics. 48 (2): 124–30. doi:10.3758/BF03207078. PMID 2385485.
- Changing body proportions during growth