"Infinity symbol The infinity symbol (sometimes called the lemniscate) is a mathematical symbol representing the concept of infinity. The shape of a sideways figure eight has a long pedigree; for instance, it appears in the cross of Saint Boniface, wrapped around the bars of a Latin cross. However, John Wallis is credited with introducing the infinity symbol with its mathematical meaning in 1655, in his ""De sectionibus conicis"". Wallis did not explain his choice of this symbol, but it has been conjectured to be a variant form of a Roman numeral for 1,000 (originally CIƆ, also CƆ), which was sometimes"
"Lemniscate of Gerono In algebraic geometry, the lemniscate of Gerono, or lemniscate of Huygens, or figure-eight curve, is a plane algebraic curve of degree four and genus zero and is a lemniscate curve shaped like an formula_1 symbol, or figure eight. It has equation It was studied by Camille-Christophe Gerono. Because the curve is of genus zero, it can be parametrized by rational functions; one means of doing that is Another representation is which reveals that this lemniscate is a special case of a Lissajous figure. The dual curve (see Plücker formula), pictured below, has therefore a somewhat different character."
"Its equation is Lemniscate of Gerono In algebraic geometry, the lemniscate of Gerono, or lemniscate of Huygens, or figure-eight curve, is a plane algebraic curve of degree four and genus zero and is a lemniscate curve shaped like an formula_1 symbol, or figure eight. It has equation It was studied by Camille-Christophe Gerono. Because the curve is of genus zero, it can be parametrized by rational functions; one means of doing that is Another representation is which reveals that this lemniscate is a special case of a Lissajous figure. The dual curve (see Plücker formula), pictured below, has therefore a"
"Lemniscate In algebraic geometry, a lemniscate is any of several figure-eight or -shaped curves. The word comes from the Latin ""lēmniscātus"" meaning ""decorated with ribbons"", from the Greek λημνίσκος meaning ribbons, or alternatively may refer to the wool from which the ribbons were made. Curves that have been called a lemniscate include three quartic plane curves: the hippopede or lemniscate of Booth, the lemniscate of Bernoulli, and the lemniscate of Gerono. The study of lemniscates (and in particular the hippopede) dates to ancient Greek mathematics, but the term ""lemniscate"" for curves of this type comes from the work of Jacob"
"Lemniscate of Bernoulli In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points ""F"" and ""F"", known as foci, at distance 2""a"" from each other as the locus of points ""P"" so that ""PF""·""PF"" = ""a"". The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from ""lemniscatus"", which is Latin for ""decorated with hanging ribbons"". It is a special case of the Cassini oval and is a rational algebraic curve of degree 4. This lemniscate was first described in 1694 by Jakob Bernoulli as a modification"
"curve, a three-dimensional curve formed by intersecting a sphere with a cylinder, also has a figure eight shape, and has the lemniscate of Gerono as its planar projection. Other figure-eight shaped algebraic curves include Lemniscate In algebraic geometry, a lemniscate is any of several figure-eight or -shaped curves. The word comes from the Latin ""lēmniscātus"" meaning ""decorated with ribbons"", from the Greek λημνίσκος meaning ribbons, or alternatively may refer to the wool from which the ribbons were made. Curves that have been called a lemniscate include three quartic plane curves: the hippopede or lemniscate of Booth, the lemniscate of Bernoulli,"
"linkage consisting of AB, BE and EG and the base link is AG, both joints on the framework of the engine. As the beam rocks, point F (which is drawn to aid this explanation, but which is not visible on the machine itself) describes an elongated figure-of-eight (more precisely, a lemniscate of Bernoulli) in mid-air. Since the motion of the walking beam is constrained to a small angle, F describes only a short section of the figure-of-eight, which is quite close to a vertical straight line. The figure-of-eight is symmetrical as long as arms AB and EG are equal in"
"case of elliptic functions with complex multiplication by is called the ""lemniscatic case"" in some sources. Using the elliptic integral the formula of the arc length formula_8 can be given as The following theorem about angles occurring in the lemniscate is due to German mathematician Gerhard Christoph Hermann Vechtmann, who described it 1843 in his dissertation on lemniscates. Dynamics on this curve and its more generalized versions are studied in quasi-one-dimensional models. Lemniscate of Bernoulli In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points ""F"" and ""F"", known as foci, at distance 2""a"" from"
"(when the half-distance between the points is equal to the square root of the constant) this gives rise to a lemniscate. In 1694, Johann Bernoulli studied the lemniscate case of the Cassini oval, now known as the lemniscate of Bernoulli (shown above), in connection with a problem of ""isochrones"" that had been posed earlier by Leibniz. Like the hippopede, it is an algebraic curve, the zero set of the polynomial formula_2. Bernoulli's brother Jacob Bernoulli also studied the same curve in the same year, and gave it its name, the lemniscate. It may also be defined geometrically as the locus"
"of points whose product of distances from two foci equals the square of half the interfocal distance. It is a special case of the hippopede (lemniscate of Booth), with formula_3, and may be formed as a cross-section of a torus whose inner hole and circular cross-sections have the same diameter as each other. The lemniscatic elliptic functions are analogues of trigonometric functions for the lemniscate of Bernoulli, and the lemniscate constants arise in evaluating the arc length of this lemniscate. Another lemniscate, the lemniscate of Gerono or lemniscate of Huygens, is the zero set of the quartic polynomial formula_4. Viviani's"
"is the central fragment of a cross-slab. The surviving shaft of the cross is decorated with a diagonal key pattern. The back of the stone has,from top to bottom, a horse and rider, a double disc symbol, a crescent and a dog wearing a collar. Meigle 7 is the top portion of a rounded cross-slab. The cross is decorated with a diagonal key pattern. The back of the monument has a double disc and Z-rod and a comb. Meigle 8 is a small fragment measuring across. It has an eroded cross on one side and the upper portion of two"
"The constants , , and are given by The case , may be handled by a scaling transformation. However, this may involve complex numbers. If it is desired to remain within real numbers, there are two cases to consider: and . The period parallelogram is either a square or a rhombus. The lemniscate sine (Latin: ""sinus lemniscatus"") and lemniscate cosine (Latin: ""cosinus lemniscatus"") functions ' aka ' and ' aka ' are analogues of the usual sine and cosine functions, with a circle replaced by a lemniscate. They are defined by where and where They are doubly periodic (or elliptic)"
"of radius ""b"" and a lemniscate of Booth, a figure eight shaped curve. A special case of this is ""a""=""c"", ""b""=√2""c"" which produces the lemniscate of Bernoulli. Finally, if ""d"">""b"" then the points ±""d"" are still solutions to the Cartesian equation of the curve, but the curve does not cross these points and they are acnodes. The curve again has a figure eight shape though the shape is distorted if ""d"" is close to ""b"". Given ""b"">""a""+""c"", the shape of the curve is determined by the relative sizes of ""a"" and ""c"". If ""a""<""c"" then the curve has the form"
"a horse together), or ""hippopede"" in Greek. The name ""lemniscate of Booth"" for this curve dates to its study by the 19th-century mathematician James Booth. The lemniscate may be defined as an algebraic curve, the zero set of the quartic polynomial formula_1 when the parameter ""d"" is negative. For positive values of ""d"" one instead obtains the oval of Booth. In 1680, Cassini studied a family of curves, now called the Cassini oval, defined as follows: the locus of all points, the product of whose distances from two fixed points, the curves' foci, is a constant. Under very particular circumstances"
"increscent and a decrescent a cross in pale point downwards, all Or. On a helmet a dragon Sable, exhaling fire Gules, on two crescents pointing up, Or. Mantling Sable, lined Or"" Modern version from the 17th century replaced a cross between crescents with the sword in pale point downwards. On a crowned helmet, five ostrich feathers. The last image is of the seal of Dobieslaw de Koszyce from 1381 that is identical to an early sign found on the entry of the church in Wysocice of Nicolaus Ostoja de Sciborzyce (Lesser Poland) from about 1232. Those coat of arms as"
"badge of the Lancastrian house and party, the white swan, as in the Dunstable Swan Jewel, usually being its pendant. In one of Henry VI's own collars the S was joined to the broomcod of the French device, symbolizing the king's claim to the two kingdoms. The kings of the house of York and their chief followers wore the Yorkist collar of suns and roses, with the white lion of March, the Clare bull, or Richard's white boar for a pendant device. Henry VIII brought back the collar of Esses, a portcullis or a Tudor rose hanging from it, although"
"haloed or nimbed, and each beast symbol holds a book in its fore or hind limbs. Each miniature is also accompanied by a set of two Latin inscriptions written in capital letters, one at the top flanking the human bust and the other at the bottom flanking the beast symbol. Within the top roundel of this miniature the Evangelist is shown with his right hand in a gesture of benediction with his two index fingers pointing to his Gospel book that he holds in his left hand. His tetramorph beast symbol within the arch consists of a full-figure frontal standing"
"eagle, whilst eagles also fly upwards with them. The personified male figure (left) holding the obelisk represents the Campus Martius. Augustus had placed this obelisk there as a sundial and it was the site of the ritual of imperial deification ceremonies. The personified female figure in armour (right) saluting the emperor and empress represents Roma, and her shield depicts the legendary founders of Rome, Romulus and Remus, suckled by a she-wolf. On these two almost identical sides, members of the cavalry circle the standing figures, two carrying military standards and the rest fully armored. Lacking a sense of space and"
"of the Speaker. Shown on the left is the current Mace. On the right is the original Mace from the time of the first parliament in 1792. The crossed Maces are joined by the shield of arms of Ontario. The crown on the wreath represents national and provincial loyalties; its rim is studded with the provincial gemstone, the amethyst. The griffin, an ancient symbol of justice and equity, holds a calumet, which symbolizes the meeting of spirit and discussion that Ontario's First Nations believe accompanies the use of the pipe. The deer represent the natural riches of the province. The"
"right carry negative connotations, the exact opposite situation prevails at the lowest levels. The general preference for the left side, however, is resumed at the middle level. Here the figures at right appear to represent vices. For example, the second caryatid from the right is a woman holding snakes to her breast; she may represent Luxuria (unchastity). The caryatids at left, on the other hand, appear to represent virtues. For example, the second figure from the left is a man wearing a plaited belt; he may represent Fortitudo (bravery). The uppermost register, in which Christ appears flanked by the twelve"
"ivory, but the fruit-filled fold in the woman's robe is of the same form and fulfils the same symbolic function. Counterbalancing this first female figure, in the top right hand corner of the central panel, is a statuette of a winged Victory standing over a globe inscribed with the sign of the cross, holding a palm (symbol of victory) in her left hand and in her right hand (now broken) she almost certainly held a crown to be placed on the emperor's head. This type of statuette personification is also one of the links to the iconography of the triumphant"
"worked in bronze, holding shields which display the attributes of the Theological Virtues. Between them are marble bas-reliefs of the sacrifice of Abraham and of Melchizedek, expressing the double aspect of the Mass as Sacrifice and as Sacrament. The tabernacle is composed of two statues holding an ark; the men are Melchizedek, representing the natural law, and Aaron, representing the Mosaic law. The ark they support represents the Church. On its door is the Lamb of God, flanked by a dove, symbol of the pure soul, and a wolf, symbol of the perverse soul. At its corners stand figures of"
"blue, and beak and talons in red. The right half of the shield shows the arms of Madame du Roscoat, the foundress of the Sisters of Providence at Ruille-sur-Loir, France. The three eaglets are emblematic of the Holy Trinity, the motto of the du Roscoat family being ""Trino Soli sit honor et gloria"" (""To the Triune God alone honor and glory""). The left field is charged with devices symbolic or significant of some fact connected with the history of Saint Mary-of-the-Woods. The rayed star, charged with the letter ""M"" in blue, is an emblem of Mary Mother of God, the"
"animals on the reverse, facing each other with forelegs in the opposing beast's mouth. A symbol above them may represent a tool. Meigle 9 is a recumbent tombstone. It has a shallow slot in the top and sculpted panels on both long sides. One of the panels depicts a griffin, an interlace pattern, an elongated animal wrapped into a knot and two animals facing each other. The other panel is composed of an animal, a sitting person with his limbs entwined with the legs of a bird, another animal, some spiral patterns and a final section that is badly eroded."
"representing gem-set jewellery. The Crest is in the form of a lynx. This species of wildcat is traditionally renowned for its keenness of sight and, with perhaps just a touch of humour, was employed here as a perfect symbol for gemmologists and gemmology students. In its paws it holds one of the oldest heraldic emblems, an ‘escarbuncle’. This is a symbol of supremacy, but also represents a brilliant jewel with light radiating from it. Its tips are jewels of many different colours. Gem-A is often referred to as the central jewel, with gem education and knowledge radiating from it with"
"contact with Michelangelo's Sistine Chapel frescoes and Rome's classical remains, such as the Farnese Hercules or the Laocoön group. A vigorous and plastic Hercules is depicted with two women flanking him, who represent the opposite destinies which life could reserve him: on the left Virtue is calling him to the hardest path leading to glory through hardship, while the second, a woman with worldly pleasures, the easier path, is enticing him to vice. Behind Hercules is a palm, which, through the leaves and the branches (a symbol of military victory and fame), hints to Hercules' future heroic life. At the"
"the linkage is fixed as a base, the free joints move on equal circles, but in a parallelogram they move in the same direction with equal velocities while in the antiparallelogram they move in opposite directions with unequal velocities. As James Watt discovered, if an antiparallelogram has its long side fixed in this way it forms a variant of Watt's linkage, and the midpoint of the unfixed long edge will trace out a lemniscate or figure eight curve. For the antiparallelogram formed by the sides and diagonals of a square, it is the lemniscate of Bernoulli. The antiparallelogram is an"
"Ophite Diagrams The Ophite Diagrams are ritual and esoteric diagrams used by the Ophite sect of Gnosticism, who revered the serpent from the Garden of Eden as a symbol of wisdom, which the malevolent Demiurge tried to hide from Adam and Eve. Celsus and his opponent Origen (""Contra Celsum,"" §§ -) both describe the diagrams, though not in the same way. Celsus describes them as ten separate circles, circumscribed by one circle, the world-soul, Leviathan, divided by a thick black line, Tartarus, together with a square, with words said at the gates of Paradise. Further to this, the Ophites are"
"physical and spiritual. In the centre, the four sectors are separated by a cross which depicts the four directions namely North, South, East and West. A candle on the top of the right side stands for knowledge. It eliminates ignorance (darkness) and bestows wisdom (brightness). A computer on the bottom of the right side symbolizes science and technology. At the bottom of the left side a man bearing a book stands for education and training. A cross on the left top symbolizes sanctity, prosperity and godliness. Rays from the cross blesses and purifies all the things. Around the shield, the"
"diagram (Myer, pp. 311-13). But the serpent as symbol is found likewise in connection with the mysteries of Egypt, Greece, Phoenicia, Syria, and even Babylonia and India. Ophite Diagrams The Ophite Diagrams are ritual and esoteric diagrams used by the Ophite sect of Gnosticism, who revered the serpent from the Garden of Eden as a symbol of wisdom, which the malevolent Demiurge tried to hide from Adam and Eve. Celsus and his opponent Origen (""Contra Celsum,"" §§ -) both describe the diagrams, though not in the same way. Celsus describes them as ten separate circles, circumscribed by one circle, the"
"and fourth fields three coronets or, placed two above one. In the second and third fields three sinisterbendwise streams argent, a lion crowned with an open crown or with armaments gules. The inescutcheon is party per pale the arms for the House of Vasa and the House of Bernadotte. The main shield is crowned by a royal crown and surrounded by the insignia of the Order of the Seraphim. Supported by two lions regardant or crowned, with parted tails and armaments gules, standing on a postament. All surrounded by hermine mantling crowned with a royal crown and tied up with"
"victory, but looking mournfully at the Book of Remembrance, and behind her are two other persons, one symbolising Canadian motherhood and the other First Nations. The fourth quadrant shows Joan of Arc bearing a shield and standing before the royal coat of arms of France. Similar to the other windows, this one shows four figures across the top portion. The first of these is the figure of the ""Victory of Peace"", holding both a palm branch and the sword of judgement, while a dove flies overhead. The second person shown is that of ""Prosperity"", who holds a wheat sheaf and"
"if a barrier to the other panels, while her text is in a straight horizontal rather than curved. When the wings are closed across the central panel, the exterior reveals a ""memento mori"" or vanitas motif of a skull and cross with is decorated with Latin inscriptions. The outer left hand wing shows a yellow-brown skull leaning against a broken brick or stone fragment alongside the coat of arms of the Braque family -a sheaf of wheat- seen on the upper right portion of the panel. It has been suggested that the skull is a future state representation of the"