Vitruvian Man

 

The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci around the year 1487 It is accompanied by notes based on the work of Vitruvius. The drawing, which is in pen and ink on paper, depicts a nude male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called theCanon of Proportions or, less often, Proportions of Man. It is stored in the Gallerie dell’Accademia in Venice, Italy, and, like most works on paper, is displayed only occasionally.^[2][3]

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. Other artists had attempted to depict the concept, with less success. The drawing is traditionally named in honour of the architect.

 

This image exemplifies the blend of art and science during the Renaissance and provides the perfect example of Leonardo’s keen interest in proportion. In addition, this picture represents a cornerstone of Leonardo’s attempts to relate man to nature. Encyclopaedia Britannica online states, “Leonardo envisaged the great picture chart of the human body he had produced through his anatomical drawings and Vitruvian Man as a cosmografia del minor mondo (cosmography of the microcosm). He believed the workings of the human body to be an analogy for the workings of the universe.” It is also believed by some^[who?] that Leonardo symbolized the material existence by the square and spiritual existence by the circle. Thus he attempted to depict the correlation between these two aspects of human existence.^[4] 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 Vitruvius, who wrote that in the human body:

• a palm is the width of four fingers
• a foot is the width of four palms (i.e., 12 inches)
• a cubit is the width of six palms
• a pace is four cubits

• a man’s height is four cubits (and thus 24 palms)
• 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 distance from the bottom of the neck to the hairline is one-sixth of a man’s height
• the maximum width of the shoulders is a quarter of a man’s height
• the distance from the middle of the chest to the top of the head is a quarter of a man’s height
• the distance from the elbow to the tip of the hand is one-fourth 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
• the length of a man’s foot is one-sixth of his height

ISO 216

ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today. It is the standard which defines the commonly available A4 paper size. The underlying principle is that when rectangles with width/length ratio  are cut or folded in half the rectangles thus formed retain the original width/length ratio.

 

The international ISO standard is based on the German DIN standard 476 (DIN 476) from 1922.

Some of the formats contained therein were independently invented in France during its revolution, but were later forgotten.

 

 

The aspect ratio used by this standard was mentioned in a letter by the German Georg Christoph Lichtenberg, written on 25 October 1786.

• ISO 216:1975, defines two series of paper sizes: A and B
• ISO 269:1985, defines a C series for envelopes
• ISO 217:1995, defines two untrimmed series of raw paper sizes: RA and SRA

 

 

 

Paper in the A series format has a  aspect ratio, although this is rounded to the nearest millimetre. A0 is defined so that it has an area of 1 m², prior to the above mentioned rounding. Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the preceding paper size, cutting parallel to its shorter side (so that the long side of A(n+1) is the same length as the short side of An, again prior to rounding).

The most frequently used of this series is the size A4 (210 × 297 mm). A4 paper is 6 mm narrower and 18 mm longer than the “Letter” paper size, 8½ × 11 inches (216 × 279 mm), commonly used in North America.

The geometric rationale behind the square root of 2 is to maintain the aspect ratio of each subsequent rectangle after cutting the sheet in half, perpendicular to the larger side. Given a rectangle with a longer side, x, and a shorter side, y, the following equation shows how the aspect ratio of a rectangle compares to that of a half rectangle:  which reduces to  or an aspect ratio of 

The formula that gives the larger border of the paper size An in metres and without rounding off is the geometric sequence: a_n = 2^{1 / 4 − n / 2}. The paper size An thus has the dimension a_n × a_{n + 1}.

The exact millimetre measurement of the long side of An is given by .

Braille

The Braille system is a method that is widely used by blind people to read and write. Braille was devised in 1821 by Louis Braille, a Frenchman. Each Braille character or cell is made up of six dot positions, arranged in a rectangle containing two columns of three dots each. A dot may be raised at any of the six positions to form sixty-four (26) permutations, including the arrangement in which no dots are raised. For reference purposes, a particular permutation may be described by naming the positions where dots are raised, the positions being universally numbered 1 to 3, from top to bottom, on the left, and 4 to 6, from top to bottom, on the right. For example, dots 1-3-4 would describe a cell with three dots raised, at the top and bottom in the left column and on top of the right column, i.e., the letter m. The lines of horizontal Braille text are separated by a space, much like visible printed text, so that the dots of one line can be differentiated from the Braille text above and below. Punctuation is represented by its own unique set of characters. The Braille system was based on a method of communication originally developed by Charles Barbier in response to Napoleon’s demand for a code that soldiers could use to communicate silently and without light at night called night writing. Barbier’s system was too complex for soldiers to learn, and was rejected by the military. In 1821 he visited the National Institute for the Blind in Paris, France, where he met Louis Braille. Braille identified the major failing of the code, which was that the human finger could not encompass the whole symbol without moving, and so could not move rapidly from one symbol to another. His modification was to use a 6 dot cell — the Braille system — which revolutionized written communication for the blind.

Bora (rings)

A Bora is the name given both to an initiation ceremony of Indigenous Australians, and to the site on which the initiation is performed. At such a site, young boys are transformed into men. The initiation ceremony differs from culture to culture, but often involves circumcision and scarification, and may also involve the removal of a tooth or part of a finger. The ceremony, and the process leading up to it, involves the learning of sacred songs, stories, dances, and traditional lore. Many different clans will assemble to participate in an initiation ceremony. The word Bora was originally from South-East Australia, but is now often used throughout Australia to describe an initiation site or ceremony. It is called a Burbung in the language of the Darkinjung, to the North of Sydney. The name is said to come from that of the belt worn by initiated men. The appearance of the site varies from one culture to another, but it is often associated with stone arrangements, rock engravings, or other art works. Women are generally prohibited from entering a bora. In South East Australia, the Bora is often associated with the creator-spirit Baiame. In the Sydney region, large Earth mounds were made, shaped as long bands or simple circles. Sometimes the boys would have to pass along a path marked on the ground representing the transition from childhood to manhood, and this path might be marked by a stone arrangement or by footsteps, or mundoes, cut into the rock. In other areas of South-East Australia, a Bora site might consist of two circles of stones, and the boys would start the ceremony in the larger, public, one, and end it in the other, smaller, one, to which only initiated men are admitted. Bora rings, found in South-East Australia, are circles of foot-hardened earth surrounded by raised embankments. They were generally constructed in pairs (although some sites have three), with a bigger circle about 22 metres in diameter and a smaller one of about 14 metres. The rings are joined by a sacred walkway. Matthews (1897) gives an excellent eye-witness account of a Bora ceremony, and explains the use of the two circles.

Carolingian cross

 

A variation of the Everlasting Cross is the Carolingian Cross, named after the Carolingian dynasty, a Frankish noble family that can be traced back to the seventh century. One member of this family, Pepin the Short, was crowned King of the Franks by the church, who saw this as a useful way to extend their authority over the secular world. A later and greater Carolingian monarch was Charlemagne, crowned in 800 A.D. making Western Europe an extension of the Roman Empire.

Coincidentally, the cross has a similarly sounding name to Cardinham Cross, an ancient Celtic Cross found in the walls of the 15th century village church of Cardinham, near Bodmin, Cornwall, England. This Cardinham Cross incorporates the Carolingian design.

The Carolingian Cross is made by extending the lines of aTriquetra (from the Latin tri ’three’ and quetrus ’cornered’). In Christian art, the triquetra represents the Trinity as one God. The triquetra is found also in Celtic knotwork, sometimes referred to as a Knotted Cross or Celtic Twirls Cross, and is popular with Neopagans to represent the interdependence in nature of Land, Sea and Sky, or the spiritual interdependence in man’s Mind, Body and Soul.

Triquetra

Triquetra (IPA: [tɹaɪ'kwεtɹə]) is a word derived from the Latin tri- (“three”) and quetrus (“cornered”). Its original meaning was simply “triangle” and it has been used to refer to various three-cornered shapes. Nowadays, it has come to refer exclusively to a certain more complicated shape formed of three vesicae piscis, sometimes with an added circle in or around it. This widely recognized symbol has been used in for the past two centuries a sign of special things and persons that are threefold.

Germanic paganism

The triquetra has been found on runestones in Northern Europe and on early Germanic coins. It presumably had pagan religious meaning and it bears a resemblance to the Valknut, a symbol associated with Odin.

Celtic art

The triquetra is often found in Insular art, most notably metal work and in illuminated manuscripts like the Book of Kells. The fact that the triquetra very rarely stood alone in medieval Celtic has cast a reasonable doubt on its use as a symbol in context where it was used primarily as a space filler or ornament in much more complex compositions. But Celtic art lives on as both a living folk art tradition and through several revivals. This widely recognized knot has been used in for the past two centuries a sign of special things and persons that are threefold, such as Mother, Daughter and Grandmother – Past, Present and Future -and especially the Holy Trinity, the Father, Son and Holy Spirit. It can also mean Self, brother, and sister. 

Christian use

The symbol was later used by Christians as a symbol of the Trinity (Father, Son and Holy Spirit). This appropriation was particularly easy because the triquetra conveniently incorporated three shapes that could be interpreted as Christian Ιχθυς symbols.

A common representation of the symbol is with a circle that goes through the three interconnected loops of the Triquetra. The circle emphasizes the unity of the whole combination of the three elements.

Neopaganism

Modern Pagans use the triquetra to symbolize a variety of concepts and mythological figures.

Germanic Neopagan groups who use the triquetra to symbolize their faith generally believe it is originally of Norse and Germanic origins. Celtic Reconstructionist Pagans use the triquetra either to represent one of the various triplicities in their cosmology and theology (such as the tripartite division of the world into the realms of Land, Sea and Sky), or as a symbol of one of the specific triple Goddesses, for example, The Morrígan.

The symbol is also sometimes used by Wiccans and some New Agers to symbolize either the Wiccan triple goddess, the interconnected parts of our existence (Mind, Body, and Soul), or many other concepts that seem to fit into this idea of a unity.

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Tree of life

The concept of a many-branched tree illustrating the idea that all life on earth is related has been used in science, religion, philosophy, mythology and other areas. A tree of life is variously, a) a mystical concept alluding to the interconnectedness of all life on our planet, b) a metaphor for common descent in the evolutionary sense, and c) a motif in various world theologies, mythologies and philosophies.Various trees of life are recounted in folklore, culture and fiction, often relating to immortality or fertility. They had their origin in religious symbolism.

picture: A Tree of Life, in the form of ten interconnected nodes, is an important part of the Kabbalah. As such, it resembles the ten Sephirot.

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Hourglass Nebula

 

The Engraved Hourglass Nebula (also known as MyCn 18) is a young planetary nebula situated in the southern constellation Musca about 8,000 light-years away from Earth. It was discovered by Annie Jump Cannon and Margaret W. Mayall during their work on an extended Henry Draper Catalogue. At the time [January 18, 1996] it was designated simply as a small faint planetary nebula. Much improved telescopes and imaging techniques allowed the hourglass shape of the nebula to be discovered by Raghvendra Sahai and John Trauger of the Jet Propulsion Laboratory on January 18, 1996. It is conjectured that MyCn 18’shourglass shape is produced by the expansion of a fast stellar wind within a slowly expanding cloud which is denser near its equator than its poles.

The Hourglass Nebula was photographed by the Wide Field and Planetary Camera 2 of the Hubble Space Telescope.

The Hourglass Nebula was featured on the cover of the April 1997 issue of National Geographic. The nebula’s unique appearance led the magazine’s editors to comment, “Astronomers looked 8,000 light-years into the cosmos with the Hubble Space Telescope, and it seemed that the eye of God was staring back.”

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Mandorla

 

A Mandorla is a Vesica Piscis shaped aureola which surrounds the figures of Christ and the Virgin Mary in traditional Christian art. It is especially used to frame the figure of Christ in Majesty in early medieval and Romanesque art, as well as Byzantine art of the same periods. The term refers to the almond like shape: “mandorla” means almond nut in Italian. In iconsof the Eastern Orthodox Church, the mandorla is used to depict sacred moments which transcend time and space, such as the Resurrection, Transfiguration, and the Dormition of the Theotokos. These mandorla will often be painted in several concentric patterns of color which grow darker as they come close to the center. This is in keeping with the church’s use ofApophatic theology, as described by Dionysius the Areopagite and others. As holiness increases, there is no way to depict its brightness, except by darkness.

The symbol is also used in non-Christian contexts. In various religions the almond seed has been associated with divine virgin birth. For instance the virgin nymph Nana miraculously conceived of Attis by putting a ripe almond in her bosom.In a famous romanesque fresco of Christ in Glory at Sant Climent de Taüll the inscription “Ego Sum Lux Mundi” is incorporated in the Mandorla design.

 

The tympanum at Conques has Christ, with one of those beautiful gestures carved in romanesque sculpture, indicate the angels at his feet bearing candlesticks. Six surrounding stars, resembling blossoming flowers, indicate the known planets including the moon. Here the symbolism implies Christ as the Sun. 

In one special case, at Cervon (Nièvre), Christ is seated surrounded by eight stars, resembling blossoming flowers. At Conques the flowers are six-petalled. At Cervon, where the almond motif is repeated in the rim of the mandorla, they are five-petalled, as are almond flowers -the first flowers to appear at the end of winter, even before the leaves of the almond tree. Here one is tempted to seek for reference in the symbolism of the nine branched Chanukkiyah candelabrum. It should be remembered that in the XII century a great school of Judaic thought radiated from Narbonne, coinciding with the origins of theKabbalah. Furthermore, at Cervon the eight star/flower only is six petalled: the Root of David, the Morningstar, mentioned at the close of Book of Revelation (22:16)  ( In one of the oldest manuscripts of the complete Hebrew Bible, the Leningrad Codex, one finds the Star of David imbedded in an octagon )

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In the symbolism of Hildegarde von Bingen the mandorla refers to the Cosmos.

compasses

 

A compass, magnetic compass or mariner’s compass is a navigational instrument for determining direction relative to the earth’s magnetic poles. It consists of a magnetized pointer (usually marked on the North end) free to align itself with Earth’s magnetic field. The face of the compass generally highlights the cardinal points of north, south, east and west. The compass greatly improved the safety and efficiency of travel, especially ocean travel. A compass can be used to calculate heading, used with a sextant to calculate latitude, and with a marine chronometer to calculate longitude. It thus provides a much improved navigational capability that has only been partially supplanted by modern devices such as the gyrocompass and the Global Positioning System (GPS).

A compass is any magnetically sensitive device able to indicate the direction of the magnetic north of a planet’s magnetosphere. Often compasses are built as a stand alone sealed instrument with a magnetized bar or needle turning freely upon a pivot, or moving in a fluid, thus able to point in a northerly and southerly direction. An early compass was invented in ancient China before 1044. The dry compass was invented in medievalEurope around 1300.This was supplanted in the early 20th century by the liquid-filled magnetic compass.

Other, more accurate, devices have been invented for determining north that do not depend on the Earth’s magnetic field for operation (known in such cases as true north, as opposed to magnetic north). A gyrocompass orastrocompass can be used to find true north, while being unaffected by stray magnetic fields, nearby electrical power circuits or nearby masses of ferrous metals. A recent development is the electronic compass, or Fibre optic gyrocompass, which detects the magnetic directions without potentially fallible moving parts. This device frequently appears as an optional subsystem built into GPS receivers.

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How to make a compass