Borromean rings

In mathematics, the Borromean rings consist of three topological circles which are linked despite the fact that no two of them are linked (they form a Brunnian link). This link cannot be formed from actual geometrically round circles, although you can use ellipses of arbitrarily small eccentricity. Borromean rings - History of origin and depictions. The name, Borromean rings, comes from their use in the coat of arms of the aristocratic Borromeo family in Italy. The link itself is much older and has appeared ...

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The name, Borromean rings, comes from their use in the coat of arms of the aristocratic Borromeo family in Italy. The link itself is much older and has appeared in the form of the valknut on Norse image stones dating back to the 7th century. The Borromean rings have been used in different contexts to indicate strength in unity, e.g. in religion or art. In particular, some have used the design to symbolize the Trinity. The psychoanalyst Jacques Lacan famously found inspiration in the Borromean rings as a model for his topology of the human mind, with each ring representing a fundamental Lacanian com ...

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Borromean rings, Borromean rings - History of origin and depictions, Borromean rings - Molecular Borromean rings

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Creating a knot is easy. Begin with a one-dimensional line segment, wrap it around itself arbitrarily, and then fuse its two free ends together to form a closed loop. One of the biggest unresolved problems in knot theory is to give a method to decide in every case whether two such embeddings are different or the same. Before we can do this, we must decide what it means for embeddings to be "the same". We consider two embeddings of a loop to be the same if we can get from one to the other by a series of slides and distortions of the st ...

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Knot theory, Knot theory - History, Knot theory - An introduction to knot theory, Knot theory - Knot diagrams, Knot theory - Reidemeister moves, Knot theory - Higher dimensions, Knot theory - Adding knots, Knot theory - Other resources

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Christian symbolism is the use of actions or objects to represent the truths of the Christian faith, either as a reminder of those truths or as a way of spiritually connecting with the underlying truth or act. Christian symbolism - Sacraments. The most important symbols in the Christian church are the sacraments. These rites, which vary between denominations but may include holy communion, baptism, ordination and marriage, are commonly described as an outward and visible sign of an inward and spiritual g ...

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Knot theory originated in an idea of Lord Kelvin's (1867), that atoms were knots of swirling vortices in the æther. He believed that an understanding and classification of all possible knots would explain why atoms absorb and emit light at only the discrete wavelengths that they do. We now know that this idea was mistaken, and that the discrete wavelengths depend on quantum energy levels.[1]^{See also:}

Knot theory, Knot theory - History, Knot theory - An introduction to knot theory, Knot theory - Knot diagrams, Knot theory - Reidemeister moves, Knot theory - Higher dimensions, Knot theory - Adding knots, Knot theory - Other resources

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Carlo Borromeo (October 2, 1538 - November 4, 1584), saint and cardinal of the Roman Catholic Church, son of Ghiberto Borromeo, count of Arona, and Margarita de' Medici, was born at the castle of Arona on Lago Maggiore. He was of the aristocratic Borromeo family, whose coat of arms included the Borromean rings, sometimes taken to symbolize the Holy Trinity. When he was about twelve years old, Carlo's uncle, Giulio Cesare Borromeo, resigned to him an abbacy, the revenue of which he applied wholly in charity to the poor. He studi ...

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The valknut (Old Norse valr, slain warriors + knut, knot) is a symbol consisting of three interlocked triangles. It is also called: heart of the slain heart of Vala Hrungnir's heart Odin's knot It appears on Scandinavian image stones in connection with Odin, e.g. on the 7th century Tängelgarda stone from Gotland. According to H. R. Ellis Davidson (p. 146), the valknut — is thought to symbolize the power of the god [Odin] to b ...

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• Valknut - Neopaganism

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List of geometry topics - Euclidean plane geometry. 2D computer graphics 2D geometric model Curve of constant width Coordinate notation Brahmagupta's formula Equilateral triangle Pythagorean triangle Pedal triangle Symmedian Altitude (triangle) Pons Asinorum Euler's line Trapezoid, trapezium Isosceles trapezoid Golden angle Complex geometry Conic section ...

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List of geometry topics, List of geometry topics - Types methodologies and terminologies of geometry, List of geometry topics - Euclidean geometry foundations, List of geometry topics - Euclidean plane geometry, List of geometry topics - 3-dimensional Euclidean geometry solid geometry, List of geometry topics - n-dimensional Euclidean geometry, List of geometry topics - Non-Euclidean geometry, List of geometry topics - Numerical geometry, List of geometry topics - Geometric algorithms, List of geometry topics - Mathematical morphology, List of geometry topics - Generalizations, List of geometry topics - Various, List of geometry topics - Applications

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Born in the small village of Celico near Cosenza in Calabria, at the time part of the Kingdom of Sicily, he was the son of Mauro the notary, who was well placed, and Gemma, his wife. He was educated at Cosenza, where he became first a clerk in the courts, and then a notary himself, and worked in 1166–67 for Etienne du Perche, archbishop of Palermo and chancellor of Marguerite, regent for the young William II of Sicily. About 1169, he went on pilgrimage to the Holy Land, an episode about which we know very little, save that he underwent a s ...

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Joachim of Fiore, Joachim of Fiore - Biography, Joachim of Fiore - Books, Joachim of Fiore - Theory of the three ages, Joachim of Fiore - Condemnation, Joachim of Fiore - Neojoachimism

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Also common in most Christian religious symbolism are emblems, figures or ideas drawn from the cultures which Christianity has superseded, so that symbols existing in those cultures have been adopted but imbued with Christian meaning. The phoenix standing for the Resurrection, or the Egg representing rebirth, are examples of this incorporation of pagan symbols, for use in Christian art and customs. Often a pagan symbol was given a Christian meaning allowing incorporation of traditional practices into the faith of the new converts. Christ ...

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Christian symbolism, Christian symbolism - Sacraments, Christian symbolism - Other Symbols, Christian symbolism - Symbols drawn from outside, Christian symbolism - Diverse influences and meaning illustrated, Christian symbolism - Examples

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Some variations of the Shield of the Trinity diagram are shown in the image below (click on the caption to see a larger clearer version): A shield-shaped version of the diagram placed on a red shield (heraldic "gules") was attributed as the arms of God (or of the Trinity) by heralds in medieval England and France. The "banner of the Trinity" which Jean Le Fevre, Seigneur of St. Remy, and Jehan de Wavrin attest that Henry V of England displayed at Agincourt would have been the same (but with the emblem on a red flag instead of a red sh ...

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Shield of the Trinity, Shield of the Trinity - Basic description, Shield of the Trinity - Brief history, Shield of the Trinity - Name, Shield of the Trinity - Variations, Shield of the Trinity - Orientation of diagram and placement of outer node captions, Shield of the Trinity - Significance, Shield of the Trinity - Selected References, Shield of the Trinity - Links to depictions of the Shield of the Trinity diagram, Shield of the Trinity - 13th century manuscripts, Shield of the Trinity - 15th or 16th century manuscripts and books, Shield of the Trinity - 15th or 16th century stained-glass windows and carvings in churches, Shield of the Trinity - Some modern church decorations

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The mystical basis of his teaching is his doctrine of the "Eternal Gospel," founded on aninterpretation of the text in Revelation xiv, 6. His theories can be considered millenarist; he believed that history, on analogy with the Trinity, was divided into three fundamental epochs: The Age of the Father, corresponding to the Old Testament, characterized by obedience of mankind to the Rules of God; The Age of the Son, between the advent of Christ and 1260, represented by the New Testament, when the Man ...

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Joachim of Fiore, Joachim of Fiore - Books, Joachim of Fiore - Theory of the three ages, Joachim of Fiore - Condemnation, Joachim of Fiore - Neojoachimism

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Thomas Aquinas confuted his theories in his Summa Theologica, but in The Divine Comedy, Dante Alighieri placed him in paradise. Among the more spiritually-inclined of the Franciscans,a "Joachist" group arose, many of whom saw Antichrist already in the world in the person of Frederick II, Holy Roman Emperor (who died, however, in 1250). As the appointed year approached, spurious works began to circulate under Joachim's name: De Oneribus Prophetarum, an Expositio Sybillae et Merlini ("Exposition of the Sibyl ...

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Joachim of Fiore, Joachim of Fiore - Biography, Joachim of Fiore - Books, Joachim of Fiore - Theory of the three ages, Joachim of Fiore - Condemnation, Joachim of Fiore - Neojoachimism

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Symbols were widely used by the early Christian church. Symbols were inscribed on Christian tombs from the earliest days. One of the most widely used in the early church was that of the fish, which derived from a Greek acrostic Jesus Christ, God's Son, Saviour. Interestingly the cross (which is today one of the most widely recognised symbols in the world) was not commonly used as a symbol until later. In Eastern Orthodo ...

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Christian symbolism, Christian symbolism - Sacraments, Christian symbolism - Other Symbols, Christian symbolism - Symbols drawn from outside, Christian symbolism - Diverse influences and meaning illustrated, Christian symbolism - Examples

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The mystical basis of his teaching is his doctrine of the "Eternal Gospel," founded on an interpretation of the text in Revelation xiv, 6. His theories can be considered millenarist; he believed that history, by analogy with the Trinity, was divided into three fundamental epochs: The Age of the Father, corresponding to the Old Testament, characterized by obedience of mankind to the Rules of God; The Age of the Son, between the advent of Christ and 1260, represented by the New Testament, when the Man ...

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Joachim of Fiore, Joachim of Fiore - Biography, Joachim of Fiore - Books, Joachim of Fiore - Theory of the three ages, Joachim of Fiore - Condemnation, Joachim of Fiore - Neojoachimism

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The most important symbols in the Christian church are the sacraments. These rites, which vary between denominations but may include holy communion, baptism, ordination and marriage, are commonly described as an outward and visible sign of an inward and spiritual grace or, as in the Catholic system, "outward signs and media of grace." In other words, at the very least, the rite is a symbol of the spiritual change or event that takes place within the participant. For example in communion the bread and wine are, at the least, symbolic o ...

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Christian symbolism, Christian symbolism - Sacraments, Christian symbolism - Other Symbols, Christian symbolism - Symbols drawn from outside, Christian symbolism - Diverse influences and meaning illustrated, Christian symbolism - Examples

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Thomas Aquinas confuted his theories in his Summa Theologica, but in The Divine Comedy, Dante Alighieri placed him in paradise. Among the more spiritually-inclined of the Franciscans,a "Joachist" group arose, many of whom saw Antichrist already in the world in the person of Frederick II, Holy Roman Emperor (who died, however, in 1250). As the appointed year approached, spurious works began to circulate under Joachim's name: De Oneribus Prophetarum, an Expositio Sybillae et Merlini ("Exposition of the Sibyl ...

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Joachim of Fiore, Joachim of Fiore - Books, Joachim of Fiore - Theory of the three ages, Joachim of Fiore - Condemnation, Joachim of Fiore - Neojoachimism

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The only name for this diagram which was in any regular use during the middle ages was "Scutum Fidei" (a Latin phrase meaning "Shield of the Faith", taken from the Vulgate of Ephesians verse 6:16). For example, in this ca. 1247-1258 manuscript of John of Wallingford's writings, the quote from Ephesians 6:16 is placed directly above the diagram. While the diagram seems to have been thought of as the armorial bearings of the Trinity from at least the mid-13th century (when it was included among the ca. 1250-1259 A.D. heraldic shields in ...

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Shield of the Trinity, Shield of the Trinity - Basic description, Shield of the Trinity - Brief history, Shield of the Trinity - Name, Shield of the Trinity - Variations, Shield of the Trinity - Orientation of diagram and placement of outer node captions, Shield of the Trinity - Significance, Shield of the Trinity - Selected References, Shield of the Trinity - Links to depictions of the Shield of the Trinity diagram, Shield of the Trinity - 13th century manuscripts, Shield of the Trinity - 15th or 16th century manuscripts and books, Shield of the Trinity - 15th or 16th century stained-glass windows and carvings in churches, Shield of the Trinity - Some modern church decorations

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The main achievement of the Shield of the Trinity diagram is to transfer a large part of the essential "mystery" or "paradox" of the Christian doctrine of the Trinity from the realm of complex verbal philosophical abstractions and esoteric theological vocabulary to the realm of simple logic, as presented in the relatively easily graspable form of a concrete and conveniently compact visual diagram. It is remarkable as a basically-successful attempt, roughly 800 years old, to represent a complex set of abstract concepts in precise graphic form ...

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Shield of the Trinity, Shield of the Trinity - Basic description, Shield of the Trinity - Brief history, Shield of the Trinity - Name, Shield of the Trinity - Variations, Shield of the Trinity - Orientation of diagram and placement of outer node captions, Shield of the Trinity - Significance, Shield of the Trinity - Selected References, Shield of the Trinity - Links to depictions of the Shield of the Trinity diagram, Shield of the Trinity - 13th century manuscripts, Shield of the Trinity - 15th or 16th century manuscripts and books, Shield of the Trinity - 15th or 16th century stained-glass windows and carvings in churches, Shield of the Trinity - Some modern church decorations

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This diagram consists of four nodes (generally circular in shape) interconnected by six links. The three nodes at the edge of the diagram are labelled with the names of the three persons of the Trinity (traditionally the Latin-language names, or scribal abbreviations thereof): The Father ("PATER"), The Son ("FILIUS"), and The Holy Spirit ("SPIRITUS SANCTUS"). The node in the center of the diagram (within the triangle formed by the other three nodes) is labelled God (Latin "DEUS"), while the three links connecting the center node with the outer nodes are labelled "is" (Latin "EST"), and the three links connecting the outer n ...

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Shield of the Trinity, Shield of the Trinity - Basic description, Shield of the Trinity - Brief history, Shield of the Trinity - Name, Shield of the Trinity - Variations, Shield of the Trinity - Orientation of diagram and placement of outer node captions, Shield of the Trinity - Significance, Shield of the Trinity - Selected References, Shield of the Trinity - Links to depictions of the Shield of the Trinity diagram, Shield of the Trinity - 13th century manuscripts, Shield of the Trinity - 15th or 16th century manuscripts and books, Shield of the Trinity - 15th or 16th century stained-glass windows and carvings in churches, Shield of the Trinity - Some modern church decorations

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