In geometry, a torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis, coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a sphere. If the revolved curve is not a circle, the surface is a toroid. Real-world objects that approximate a torus of revolution include swim inner tubes. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a solid torus, formed by rotating a disk, rather than a circle, around an axis. A solid torus is a torus plus the volume inside the torus. Real-world objects that approximate a solid torus include O-rings, non-inflatable lifebuoys, ring doughnuts.

In topology, a ring torus is homeomorphic to the Cartesian product of two circles: S1 × S1, the latter is taken to be the definition in that context. It is a compact 2-manifold of genus 1; the ring torus is one way to embed this space into Euclidean space, but another way to do this is the Cartesian product of the embedding of S1 in the plane with itself. This produces a geometric object called the Clifford torus, a surface in 4-space. In the field of topology, a torus is any topological space, topologically equivalent to a torus. A coffee cup and a doughnut are both topological tori. An example of a torus can be constructed by taking a rectangular strip of flexible material, for example, a rubber sheet, joining the top edge to the bottom edge, the left edge to the right edge, without any half-twists. A torus can be defined parametrically by: x = cos ⁡ φ y = sin ⁡ φ z = r sin ⁡ θ where θ, φ are angles which make a full circle, so that their values start and end at the same point, R is the distance from the center of the tube to the center of the torus, r is the radius of the tube.

R is known as the "major radius" and r is known as the "minor radius". The ratio R divided by r is known as the "aspect ratio"; the typical doughnut confectionery has an aspect ratio of about 3 to 2. An implicit equation in Cartesian coordinates for a torus radially symmetric about the z-axis is 2 + z 2 = r 2, or the solution of f = 0, where f = 2 + z 2 − r 2. Algebraically eliminating the square root gives a quartic equation, 2 = 4 R 2; the three classes of standard tori correspond to the three possible aspect ratios between R and r: When R > r, the surface will be the familiar ring torus or anchor ring. R = r corresponds to the horn torus, which in effect is a torus with no "hole". R < r describes the self-intersecting spindle torus. When R = 0, the torus degenerates to the sphere; when R ≥ r, the interior 2 + z 2 < r 2 of this torus is diffeomorphic to a product of a Euclidean open disk and a circle. The volume of this solid torus and the surface area of its torus are computed using Pappus's centroid theorem, giving

Greek Old Calendarists

Greek Old Calendarists known as "Genuine Orthodox Christians", are groups of Old Calendarist Orthodox Christians that remained committed to the traditional Orthodox practice and are not in communion with many other Orthodox churches such as the Orthodox Church of Greece, the Patriarchate of Constantinople, or the Church of Cyprus. The split began with a disagreement over the abandonment of the traditional church calendar in preference to the adoption of the Revised Julian calendar, similar to the papal Gregorian calendar but will pull ahead by one day in the year 2800 and over other liturgical reforms that were introduced; until 1923 the Eastern Orthodox Church universally used the Julian calendar, whereas the Roman Catholic Church, under Pope Gregory XIII, conducted a calendar reform and adopted the mediaeval Gregorian calendar in 1582. The difference between the two calendars is 13 days between 1900 and 2100. For civil and governmental uses, the Julian calendar remained the official calendar in most Orthodox Christian nations until the early 20th century.

The Gregorian calendar was adopted for civil uses by Bulgaria in 1916, the Ottoman Empire in 1917, Soviet Russia in 1918 and Romania and Yugoslavia in 1919. Greece adopted the "political calendar", a system devised in 1785, on 17 February/1 March 1923; this dropped all centennial leap years except those giving remainder 0 or 400 on division by 900. With the growing acceptance of this calendar, it was realised that it would diverge from the Gregorian within eighty years, steps were taken to ameliorate this. In May 1923, the controversial Pan-Orthodox Congress of Constantinople, called by Patriarch Meletius IV of Constantinople, adopted this calendar under the name of Revised Julian calendar, incorporating a modification of Serbian astronomer Milutin Milanković which ensured it would not diverge from the Gregorian for a further 800 years; this replaced the tabular Easter of the Julian calendar with the astronomical Easter. Not all Orthodox churches were represented at the congress or adopted its decisions, the Russian Orthodox Church and other Orthodox churches, governing a majority of Orthodox Christians, have continued to use the Julian calendar liturgically to this day.

In 1924, the Synod of Bishops of the Church of Greece, following the lead of other Orthodox churches, voted to accept the Revised Julian calendar for fixed feasts, maintaining the traditional Julian calendar Paschalion for calculating the date of Pascha and all of the moveable feasts dependent on it. The calendar change was not without controversy. Dissent arose from among both clergy and laity, encouraged by countless priests and monks from all over Greece and Mount Athos who traveled throughout Greece preaching in churches and serving as confessors, or spiritual guides, to thousands of Christians. On Mount Athos the Julian calendar is used to this day. In 1935, three bishops from the Church of Greece returned their dioceses to the Julian calendar, consecrated four like-minded clergy to episcopal dignity, created the church of the "Genuine Orthodox Christians", declared that the official Orthodox Church of Greece had fallen into schism. By 1937, the movement split within itself over the question of whether or not Orthodox jurisdictions that had adopted the Revised Julian calendar were still Orthodox.

After a successful grassroots effort to resist the Greek state's new doctrine and its new calendar that originated in Western Christendom, the popularity of the old calendar was attacked. The Church of Greece is the official state church and resorted to the use of state power to suppress the movement. By the 1960s and 1970s, the ecumenical activities of a number of Orthodox leaders infused the Old Calendar Church with new followers in Greece in 1965–72 when the monasteries of Mount Athos broke communion with the Patriarchate of Constantinople; the Old Calendarists were more successful in the United States, where religion is not regulated by the state. The Old Calendarists went their own way without further official recognition from the broader Orthodox communion until 1960, when the Russian Orthodox Church Outside Russia consecrated new bishops for one of the two major Old Calendarist jurisdictions. ROCOR recognized the other major jurisdiction in 1971, consecrating bishops for them as their apostolic succession had been through a single bishop, dubious in the Orthodox Church.

However, excepting for groups split-off from ROCOR, no official inter-communion exists between the Greek Old Calendarists and ROCOR at the present day, due to the recent reunification of ROCOR and the Russian Orthodox Church. In 1998, plagued by moral and financial scandals, two bishops who had broken off from the Church of the Genuine Orthodox Christians in the United States were re-baptized and re-ordained by the Ecumenical Patriarchate and put under the leadership of the Greek Orthodox Church in the U. S.. In exchange, the few priests that went with them were accepted as Orthodox priests, their churches were allowed to maintain their use of the Julian calendar; these parishes were forced to switch to the Revised Julian calendar although allowed to remain using their more traditional liturgy. In the present day, there are five major Old Calendarist divisions present in Greece, three Florinite and two Matthewite, all of which have parishes in many other countries. Among the Florinites, the largest is the Church of the Genuine Orthodox Christians of Greece under Archbishop Kallinikos.

Another is the Holy Metropol

A. E. Coppard

Alfred Edgar Coppard was an English writer and poet, noted for his influence on the short story form. Coppard was born the son of a tailor and a housemaid in Folkestone, had little formal education. Coppard grew up in poverty-stricken circumstances, he left school at the age of nine to work as an errand boy for a Jewish trouser maker in Whitechapel during the period of the Jack the Ripper murders. In the early 1920s, still unpublished, he was in Oxford and a leading light of a literary group, the New Elizabethans, who met in a pub to read Elizabethan drama. W. B. Yeats sometimes attended the meetings. At this period he met Edgell Rickword, amongst others. Coppard was a member of the Independent Labour Party for a period. Coppard's fiction was influenced by Thomas Hardy and, on its initial publication, favourably compared to that of H. E. Bates. Coppard's work enjoyed a surge in popularity in the US after his Selected Tales was chosen as a selection by the Book of the Month Club. In the profile in Twentieth Century Authors, Coppard lists Abraham Lincoln as the politician he most admired.

Coppard listed Sterne, James, Shaw and Joyce as authors he valued. Some of Coppard's collections, such as Adam and Eve and Pinch Me and Fearful Pleasures, contain stories with fantastic elements, either of supernatural horror or allegorical fantasy. In Nancy Cunard's 1937 book Authors take Sides on the Spanish War, Coppard took the side of the Republicans. A. E. Coppard was the uncle of George Coppard, a British soldier who served with the Machine Gun Corps during World War I, known for his memoirs With A Machine Gun to Cambrai. Coppard's short stories were praised by Ford Madox Frank O'Connor. Coppard's book Nixey's Harlequin received good reviews from L. A. G. Strong, Gerald Bullett, The Times Literary Supplement. Coppard's supernatural fiction was admired by Algernon Blackwood. Brian Stableford argues that Coppard's fantasy has a similar style to that of Walter de la Mare and that "many of his mercurial and oddly plaintive fantasies are disturbing". Adam & Eve & Pinch Me Clorinda Walks in Heaven The Black Dog and Other Stories Fishmonger's Fiddle: Tales The Field of Mustard Silver Circus Count Stefan The Higgler Nixey's Harlequin Fares Please!

Crotty Shinkwin and The Beauty Spot Dunky Fitlow Ring the Bells of Heaven Emergency Exit Pink Furniture Polly Oliver Ninepenny Flute You Never Know, Do You? Ugly Anna Fearful Pleasures Selected Tales The Dark Eyed Lady – Fourteen Tales Collected Tales Lucy in Her Pink Coat Selected Stories The Collected Tales of A. E. Coppard The Higgler and Other Stories The Man from the Caravan and Other Stories Father Raven and Other Tales Weep not my wanton: selected short stories Hips and Haws Yokohoma Garland & Other Poems Pelaga and Other Poems The Collected Poems of A. E. Coppard Cherry Ripe: Poems Simple Day: Selected Poems The Hundredth Story of A. E. Coppard Cheefoo Good Samaritans These Hopes of Heaven Tapster's Tapestry:A Tale Rummy: that noble game expounded in prose, poetry and engraving. Songs from Robert Burns. Selected by A. E. Coppard, with wood engravings by Mabel M. Annesley Consequences, a complete story in the manner of the old parlour game, in nine chapters, each by a different author The Fairies Return, or New Tales for Old It's Me, O Lord!

Fabes, Gilbert H. The First Editions of A. E. Coppard, A. P. Herbert and Charles Morgan, 1933 London: Myers. Saul, George Brandon, A. E. Coppard: His Life and Poetry,1932, University of Pennsylvania, PhD dissertation. Schwartz, Jacob with foreword and notes by A. E. Coppard, A Bibliography of A. E. Coppard - The Writings of Alfred Edgar Coppard, 1931. Jehin, A. Remarks on the Style of A. E. Coppard. Buenos Aires, 1944. Bleiler, Everett; the Checklist of Fantastic Literature. Chicago: Shasta Publishers. Pp. 83–84. Works by A. E. Coppard at Project Gutenberg Works by A. E. Coppard at Faded Page Works by or about A. E. Coppard at Internet Archive Works by A. E. Coppard at LibriVox AE Coppard at the Supernatural Fiction Database "Archival material relating to A. E. Coppard". UK National Archives. A. E. Coppard at the Internet Speculative Fiction Database A. E. Coppard at Library of Congress Authorities, with 57 catalogue records