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Galanthus

Galanthus (from Ancient Greek, (, "milk") + (, "flower")), or snowdrop, is a small genus of approximately 20 species of bulbous perennial herbaceous plants in the family Amaryllidaceae. The plants have two linear leaves and a single small white drooping bell-shaped flower with six petal-like (petaloid) tepals in two circles (whorls). The smaller inner petals have green markings.

Snowdrops have been known since the earliest times under various names, but were named Galanthus in 1753. As the number of recognised species increased, various attempts were made to divide the species into subgroups, usually on the basis of the pattern of the emerging leaves (vernation). In the era of molecular phylogenetics this characteristic has been shown to be unreliable and now seven molecularly defined clades are recognised that correspond to the biogeographical distribution of species. New species continue to be discovered.

Most species flower in winter, before the vernal equinox (20 or 21 March in the Northern Hemisphere), but some flower in early spring and late autumn. Sometimes snowdrops are confused with the two related genera within the tribe Galantheae, snowflakes Leucojum and Acis.

General
All species of Galanthus are perennial petaloid herbaceous bulbous (growing from bulbs) monocot plants. The genus is characterised by the presence of two leaves, pendulous white flowers with six free perianth segments in two whorls. The inner whorl is smaller than the outer whorl and has green markings.

Vegetative
These are basal, emerging from the bulb initially enclosed in a tubular membranous sheath of cataphylls. Generally, these are two (sometimes three) in number and linear, strap-shaped, or oblanceolate. Vernation, the arrangement of the emerging leaves relative to each other, varies among species. These may be applanate (flat), supervolute (conduplicate), or explicative (pleated). In applanate vernation, the two leaf blades are pressed flat to each other within the bud and as they emerge; explicative leaves are also pressed flat against each other, but the edges of the leaves are folded back (externally recurved) or sometimes rolled; in supervolute plants, one leaf is tightly clasped around the other within the bud and generally remains at the point where the leaves emerge from the soil (for illustration, see Stearn and Davis). In the past, this feature has been used to distinguish between species and to determine the parentage of hybrids, but now has been shown to be homoplasious, and not useful in this regard.
 * Leaves:

The scape (flowering stalk) is erect, leafless, terete, or compressed.

Reproductive
At the top of the scape is a pair of bract-like spathes (valves) usually fused down one side and joined by a papery membrane, appearing monophyllous (single). From between the spathes emerges a solitary (rarely two), pendulous, nodding, bell-shaped white flower, held on a slender pedicel. The flower bears six free perianth segments (tepals) rather than true petals, arranged in two whorls of three, the outer whorl being larger and more convex than the inner whorl. The outer tepals are acute to more or less obtuse, spathulate or oblanceolate to narrowly obovate or linear, shortly clawed, and erect spreading. The inner tepals are much shorter (half to two thirds as long), oblong, spathulate or oblanceolate, somewhat unguiculate (claw like); tapering to the base and erect. These tepals also bear green markings at the base, the apex, or both, that when at the apex, are bridge-shaped over the small sinus (notch) at the tip of each tepal, which are emarginate. Occasionally, the markings are either green-yellow, yellow, or absent, and the shape and size varies by species.
 * Inflorescence :

The six stamens are inserted at the base of the perianth, and are very short (shorter than the inner perianth segments), the anthers basifixed (attached at their bases) with filaments much shorter than the anthers; they dehisce (open) by terminal pores or short slits.
 * Androecium :

The inferior ovary is three-celled. The style is slender and longer than the anthers; the stigma is minutely capitate. The ovary ripens into a three-celled capsule fruit. This fruit is fleshy, ellipsoid or almost spherical, opening by three flaps, with seeds that are light brown to white and oblong with a small appendage or tail (elaiosome) containing substances attractive to ants, which distribute the seeds.
 * Gynoecium, fruit and seeds:

The chromosome number is 2n=24.

Floral formula: $$\star\; P_{3+3} \; A_{3+3} \; G_{\overline{(3)}}$$

Distribution and habitat
The genus Galanthus is native to Europe and the Middle East, from the Spanish and French Pyrenees in the west through to the Caucasus and Iran in the east, and south to Sicily, the Peloponnese, the Aegean, Turkey, Lebanon, and Syria. The northern limit is uncertain because G. nivalis has been widely introduced and cultivated throughout Europe. G. nivalis and some other species valued as ornamentals have become widely naturalised in Europe, North America, and other regions. In the Udmurt republic of Russia, Galanthus are found even above the 56th parallel.

Galanthus nivalis is the best-known and most widespread representative of the genus Galanthus. It is native to a large area of Europe, stretching from the Pyrenees in the west, through France and Germany to Poland in the north, Italy, northern Greece, Bulgaria, Romania, Ukraine, and European Turkey. It has been introduced and is widely naturalised elsewhere. Although it is often thought of as a British native wild flower, or to have been brought to the British Isles by the Romans, it most likely was introduced around the early sixteenth century, and is currently not a protected species in the UK. It was first recorded as naturalised in the UK in Worcestershire and Gloucestershire in 1770. Most other Galanthus species are from the eastern Mediterranean, while several are found in the Caucasus, in southern Russia, Georgia, Armenia, and Azerbaijan. Galanthus fosteri is found in Jordan, Lebanon, Syria, Turkey, and, perhaps, Palestine.

Most Galanthus species grow best in woodland, in acid or alkaline soil, although some are grassland or mountain species.

Early
Snowdrops have been known since early times, being described by the classical Greek author Theophrastus, in the fourth century BCE, in his Περὶ φυτῶν ἱστορία (Latin: Historia plantarum, Enquiry into plants). He gave it, and similar plants, the name λευκόἲον (λευκος, leukos "white" and ἰόν, ion "violet") from which the later name Leucojum was derived. He described the plant as "ἑπεἰ τοῖς γε χρώμασι λευκἂ καἱ οὐ λεπυριώδη" (in colour white and bulbs without scales) and of their habits "Ἰῶν δ' ἁνθῶν τὀ μἑν πρῶτον ἑκφαἱνεται τὁ λευκόἲον, ὅπου μἑν ό ἀἠρ μαλακώτερος εὐθὑς τοῦ χειμῶνος, ὅπου δἐ σκληρότερος ὕστερον, ἑνιαχοῡ τοῡ ἣρος" (Of the flowers, the first to appear is the white violet. Where the climate is mild, it appears with the first sign of winter, but in more severe climates, later in spring)

Rembert Dodoens, a Flemish botanist, described and illustrated this plant in 1583 as did Gerard in England in 1597 (probably using much of Dodoens' material), calling it Leucojum bulbosum praecox (Early bulbous violet). Gerard refers to Theophrastus's description as Viola alba or Viola bulbosa, using Pliny's translation, and comments that the plant had originated in Italy and had "taken possession" in England "many years past". The genus was formally named Galanthus and described by Carl Linnaeus in 1753, with the single species, Galanthus nivalis, which is the type species. Consequently, Linnaeus is granted the botanical authority. In doing so, he distinguished this genus and species from Leucojum (Leucojum bulbosum trifolium minus), a name by which it previously had been known.

Modern
In 1763 Michel Adanson began a system of arranging genera in families. Using the synonym Acrocorion (also spelt Akrokorion), he placed Galanthus in the family Liliaceae, section Narcissi. Lamarck provided a description of the genus in his encyclopedia (1786), and later, Illustrations des genres (1793). In 1789 de Jussieu, who is credited with the modern concept of genera organised in families, placed Galanthus and related genera within a division of Monocotyledons, using a modified form of Linnaeus' sexual classification, but with the respective topography of stamens to carpels rather than just their numbers. In doing so, he restored the name Galanthus and retained their placement under Narcissi, this time as a family (known as Ordo, at that time) and referred to the French vernacular name, Perce-neige (Snow-pierce), based on the plants tendency to push through early spring snow (see Ecology for illustration). The modern family of Amaryllidaceae, in which Galanthus is placed, dates to Jaume Saint-Hilaire (1805) who replaced Jussieu's Narcissi with Amaryllidées. In 1810, Brown proposed that a subgroup of Liliaceae be distinguished on the basis of the position of the ovaries and be referred to as Amaryllideae, and in 1813, de Candolle separated them by describing Liliacées Juss. and Amaryllidées Brown as two quite separate families. However, in his comprehensive survey of the Flora of France (Flore française, 1805–1815) he divided Liliaceae into a series of Ordres, and placed Galanthus into the Narcissi Ordre. This relationship of Galanthus to either liliaceous or amaryllidaceaous taxa (see Taxonomy of Liliaceae) was to last for another two centuries until the two were formally divided at the end of the twentieth century. Lindley (1830) followed this general pattern, placing Galanthus and related genera such as Amaryllis and Narcissus in his Amaryllideae (which he called The Narcissus Tribe in English). By 1853, the number of known plants was increasing considerably and he revised his schema in his last work, placing Galanthus together, and the other two genera in the modern Galantheae in tribe Amarylleae, order Amaryllidaceae, alliance Narcissales. These three genera have been treated together taxonomically by most authors, on the basis of an inferior ovary. As the number of plant species increased, so did the taxonomic complexity. By the time Bentham and Hooker published their Genera plantarum (1862–1883) ordo Amaryllideae contained five tribes, and tribe Amarylleae three subtribes (see Bentham & Hooker system). They placed Galanthus in subtribe Genuinae and included three species.

Phylogeny
Galanthus is one of three closely related genera making up the tribe Galantheae within subfamily Amaryllidoideae (family Amaryllidaceae). Sometimes snowdrops are confused with the other two genera, Leucojum and Acis (both called snowflakes). Leucojum species are much larger and flower in spring (or early summer, depending on the species), with all six tepals in the flower being the same size, although some "poculiform" (goblet- or cup-shaped) Galanthus species may have inner segments similar in shape and length to the outer ones. Galantheae are likely to have arisen in the Caucusus.

Subdivision

Galanthus has approximately 20 species, but new species continue to be described. G. trojanus was identified in Turkey in 2001. G. panjutinii (Panjutin's snowdrop) was discovered in 2012 in five locations in a small area (estimated at 20 km2) of the northern Colchis area (western Transcaucasus) of Georgia and Russia. G. samothracicus was identified in Greece in 2014. Since it has not been subjected to genetic sequencing, it remains unplaced. It resembles G. nivalis, but is outside the distribution of that species.

Many species are difficult to identify, however, and traditional infrageneric classification based on plant morphology alone, such as those of Stern (1956), Traub (1963) and Davis (1999, 2001), has not reflected what is known about its evolutionary history, due to the morphological similarities among the species and relative lack of easily discernible distinguishing characteristics. Stern divided the genus into three series according to leaf vernation (the way the leaves are folded in the bud, when viewed in transverse section, see Description); Stern further utilised characteristics such as the markings of the inner segments, length of the pedicels in relation to the spathe, and the colour and shape of the leaves in identifying and classifying species
 * section Nivales Beck (flat leaves)
 * section Plicati Beck (plicate leaves)
 * section Latifolii Stern (convolute leaves)

Traub considered them as subgenera;
 * subgenus Galanthus
 * subgenus Plicatanthus Traub & Moldk.
 * subgenus Platyphyllanthe Traub

By contrast Davis, with much more information and specimens, included biogeography in addition to vernation, forming two series. He used somewhat different terminology for vernation, namely applanate (flat), explicative (plicate), and supervolute (convolute). He merged Nivalis and Plicati into series Galanthus, and divided Latifolii into two subseries, Glaucaefolii (Kem.-Nath) A.P.Davis and Viridifolii (Kem.-Nath) A.P.Davis.

Early molecular phylogenetic studies confirmed the genus was monophyletic and suggested four clades, which were labelled as series, and showed that Davis' subseries were not monophyletic. An expanded study in 2013 demonstrated seven major clades, corresponding to biogeographical distribution. This study used nuclear encoded nrITS (Nuclear ribosomal internal transcribed spacer), and plastid encoded genes matK (Maturase K), trnL-F, ndhF, and psbK–psbI, and examined all species recognised at the time, as well as two naturally occurring putative hybrids. The morphological characteristic of vernation that earlier authors had mainly relied on was shown to be highly homoplasious. A number of species, such as G. nivalis and G. elwesii demonstrated intraspecific biogeographical clades, indicating problems with speciation and there may be a need for recircumscription. These clades were assigned names, partly according to Davis' previous groupings. In this model clade, the group containing G. platyphyllus is sister to the rest of the genus.

By contrast, another study performed at the same time, using both nuclear and chloroplast DNA, but limited to the 14 species found in Turkey, largely confirmed Davis' series and subseries, and with biogeographical correlation. Series Galanthus in this study corresponded to clade nivalis, subseries Glaucaefolii with clade Elwesii and subseries Viridifolii with clades Woronowii and Alpinus. However, the model did not provide complete resolution.

Clades
sensu Ronsted et al. 2013
 * Platyphyllus clade (Caucasus, W. Transcaucasus, NE Turkey)
 * Galanthus krasnovii Khokhr. 1963
 * Galanthus platyphyllus Traub & Moldenke 1948
 * Galanthus panjutinii Zubov & A.P.Davis 2012
 * Trojanus clade (NW Turkey)
 * Galanthus trojanus A.P.Davis & Özhatay 2001
 * Ikariae clade (Aegean Islands)
 * Galanthus ikariae Baker 1893
 * Elwesii clade (Turkey, Aegean Islands, SE Europe)
 * Galanthus cilicicus Baker 1897
 * Galanthus elwesii Hook.f. 1875 (2 variants)
 * Galanthus gracilis Celak. 1891
 * Galanthus peshmenii A.P.Davis & C.D.Brickell 1994
 * Nivalis clade (Europe, NW Turkey)
 * Galanthus nivalis L. 1753
 * Galanthus plicatus M.Bieb. 1819 (2 subspecies)
 * Galanthus reginae-olgae Orph. 1874 (2 subspecies)
 * Woronowii clade (Caucasus, E. and NE Turkey, N. Iran)
 * Galanthus fosteri Baker 1889
 * Galanthus lagodechianus Kem.-Nath. 1947
 * Galanthus rizehensis Stern 1956
 * Galanthus woronowii Losinsk. 1935
 * Alpinus clade (Caucasus, NE Turkey, N.Iran)
 * Galanthus × allenii Baker 1891
 * Galanthus angustifolius Koss 1951
 * Galanthus alpinus Sosn. (2 variants) 1911
 * Galanthus koenenianus Lobin 1993
 * Galanthus transcaucasicus Fomin 1909
 * Unplaced
 * Galanthus bursanus Zubov, Konca & A.P.Davis 2019 (NW Turkey)
 * Galanthus samothracicus Kit Tan & Biel 2014 (Greece)

 * Selected species
 * Common snowdrop, Galanthus nivalis, grows to around 7–15 cm tall, flowering between January and April in the northern temperate zone (January–May in the wild). Applanate vernation Grown as ornamental.
 * Crimean snowdrop, Galanthus plicatus, 30 cm tall, flowering January/March, white flowers, with broad leaves folded back at the edges (explicative vernation)
 * Giant snowdrop, Galanthus elwesii, a native of the Levant, 23 cm tall, flowering January/February, with large flowers, the three inner segments of which often have a much larger and more conspicuous green blotch (or blotches) than the more common kinds; supervolute vernation. Grown as ornamental.
 * Galanthus reginae-olgae, from Greece and Sicily, is quite similar in appearance to G. nivalis, but flowers in autumn before the leaves appear. The leaves, which appear in the spring, have a characteristic white stripe on their upper side; applanate vernation
 * G. reginae-olgae subsp. vernalis, from Sicily, northern Greece and the southern part of former Yugoslavia, blooms at the end of the winter with developed young leaves and is thus easily confused with G. nivalis.

Etymology
Galanthus is derived from the Greek γάλα (gala), meaning "milk" and ἄνθος (anthos) meaning "flower", alluding to the colour of the flowers. The epithet nivalis is derived from the Latin, meaning "of the snow". The word "Snowdrop" may be derived from the German Schneetropfen (snow-drop), the tear drop shaped pearl earrings popular in the sixteenth and seventeenth centuries. Other, earlier, common names include Candlemas bells, Fair maids of February, and White ladies (see Symbols).

Ecology
Snowdrops are hardy herbaceous plants that perennate by underground bulbs. They are among the earliest spring bulbs to bloom, although a few forms of G. nivalis are autumn flowering. In colder climates, they will emerge through snow (see illustration). They naturalise relatively easily forming large drifts. These are often sterile, found near human habitation, and also former monastic sites. The leaves die back a few weeks after the flowers have faded. Galanthus plants are relatively vigorous and may spread rapidly by forming bulb offsets. They also spread by dispersal of seed, animals disturbing bulbs, and water if disturbed by floods.

Conservation
Some snowdrop species are threatened in their wild habitats, due to habitat destruction, illegal collecting, and climate change. In most countries collecting bulbs from the wild is now illegal. Under CITES regulations, international trade in any quantity of Galanthus, whether bulbs, live plants, or even dead ones, is illegal without a CITES permit. This applies to hybrids and named cultivars, as well as species. CITES lists all species, but allows a limited trade in wild-collected bulbs of just three species (G. nivalis, G. elwesii, and G. woronowii) from Turkey and Georgia. A number of species are on the IUCN Red List of threatened species, with the conservation status being G. trojanus as critically endangered, four species vulnerable, G. nivalis is near threatened and several species show decreasing populations. G. panjutinii is considered endangered. One of its five known sites, at Sochi, was destroyed by preparations for the 2014 Winter Olympics.

Cultivation
Galanthus species and cultivars are extremely popular as symbols of spring and are traded more than any other wild-source ornamental bulb genus. Millions of bulbs are exported annually from Turkey and Georgia. For instance export quotas for 2016 for G. elwesii were 7 million for Turkey. Quotas for G. worononowii were 5 million for Turkey and 15 million for Georgia. These figures include both wild-taken and artificially propagated bulbs.

Snowdrop gardens

Celebrated as a sign of spring, snowdrops may form impressive carpets of white in areas where they are native or have been naturalised. These displays may attract large numbers of sightseers. There are a number of snowdrop gardens in England, Wales, Scotland, and Ireland. Several gardens open specially in February for visitors to admire the flowers. Sixty gardens took part in Scotland's first Snowdrop Festival (1 Feb–11 March 2007). Several gardens in England open during snowdrop season for the National Gardens Scheme (NGS) and in Scotland for Scotland's Gardens. Colesbourne Park in Gloucestershire is one of the best known of the English snowdrop gardens, being the home of Henry John Elwes, a collector of Galanthus specimens, and after whom Galanthus elwesii is named.

Cultivars
Numerous single- and double-flowered cultivars of Galanthus nivalis are known, and also of several other Galanthus species, particularly G. plicatus and G. elwesii. Also, many hybrids between these and other species exist (more than 500 cultivars are described in Bishop, Davis, and Grimshaw's book, plus lists of many cultivars that have now been lost, and others not seen by the authors). They differ particularly in the size, shape, and markings of the flower, the period of flowering, and other characteristics, mainly of interest to the keen (even fanatical) snowdrop collectors, known as "galanthophiles", who hold meetings where the scarcer cultivars change hands. Double-flowered cultivars and forms, such as the extremely common Galanthus nivalis f. pleniflorus 'Flore Pleno', may be less attractive to some people, but they can have greater visual impact in a garden setting. Cultivars with yellow markings and ovaries rather than the usual green are also grown, such as 'Wendy's Gold'. Many hybrids have also occurred in cultivation.

Awards
, the following have gained the Royal Horticultural Society's Award of Garden Merit:

 * Galanthus 'Ailwyn'
 * Galanthus 'Atkinsii'
 * Galanthus 'Bertram Anderson'
 * Galanthus elwesii
 * Galanthus elwesii 'Comet'
 * Galanthus elwesii 'Godfrey Owen'
 * Galanthus elwesii 'Mrs Macnamara'
 * Galanthus elwesii var. monostictus
 * Galanthus 'John Gray'
 * Galanthus 'Lady Beatrix Stanley'
 * Galanthus 'Magnet'
 * Galanthus 'Merlin'
 * Galanthus nivalis
 * Galanthus nivalis f. pleniflorus 'Flore Pleno'
 * Galanthus nivalis 'Viridapice'
 * Galanthus plicatus
 * Galanthus plicatus 'Augustus'
 * Galanthus plicatus 'Diggory'
 * Galanthus plicatus 'Three Ships'
 * Galanthus reginae-olgae subsp. reginae-olgae
 * Galanthus 'S. Arnott'
 * Galanthus 'Spindlestone Surprise'
 * Galanthus 'Straffan'
 * Galanthus 'Trumps'
 * Galanthus woronowii

Propagation
Propagation is by offset bulbs, either by careful division of clumps in full growth ("in the green"), or removed when the plants are dormant, immediately after the leaves have withered; or by seeds sown either when ripe, or in spring. Professional growers and keen amateurs also use such methods as "twin-scaling" to increase the stock of choice cultivars quickly.

Toxicity
Snowdrops contain an active lectin or agglutinin named GNA for Galanthus nivalis agglutinin.

Medicinal use
In 1983, Andreas Plaitakis and Roger Duvoisin suggested that the mysterious magical herb, moly, that appears in Homer's Odyssey is the snowdrop. One of the active principles present in the snowdrop is the alkaloid galantamine, which, as an acetylcholinesterase inhibitor, could have acted as an antidote to Circe's poisons. Further supporting this notion are notes made during the fourth century BC by the Greek scholar Theophrastus who wrote in Historia plantarum that moly was "used as an antidote against poisons" although which specific poisons it was effective against remains unclear. Galantamine (or galanthamine) may be helpful in the treatment of Alzheimer's disease, although it is not a cure; the substance also occurs naturally in daffodils and other narcissi.

In popular culture
Snowdrops figure prominently in art and literature, often as a symbol in poetry of spring, purity, and religion (see Symbols), such as Walter de la Mare's poem The Snowdrop (1929). In this poem, he likened the triple tepals in each whorl ("A triplet of green-pencilled snow") to the Holy Trinity. He used snowdrop imagery several times in his poetry, such as Blow, Northern Wind (1950) – see Box. Another instance is the poem by Letitia Elizabeth Landon in which she asks "Thou fairy gift from summer, Why art thou blooming now?"
 * In the fairy-tale play The Twelve Months by Russian writer Samuil Marshak, a greedy queen decrees that a basket of gold coins shall be rewarded to anyone who can bring her galanthus flowers in the dead of winter. A young orphan girl is sent out during a snow storm by her cruel stepmother to find the spirits of the 12 months of the year, who take pity on her and not only save her from freezing to death, but also make it possible for her to gather the flowers even in winter. The Soviet traditionally animated film The Twelve Months (1956), Lenfilm film The Twelve Months (1972), and the anime film Twelve Months (1980) (Sekai meisaku dowa mori wa ikiteiru in Japan), are based on this fairy-tale play.
 * "Snowdrops" was the nickname that the British people gave during the Second World War to the military police of the United States Army (who were stationed in the UK preparatory to the invasion of the continent) because they wore a white helmet, gloves, gaiters, and Sam Browne belt against their olive drab uniforms.
 * In the German fairy tale, Snow White and the Seven Dwarfs, "Snowdrop" is used as an alternate name for the Princess Snow White.
 * The short story The Snowdrop by Hans Christian Andersen follows the fate of a snowdrop from a bulb striving toward the light to a picked flower placed in a book of poetry.
 * Russian composer Tchaikovsky wrote a series of 12 piano pieces, each one named after a month of the year with a second name suggesting something associated with that month. His "April" piece is subnamed "Snow Drop". The Russian climate having a later spring, and winter ending a bit later than in other places.
 * Johann Strauss II named his very successful waltz Schneeglöckchen (Snowdrops) op. 143 after this flower. The inspiration is especially evident in the cello introduction and in the slow unfurling of the opening waltz. Strauss composed this piece for a Russian Embassy dinner given at the Sperl ballroom in Vienna on 2 December 1853, but did not perform it publicly until the year 1854. The Sperl banquet was given in honour of her Excellency Frau Maria von Kalergis, daughter of the Russian diplomat and foreign minister Count Karl Nesselrode, and Strauss also dedicated his waltz to her.

Symbolism
Early names refer to the association with the religious feast of Candlemas (February 2) – the optimum flowering time of the plant – at which young women, robed in white, would walk in solemn procession in commemoration of the Purification of the Virgin, an alternative name for the feast day. The French name of violette de la chandaleur refers to Candlemas, while an Italian name, fiore della purificazione, refers to purification. The German name of Schneeglöckchen (little snow bells) invokes the symbol of bells.

In the language of flowers, the snowdrop is synonymous with 'hope' (and the goddess Persephone's/Proserpina's return from Hades), as it blooms in early springtime, just before the vernal equinox, and so, is seen as 'heralding' the new spring and new year.

In more recent times, the snowdrop was adopted as a symbol of sorrow and of hope following the Dunblane massacre in Scotland, and lent its name to the subsequent campaign to restrict the legal ownership of handguns in the UK.

Books

 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55
 * Chapter 2. Alan Meerow. Taxonomy and Phylogeny. pp. 17–55

Historical (chronological)

 * (see also, Naturalis Historia)
 * (see also, Bucolics)
 * see also Species Plantarum
 * (see Encyclopédie méthodique)
 * see also Species Plantarum
 * (see Encyclopédie méthodique)
 * (see Encyclopédie méthodique)
 * (see Encyclopédie méthodique)
 * (see Encyclopédie méthodique)

Images

 * , in
 * , in
 * , in

title: Galanthus


text:
Louis II, Elector of Brandenburg

Louis the Roman (Ludwig VI der Römer) (7 May 1328 – 17 May 1365) was the eldest son of Holy Roman Emperor, Louis IV the Bavarian, by his second wife, Margaret II, Countess of Hainaut, and a member of the House of Wittelsbach. Louis was Duke of Upper Bavaria as Louis VI (1347–1365) and Margrave of Brandenburg (1351–1365) as Louis II. As of 1356, he also served as Prince-Elector of Brandenburg.

Biography
Louis was born in Rome when his parents travelled there for his father's coronation as Holy Roman Emperor, hence his nickname "the Roman". When his father died in 1347, Louis succeeded him as Duke of Bavaria (as Louis VI) and Count of Holland and Hainaut together with his five brothers. Louis released Holland and Hainaut for his brothers William I and Albert I in 1349, since he expected to acquire the Polish crown by his in 1345 marriage with Cunigunde of Poland, a daughter of Casimir III and Aldona Ona of Lithuania. Later claims against William and Albert were not successful. Hence Louis supported his mother during her war with William.

In December 1351 Louis VI received Brandenburg from his older half-brother Louis V of Bavaria in exchange for the sole rule of Upper Bavaria. Less experienced than Louis V, he was also challenged by the "False Waldemar", an impostor who claimed Brandenburg and got support from several cities and Holy Roman Emperor Charles IV until the Wittelsbachs came to terms with Charles. Louis also had to abandon claims on fiefdoms in Mecklenburg and Pomerania. With the Golden Bull of 1356, Louis secured the electoral dignity. In 1358 Louis was absolved from the papal excommunication.

After Cunigunde's death in 1357, Louis married Ingeborg of Mecklenburg-Schwerin. She was a daughter of Albert II, Duke of Mecklenburg, and Euphemia of Sweden. Louis had no children with her, either, thus his younger brother Otto V succeeded him in Brandenburg. The childless dukes Louis and Otto had already promised Charles IV the succession in Brandenburg in 1364 as revenge for a conflict with their brother Stephen II over the Bavarian succession after the death of their nephew Meinhard, the son of Louis V. Louis the Roman died in Berlin in 1365.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Louis II, Elector of Brandenburg


text:
Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.

Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.

Main branches
Below are some of the main areas studied in algebraic topology:

Homotopy groups
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space.

Homology
In algebraic topology and abstract algebra, homology (in part from Greek ὁμός homos "identical") is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group.

Cohomology
In homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a cochain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries. Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology. Cohomology arises from the algebraic dualization of the construction of homology. In less abstract language, cochains in the fundamental sense should assign "quantities" to the chains of homology theory.

Manifolds
A manifold is a topological space that near each point resembles Euclidean space. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot be embedded in three dimensions, but can be embedded in four dimensions. Typically, results in algebraic topology focus on global, non-differentiable aspects of manifolds; for example Poincaré duality.

Knot theory
Knot theory is the study of mathematical knots. While inspired by knots that appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined so that it cannot be undone. In precise mathematical language, a knot is an embedding of a circle in three-dimensional Euclidean space, $$\mathbb{R}^3$$. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of $$\mathbb{R}^3$$ upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.

Complexes
A simplicial complex is a topological space of a certain kind, constructed by "gluing together" points, line segments, triangles, and their n-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex.

A CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation (often with a much smaller complex).

Method of algebraic invariants
An older name for the subject was combinatorial topology, implying an emphasis on how a space X was constructed from simpler ones (the modern standard tool for such construction is the CW complex). In the 1920s and 1930s, there was growing emphasis on investigating topological spaces by finding correspondences from them to algebraic groups, which led to the change of name to algebraic topology. The combinatorial topology name is still sometimes used to emphasize an algorithmic approach based on decomposition of spaces.

In the algebraic approach, one finds a correspondence between spaces and groups that respects the relation of homeomorphism (or more general homotopy) of spaces. This allows one to recast statements about topological spaces into statements about groups, which have a great deal of manageable structure, often making these statements easier to prove. Two major ways in which this can be done are through fundamental groups, or more generally homotopy theory, and through homology and cohomology groups. The fundamental groups give us basic information about the structure of a topological space, but they are often nonabelian and can be difficult to work with. The fundamental group of a (finite) simplicial complex does have a finite presentation.

Homology and cohomology groups, on the other hand, are abelian and in many important cases finitely generated. Finitely generated abelian groups are completely classified and are particularly easy to work with.

Setting in category theory
In general, all constructions of algebraic topology are functorial; the notions of category, functor and natural transformation originated here. Fundamental groups and homology and cohomology groups are not only invariants of the underlying topological space, in the sense that two topological spaces which are homeomorphic have the same associated groups, but their associated morphisms also correspond—a continuous mapping of spaces induces a group homomorphism on the associated groups, and these homomorphisms can be used to show non-existence (or, much more deeply, existence) of mappings.

One of the first mathematicians to work with different types of cohomology was Georges de Rham. One can use the differential structure of smooth manifolds via de Rham cohomology, or Čech or sheaf cohomology to investigate the solvability of differential equations defined on the manifold in question. De Rham showed that all of these approaches were interrelated and that, for a closed, oriented manifold, the Betti numbers derived through simplicial homology were the same Betti numbers as those derived through de Rham cohomology. This was extended in the 1950s, when Samuel Eilenberg and Norman Steenrod generalized this approach. They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms (e.g., a weak equivalence of spaces passes to an isomorphism of homology groups), verified that all existing (co)homology theories satisfied these axioms, and then proved that such an axiomatization uniquely characterized the theory.

Applications
Classic applications of algebraic topology include:
 * The Brouwer fixed point theorem: every continuous map from the unit n-disk to itself has a fixed point.
 * The free rank of the nth homology group of a simplicial complex is the nth Betti number, which allows one to calculate the Euler–Poincaré characteristic.
 * One can use the differential structure of smooth manifolds via de Rham cohomology, or Čech or sheaf cohomology to investigate the solvability of differential equations defined on the manifold in question.
 * A manifold is orientable when the top-dimensional integral homology group is the integers, and is non-orientable when it is 0.
 * The n-sphere admits a nowhere-vanishing continuous unit vector field if and only if n is odd. (For n = 2, this is sometimes called the "hairy ball theorem".)
 * The Borsuk–Ulam theorem: any continuous map from the n-sphere to Euclidean n-space identifies at least one pair of antipodal points.
 * Any subgroup of a free group is free. This result is quite interesting, because the statement is purely algebraic yet the simplest known proof is topological. Namely, any free group G may be realized as the fundamental group of a graph X. The main theorem on covering spaces tells us that every subgroup H of G is the fundamental group of some covering space Y of X; but every such Y is again a graph. Therefore, its fundamental group H is free. On the other hand, this type of application is also handled more simply by the use of covering morphisms of groupoids, and that technique has yielded subgroup theorems not yet proved by methods of algebraic topology; see.
 * Topological combinatorics.

Notable people
• Frank Adams

• Michael Atiyah

• Enrico Betti

• Armand Borel

• Karol Borsuk

• Raoul Bott

• Luitzen Egbertus Jan Brouwer

• William Browder

• Ronald Brown

• Henri Cartan

• Shiing-Shen Chern

• Albrecht Dold

• Charles Ehresmann

• Samuel Eilenberg

• Hans Freudenthal

• Peter Freyd

• Pierre Gabriel

• Israel Gelfand

• Alexander Grothendieck

• Allen Hatcher

• Friedrich Hirzebruch

• Heinz Hopf

• Michael J. Hopkins

• Witold Hurewicz

• Egbert van Kampen

• Daniel Kan

• Hermann Künneth

• Ruth Lawrence

• Solomon Lefschetz

• Jean Leray

• Saunders Mac Lane

• Mark Mahowald

• J. Peter May

• Barry Mazur

• John Milnor

• John Coleman Moore

• Jack Morava

• Joseph Neisendorfer

• Emmy Noether

• Sergei Novikov

• Grigori Perelman

• Henri Poincaré

• Lev Pontryagin

• Nicolae Popescu

• Mikhail Postnikov

• Daniel Quillen

• Jean-Pierre Serre

• Isadore Singer

• Stephen Smale

• Edwin Spanier

• Norman Steenrod

• Dennis Sullivan

• René Thom

• Hiroshi Toda

• Leopold Vietoris

• Hassler Whitney

• J. H. C. Whitehead

• Gordon Thomas Whyburn

Important theorems
• Blakers–Massey theorem

• Borsuk–Ulam theorem

• Brouwer fixed point theorem

• Cellular approximation theorem

• Dold–Thom theorem

• Eilenberg–Ganea theorem

• Eilenberg–Zilber theorem

• Freudenthal suspension theorem

• Hurewicz theorem

• Künneth theorem

• Lefschetz fixed-point theorem

• Leray–Hirsch theorem

• Poincaré duality theorem

• Seifert–van Kampen theorem

• Universal coefficient theorem

• Whitehead theorem

title: Algebraic topology


text:
Louis IV, Holy Roman Emperor

Louis IV (Ludwig; 1 April 1282 – 11 October 1347), called the Bavarian (Ludwig der Bayer, Ludovicus Bavarus), was King of the Romans from 1314, King of Italy from 1327, and Holy Roman Emperor from 1328 until his death in 1347.

Louis' election as king of Germany in 1314 was controversial, as his Habsburg cousin Frederick the Fair was simultaneously elected king by a separate set of electors. Louis defeated Frederick in the Battle of Mühldorf in 1322, and the two eventually reconciled. Louis was opposed and excommunicated by the French Pope John XXII; Louis in turn attempted to depose the pope and install an anti-pope.

Louis IV was Duke of Upper Bavaria from 1294 to 1301 together with his elder brother Rudolf I, was Margrave of Brandenburg until 1323, and Count Palatine of the Rhine until 1329, and became Duke of Lower Bavaria in 1340. He was the last Bavarian to be a king of Germany until 1742. He became Count of Hainaut, Holland, Zeeland, and Friesland in 1345 when his wife Margaret inherited those domains.

Early reign as Duke of Upper Bavaria
Louis was born in Munich, the son of Louis II, Duke of Upper Bavaria and Count Palatine of the Rhine, and Matilda, a daughter of King Rudolph I.

Though Louis was partly educated in Vienna and became co-regent of his brother Rudolf I in Upper Bavaria in 1301 with the support of his Habsburg mother and her brother, King Albert I, he quarreled with the Habsburgs from 1307 over possessions in Lower Bavaria. A civil war against his brother Rudolf due to new disputes on the partition of their lands was ended in 1313, when peace was made at Munich.

In the same year, on November 9, Louis defeated his Habsburg cousin Frederick the Fair who was further aided by duke Leopold I. Originally, he was a friend of Frederick, with whom he had been raised. However, armed conflict arose when the guardianship over the young Dukes of Lower Bavaria (Henry XIV, Otto IV, and Henry XV) was entrusted to Frederick, even though the late Duke Otto III, the former King of Hungary, had chosen Louis. On 9 November 1313, Frederick was defeated by Louis in the Battle of Gammelsdorf and had to renounce the tutelage. This victory caused a stir within the Holy Roman Empire and increased the reputation of the Bavarian Duke.

Election as German King and conflict with Frederick the Fair
The death of Holy Roman Emperor Henry VII in August 1313 necessitated the election of a successor. Henry's son John, King of Bohemia since 1310, was considered by many prince-electors to be too young, and by others to be already too powerful. One alternative was Frederick the Fair, the son of Henry's predecessor, Albert I, of the House of Habsburg. In reaction, the pro-Luxembourg party among the prince electors settled on Louis as its candidate to prevent Frederick's election.

On 19 October 1314, Archbishop Henry II of Cologne chaired an assembly of four electors at Sachsenhausen, south of Frankfurt. Participants were Louis' brother, Rudolph I of the Palatinate, who objected to the election of his younger brother, Duke Rudolph I of Saxe-Wittenberg, and Henry of Carinthia, whom the Luxembourgs had deposed as King of Bohemia. These four electors chose Frederick as King.

The Luxembourg party did not accept this election and the next day a second election was held. Upon the instigation of Peter of Aspelt, Archbishop of Mainz, five different electors convened at Frankfurt and elected Louis as King. These electors were Archbishop Peter himself, Archbishop Baldwin of Trier and King John of Bohemia - both of the House of Luxembourg - Margrave Waldemar of Brandenburg and Duke John II of Saxe-Lauenburg, who contested Rudolph of Wittenberg's claim to the electoral vote.

This double election was quickly followed by two coronations: Louis was crowned at Aachen - the customary site of coronations - by Archbishop Peter of Mainz, while the Archbishop of Cologne, who by custom had the right to crown the new king, crowned Frederick at Bonn. In the following conflict between the kings, Louis recognized in 1316 the independence of Switzerland from the Habsburg dynasty.

After several years of bloody war, victory finally seemed within the grasp of Frederick, who was strongly supported by his brother Leopold. However, Frederick's army was decisively defeated in the Battle of Mühldorf on 28 September 1322 on the Ampfing Heath, where Frederick and 1300 nobles from Austria and Salzburg were captured.

Louis held Frederick captive in Trausnitz Castle (Schwandorf) for three years, but the determined resistance by Frederick's brother Leopold, the retreat of John of Bohemia from his alliance, and a ban by Pope John XXII, who excommunicated Louis in 1324, induced Louis to release Frederick in the Treaty of Trausnitz of 13 March 1325. In this agreement, Frederick recognized Louis as legitimate ruler and undertook to return to captivity should he not succeed in convincing his brothers to submit to Louis.

As he did not manage to overcome Leopold's obstinacy, Frederick returned to Munich as a prisoner, even though the Pope had released him from his oath. Louis, who was impressed by such nobility, renewed the old friendship with Frederick, and they agreed to rule the Empire jointly. Since the Pope and the electors strongly objected to this agreement, another treaty was signed at Ulm on 7 January 1326, according to which Frederick would administer Germany as King of the Romans, while Louis would be crowned as Holy Roman Emperor in Italy. However, after Leopold's death in 1326, Frederick withdrew from the regency of the Empire and returned to rule only Austria. He died on 13 January 1330.

Coronation as Holy Roman Emperor and conflict with the Pope
After the reconciliation with the Habsburgs in 1326, Louis marched to Italy and was crowned King of Italy in Milan in 1327. Already in 1323, Louis had sent an army to Italy to protect Milan against the Kingdom of Naples, which was together with France the strongest ally of the papacy. But now the Lord of Milan Galeazzo I Visconti was deposed since he was suspected of conspiring with the pope.

In January 1328, Louis entered Rome and had himself crowned emperor by the aged senator Sciarra Colonna, called captain of the Roman people. Three months later, Louis published a decree declaring Pope John XXII (Jacques Duèze), who resided in Avignon, deposed on grounds of heresy. He then installed a Spiritual Franciscan, Pietro Rainalducci as antipope Nicholas V, who soon left Rome and a few years later submitted to Pope John XXII. In the meantime, Robert, King of Naples had sent both a fleet and an army against Louis and his ally Frederick II of Sicily. Louis spent the winter 1328/29 in Pisa and stayed then in Northern Italy. When his co-ruler Frederick of Habsburg died in 1330, Louis returned from Italy. In fulfillment of an oath, Louis founded Ettal Abbey on 28 April 1330.

Franciscan theologians Michael of Cesena and William of Ockham, and the philosopher Marsilius of Padua, who were all on bad terms with the Pope as well, joined Emperor Louis in Italy and accompanied him to his court at Alter Hof in Munich which became the first imperial residence of the Holy Roman Empire.

In 1333, Emperor Louis sought to counter French influence in the southwest of the empire so he offered Humbert II of Viennois the Kingdom of Arles which was an opportunity to gain full authority over Savoy, Provence, and its surrounding territories. Humbert was reluctant to take the crown due to the conflict that would follow with all around him, so he declined, telling the emperor that he should make peace with the church first.

Emperor Louis also allied with King Edward III of England in 1337 against King Philip VI of France, the protector of the new Pope Benedict XII in Avignon. King Philip VI had prevented any agreement between the Emperor and the Pope. Thus, the failure of negotiations with the papacy led to the declaration at Rhense in 1338 by six electors to the effect that election by all or the majority of the electors automatically conferred the royal title and rule over the empire, without papal confirmation. King Edward III was the Emperor's guest at the Imperial Diet in the Kastorkirche at Coblence in 1338 and was named Vicar-General of the Holy Roman Empire. However in 1341, the Emperor deserted Edward III but came to terms with Philip VI only temporarily. For the expected English payments were missing and Louis intended to reach an agreement with the Pope one more time.

Imperial privileges
Louis IV was a protector of the Teutonic Knights. In 1337 he allegedly bestowed upon the Teutonic Order a privilege to conquer Lithuania and Russia, although the Order had only petitioned for three small territories. Later he forbade the Order to stand trial before foreign courts in their territorial conflicts with foreign rulers.

Louis concentrated his energies also on the economic development of the cities of the empire, so his name can be found in many city chronicles for the privileges he granted. In 1330 the emperor for example permitted the Frankfurt Trade Fair, and in 1340 Lübeck, as the leading member of the Hanseatic League, received the coinage prerogative for golden gulden.

Dynastic policy

In 1323 Louis gave Brandenburg as a fiefdom to his eldest son Louis V after the Brandenburg branch of the House of Ascania had died out. With the Treaty of Pavia in 1329 the emperor reconciled the sons of his late brother Rudolph and returned the Palatinate to his nephews Rudolf and Rupert. After the death of Henry of Bohemia, the duchy of Carinthia was released as an imperial fief on 2 May 1335 in Linz to his Habsburg cousins Albert II, Duke of Austria, and Otto, Duke of Austria, while Tyrol was first placed into Luxemburg hands.

With the death of duke John I in 1340 Louis inherited Lower Bavaria and then reunited the duchy of Bavaria. John's mother, a member of the Luxemburg dynasty, had to return to Bohemia. In 1342 Louis also acquired Tyrol for the Wittelsbach by voiding the first marriage of Margarete Maultasch with John Henry of Bohemia and marrying her to his own son Louis V, thus alienating the House of Luxemburg even more.

In 1345 the emperor further antagonized the lay princes by conferring Hainaut, Holland, Zeeland, and Friesland upon his wife, Margaret II of Hainaut. The hereditary titles of Margaret's sisters, one of whom was the queen of England, were ignored. Because of the dangerous hostility of the Luxemburgs, Louis had increased his power base ruthlessly.

Conflict with Luxemburg
The acquisition of these territories and his restless foreign policy had earned Louis many enemies among the German princes. In the summer of 1346 the Luxemburg Charles IV was elected rival king, with the support of Pope Clement VI. Louis himself obtained much support from the Imperial Free Cities and the knights and successfully resisted Charles, who was widely regarded as a papal puppet ("rex clericorum" as William of Ockham called him). Also the Habsburg dukes stayed loyal to Louis. In the Battle of Crécy Charles' father John of Luxemburg was killed; Charles himself also took part in the battle but escaped.

But then Louis' sudden death avoided a longer civil war. Louis died in October 1347 from a stroke suffered during a bear-hunt in Puch near Fürstenfeldbruck. He is buried in the Frauenkirche in Munich. The sons of Louis supported Günther von Schwarzburg as new rival king to Charles but finally joined the Luxemburg party after Günther's early death in 1349 and divided the Wittelsbach possessions amongst themselves again. In continuance of the conflict of the House of Wittelsbach with the House of Luxemburg, the Wittelsbach family returned to power in the Holy Roman Empire in 1400 with King Rupert of Germany, a great-grandnephew of Louis.

Family and children
In 1308 Louis married his first wife, Beatrice of Silesia (1290-1322). Their children were:
 * 1) Mathilda (aft. 21 June 1313 – 2 July 1346, Meißen), married at Nuremberg 1 July 1329 Frederick II, Margrave of Meissen (d. 1349)
 * 2) Daughter (end September 1314 – died shortly after).
 * 3) Louis V, Duke of Bavaria (July 1315 – 17/18 September 1361), duke of Upper Bavaria, margrave of Brandenburg, count of Tyrol
 * 4) Anna (c. July 1317 – 29 January 1319, Kastl)
 * 5) Agnes (c. 1318 – died shortly after).
 * 6) Stephen II (autumn 1319 – 19 May 1375), duke of Lower Bavaria

In 1324, Louis married his second wife, Margaret II, Countess of Hainaut and Holland (1308-1356). Their children were:
 * 1) Margaret (1325 – 1374), married:
 * 2) in 1351 in Ofen Stephen, Duke of Slavonia (d. 1354), son of the King Charles I of Hungary;
 * 3) 1357/58 Gerlach von Hohenlohe.
 * 4) Anna (c. 1326 – 3 June 1361, Fontenelles) married John I of Lower Bavaria (d. 1340).
 * 5) Louis VI the Roman (7 May 1328 – 17 May 1365), duke of Upper Bavaria, elector of Brandenburg.
 * 6) Elisabeth (1329 – 2 August 1402, Stuttgart), married:
 * 7) Cangrande II della Scala, Lord of Verona (d. 1359) in Verona on 22 November 1350;
 * 8) Count Ulrich of Württemberg (died 1388 in the Battle of Döffingen) in 1362.
 * 9) William V of Holland (12 May 1330 – 15 April 1389), as William I duke of Lower Bavaria, as William III count of Hainaut
 * 10) Agnes (Munich, 1335 – 11 November 1352, Munich).
 * 11) Albert I of Holland (25 Jul 1336 – 13 December 1404), duke of Lower Bavaria, count of Hainaut and Holland.
 * 12) Otto V the Bavarian (1340/42 – 15/16 November 1379), duke of Upper Bavaria, elector of Brandenburg.
 * 13) Beatrice (1344 – 25 December 1359), married bef. 25 October 1356 Eric XII of Sweden.
 * 14) Louis (October 1347 – 1348).

title: Louis IV, Holy Roman Emperor


text:
User talk:David Merrill

No way MOS:IDENTITY

Top o' Digg
An infographic that mentions your role in the writing of the evolution article is now the top hit on Digg. Just thought you might be interested.  Flying  Toaster  19:18, 6 February 2009 (UTC)

The evolution article
Hi David,

Are you sure that you created the evolution article? Your edit to it is the ]first one recorded in the current English Wikipedia database, but there is a site called Nostalgia Wikipedia, which is a copy of the Wikipedia database from 21 December 2001. Its history of the evolution article shows an edit from 6 November 2001 by AxelBoldt. There is also a version of the article from April 2001 from the Wayback Machine, and your earliest recorded edit is from September 2001. I love checking out old Wikipedia history - see my user page. Graham 87 13:53, 3 December 2009 (UTC)

 * Yes I'm sure I started the article. Axel and I were the primary contributors for a few months. We tried to shepherd in the "creationism" submissions while maintaining NPOV. --David Merrill 08:14, 31 July 2010 (UTC)

Meetup/DC 11
Hey, just in case you missed it, there is an oppurtunity to get a free dinner this Tuesday August 11 and a chance to meet and hang out talk about WikiProject United States Public Policy and WP:GLAM/SI. Sorry that this is so late in the game, I was hoping the e-mail would be a better form of contact for active members (if you want to get on the e-mail list send me an User e-mail ). Hope that you can attend, User:Sadads (talk)11:44, 9 August 2010 (UTC)

DC Meetup #12
An off-wiki discussion is taking place concerning DC Meetup #12. Watch this page for announcements.

—NBahn (talk) 04:32, 9 September 2010 (UTC)

P.S. You are receiving this message either because you received a similar one before and didn't object, or you requested to receive a similar one in the future. If you don't wish to receive this message again, then please let me know either on my talk page or here.

Your user and talk pages
Hi David, I found your user and talk pages while doing some wikiarchaeology. . I have restored all of their earliest surviving revisions from old copies of the Wikipedia database, so they are available to everyone now. Hope you don't mind. Graham 87 12:51, 25 June 2013 (UTC)

May 2015
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title: User talk:David Merrill


text:
Compression

Compression may refer to:

Physical science

 * Compression (physics), size reduction due to forces
 * Compression member, a structural element such as a column
 * Compressibility, susceptibility to compression
 * Gas compression
 * Compression ratio, of a combustion engine
 * Compression (geology)
 * Compression or compressive strength

Information science

 * Data compression, reducing the data required for information
 * Audio compression (data), reducing the data required for audio
 * Bandwidth compression
 * Compression artifact, defect in data due to compression
 * Image compression, of digital images
 * Video compression
 * One-way compression function, a cryptographic primitive

Medicine

 * Brain compression, a medical condition
 * Compression bandage
 * Pressing on the lower abdominal area in an intravenous pyelogram
 * Cold compression therapy, for minor injuries

Other

 * Amplifier gain compression, due to nonlinearity
 * Compression (dance), several techniques
 * Compression (functional analysis)
 * Compression (phonetics), running syllables together
 * Dynamic range compression, reducing audio dynamic range

title: Compression


text:
GNU Privacy Guard

GNU Privacy Guard (GnuPG or GPG) is a free-software replacement for Symantec's cryptographic software suite PGP. The software is compliant with, the IETF standards-track specification of OpenPGP. Modern versions of PGP are interoperable with GnuPG and other OpenPGP-compliant systems. GnuPG is however expected, as of April 2024, to break compliance with the upcoming revision of OpenPGP and thus with other implementations that will continue to comply.

GnuPG is part of the GNU Project and received major funding from the German government in 1999.

Overview
GnuPG is a hybrid-encryption software program because it uses a combination of conventional symmetric-key cryptography for speed, and public-key cryptography for ease of secure key exchange, typically by using the recipient's public key to encrypt a session key which is used only once. This mode of operation is part of the OpenPGP standard and has been part of PGP from its first version.

The GnuPG 1.x series uses an integrated cryptographic library, while the GnuPG 2.x series replaces this with Libgcrypt.

GnuPG encrypts messages using asymmetric key pairs individually generated by GnuPG users. The resulting public keys may be exchanged with other users in a variety of ways, such as Internet key servers. They must always be exchanged carefully to prevent identity spoofing by corrupting public key ↔ "owner" identity correspondences. It is also possible to add a cryptographic digital signature to a message, so the message integrity and sender can be verified, if a particular correspondence relied upon has not been corrupted.

GnuPG also supports symmetric encryption algorithms. By default, GnuPG uses the AES symmetrical algorithm since version 2.1, CAST5 was used in earlier versions. GnuPG does not use patented or otherwise restricted software or algorithms. Instead, GnuPG uses a variety of other, non-patented algorithms.

For a long time, it did not support the IDEA encryption algorithm used in PGP. It was in fact possible to use IDEA in GnuPG by downloading a plugin for it, however, this might require a license for some uses in countries in which IDEA was patented. Starting with versions 1.4.13 and 2.0.20, GnuPG supports IDEA because the last patent of IDEA expired in 2012. Support of IDEA is intended "to get rid of all the questions from folks either trying to decrypt old data or migrating keys from PGP to GnuPG", and hence is not recommended for regular use.

More recent releases of GnuPG 2.x ("modern" and the now deprecated "stable" series) expose most cryptographic functions and algorithms Libgcrypt (its cryptography library) provides, including support for elliptic-curve cryptography (ECDH, ECDSA and EdDSA) in the "modern" series (i.e. since GnuPG 2.1).

Algorithms
As of 2.3 or 2.2 versions, GnuPG supports the following algorithms:
 * Public key: RSA, ElGamal, DSA, ECDH (cv25519, cv448, nistp256, nistp384, nistp521, brainpoolP256r1, brainpoolP384r1, brainpoolP512r1, secp256k1), ECDSA (nistp256, nistp384, nistp521, brainpoolP256r1, brainpoolP384r1, brainpoolP512r1, secp256k1), EdDSA (ed25519, ed448)
 * Cipher: 3DES, IDEA (for backward compatibility), CAST5, Blowfish, Twofish, AES-128, AES-192, AES-256, Camellia-128, -192 and -256
 * Hash: MD5, SHA-1, RIPEMD-160, SHA-256, SHA-384, SHA-512, SHA-224
 * Compression: Uncompressed, ZIP, ZLIB, BZIP2

History
GnuPG was initially developed by Werner Koch. The first production version, version 1.0.0, was released on September 7, 1999, almost two years after the first GnuPG release (version 0.0.0). The German Federal Ministry of Economics and Technology funded the documentation and the port to Microsoft Windows in 2000.

GnuPG is a system compliant to the OpenPGP standard, thus the history of OpenPGP is of importance; it was designed to interoperate with PGP, an email encryption program initially designed and developed by Phil Zimmermann.

On February 7, 2014, a GnuPG crowdfunding effort closed, raising €36,732 for a new website and infrastructure improvements.

Branches
Since the release of a stable GnuPG 2.3, starting with version 2.3.3 in October 2021, three stable branches of GnuPG are actively maintained:
 * A "stable branch", which currently is (as of 2021) the 2.3 branch.
 * A "LTS (long-term support) branch", which currently is (as of 2021) the 2.2 branch (which was formerly called "modern branch", in comparison to the 2.0 branch).
 * The old "legacy branch" (formerly called "classic branch"), which is and will stay the 1.4 branch.

Before GnuPG 2.3, two stable branches of GnuPG were actively maintained:
 * "Modern" (2.2), with numerous new features, such as elliptic curve cryptography, compared to the former "stable" (2.0) branch, which it replaced with the release of GnuPG 2.2.0 on August 28, 2017. It was initially released on November 6, 2014.
 * "Classic" (1.4), the very old, but still maintained stand-alone version, most suitable for outdated or embedded platforms. Initially released on December 16, 2004.

Different GnuPG 2.x versions (e.g. from the 2.2 and 2.0 branches) cannot be installed at the same time. However, it is possible to install a "classic" GnuPG version (i.e. from the 1.4 branch) along with any GnuPG 2.x version.

Before the release of GnuPG 2.2 ("modern"), the now deprecated "stable" branch (2.0) was recommended for general use, initially released on November 13, 2006. This branch reached its end-of-life on December 31, 2017; Its last version is 2.0.31, released on December 29, 2017.

Before the release of GnuPG 2.0, all stable releases originated from a single branch; i.e., before November 13, 2006, no multiple release branches were maintained in parallel. These former, sequentially succeeding (up to 1.4) release branches were:
 * 1.2 branch, initially released on September 22, 2002, with 1.2.6 as the last version, released on October 26, 2004.
 * 1.0 branch, initially released on September 7, 1999, with 1.0.7 as the last version, released on April 30, 2002.

(Note that before the release of GnuPG 2.3.0, branches with an odd minor release number (e.g. 2.1, 1.9, 1.3) were development branches leading to a stable release branch with a "+ 0.1" higher version number (e.g. 2.2, 2.0, 1.4); hence branches 2.2 and 2.1 both belong to the "modern" series, 2.0 and 1.9 both to the "stable" series, while the branches 1.4 and 1.3 both belong to the "classic" series.

With the release of GnuPG 2.3.0, this nomenclature was altered to be composed of a "stable" and "LTS" branch from the "modern" series, plus 1.4 as the last maintained "classic" branch. Also note that even or odd minor release numbers do not indicate a stable or development release branch, anymore.)

Platforms
Although the basic GnuPG program has a command-line interface, there exists various front-ends that provide it with a graphical user interface. For example, GnuPG encryption support has been integrated into KMail and Evolution, the graphical email clients found in KDE and GNOME, the most popular Linux desktops. There are also graphical GnuPG front-ends, for example Seahorse for GNOME and KGPG and Kleopatra for KDE.

GPGTools provides a number of front-ends for OS integration of encryption and key management as well as GnuPG installations via Installer packages for macOS. GPG Suite installs all related OpenPGP applications (GPG Keychain), plugins (GPG Mail) and dependencies (MacGPG), along with GPG Services (integration into macOS Services menu) to use GnuPG based encryption.

Instant messaging applications such as Psi and Fire can automatically secure messages when GnuPG is installed and configured. Web-based software such as Horde also makes use of it. The cross-platform extension Enigmail provides GnuPG support for Mozilla Thunderbird and SeaMonkey. Similarly, Enigform provides GnuPG support for Mozilla Firefox. FireGPG was discontinued June 7, 2010.

In 2005, g10 Code GmbH and Intevation GmbH released Gpg4win, a software suite that includes GnuPG for Windows, GNU Privacy Assistant, and GnuPG plug-ins for Windows Explorer and Outlook. These tools are wrapped in a standard Windows installer, making it easier for GnuPG to be installed and used on Windows systems.

Vulnerabilities
The OpenPGP standard specifies several methods of digitally signing messages. In 2003, due to an error in a change to GnuPG intended to make one of those methods more efficient, a security vulnerability was introduced. It affected only one method of digitally signing messages, only for some releases of GnuPG (1.0.2 through 1.2.3), and there were fewer than 1000 such keys listed on the key servers. Most people did not use this method, and were in any case discouraged from doing so, so the damage caused (if any, since none has been publicly reported) would appear to have been minimal. Support for this method has been removed from GnuPG versions released after this discovery (1.2.4 and later).

Two further vulnerabilities were discovered in early 2006; the first being that scripted uses of GnuPG for signature verification may result in false positives, the second that non-MIME messages were vulnerable to the injection of data which while not covered by the digital signature, would be reported as being part of the signed message. In both cases updated versions of GnuPG were made available at the time of the announcement.

In June 2017, a vulnerability (CVE-2017-7526) was discovered within Libgcrypt by Bernstein, Breitner and others: a library used by GnuPG, which enabled a full key recovery for RSA-1024 and about more than 1/8th of RSA-2048 keys. This side-channel attack exploits the fact that Libgcrypt used a sliding windows method for exponentiation which leads to the leakage of exponent bits and to full key recovery. Again, an updated version of GnuPG was made available at the time of the announcement.

In October 2017, the ROCA vulnerability was announced that affects RSA keys generated by YubiKey 4 tokens, which often are used with PGP/GPG. Many published PGP keys were found to be susceptible.

Around June 2018, the SigSpoof attacks were announced. These allowed an attacker to convincingly spoof digital signatures.

In January 2021, Libgcrypt 1.9.0 was released, which was found to contain a severe bug that was simple to exploit. A fix was released 10 days later in Libgcrypt 1.9.1.

title: GNU Privacy Guard


text:
Talk:Algebraic topology

Unsuitable as a general encyclopedic entry
This article uses too much terminology from the field that it is concerned with and is thus only of use and interest to people immersed in said field. It does not serve to introduce the topic or to explain it in any way to someone who does not have some prior training in the field. This makes it unsuited as an entry in a general encyclopedia and makes it more suited to a specialized mathematical encyclopedia. Please rewrite it to include more introductory explanations and examples.

41.204.193.43 (talk) 12:19, 25 May 2009 (UTC)

 * I am not sure that it is as easily re-written as you suggest. — Preceding unsigned comment added by 31.53.52.243 (talk) 08:30, 13 July 2017 (UTC)
 * I agree with the reply. I would also like to add that lots of topics in math have the property that you need some type of basic knowledge (master or sometimes research training) to be able to grasp them; if you try to rewrite them in a more "understandable" style a layman will still not understand, while a person with enough prior knowledge will not get anything out of it either. (A trivial example I've noted is that articles write "topological equivalence" rather than homeomorphism. This is a disservice to everybody; the person that does not know any math will not get a better understanding, while say a student of math will wonder if this is a concept that he/she has not yet encountered, so will be forced to click the link.) But this property that topics are hard to understand the first time cannot be exclusive to math. For example, I don't know biology; still, I don't expect that articles that mention "mitochondria" should be rewritten so that "mitochondria" is replaced with "cell that generate energy". (Yes, I know that mitochondria is not a cell, but we have to keep it simple so that everyone understands.) 84.55.110.150 (talk) 20:49, 23 November 2023 (UTC)

Correction
I'd just like to point out an error:

"As another example, the top-dimensional integral homology group of a closed manifold detects orientability: this group is isomorphic to either the integers or 0, according as the manifold is orientable or not. "

Shouldn't that be the integers or the group of order 2?

87.194.112.50 (talk) 16:10, 4 October 2010 (UTC)

 * I don't think it's an error (except that it doesn't say "connected closed manifold"). Perhaps you are confusing top homology with top cohomology?
 * Ambrose H. Field (talk) 22:56, 17 January 2011 (UTC)

R. Brown
Why are there so many references and notes sourced to R. Brown in this article? I am sure he is a fine topologist, but he isn't completely dominant in the field and a lot of his cited articles look to be on specialized topics not really suitable for a general overview of algebraic topology. It seems like undue weight and possible ref spamming. --Mark viking (talk) 04:38, 18 October 2013 (UTC)

 * I agree; I removed most of the material because it is not really good for an overview of algebraic topology, like you say, although it should probably be trimmed even more.Brirush (talk) 12:57, 18 October 2013 (UTC)

Assessment comment
Substituted at 01:45, 5 May 2016 (UTC)

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title: Talk:Algebraic topology


text:
Proline

Proline (symbol Pro or P) is an organic acid classed as a proteinogenic amino acid (used in the biosynthesis of proteins), although it does not contain the amino group but is rather a secondary amine. The secondary amine nitrogen is in the protonated form (NH2+) under biological conditions, while the carboxyl group is in the deprotonated −COO− form. The "side chain" from the α carbon connects to the nitrogen forming a pyrrolidine loop, classifying it as a aliphatic amino acid. It is non-essential in humans, meaning the body can synthesize it from the non-essential amino acid L -glutamate. It is encoded by all the codons starting with CC (CCU, CCC, CCA, and CCG).

Proline is the only proteinogenic secondary amino acid which is a secondary amine, as the nitrogen atom is attached both to the α-carbon and to a chain of three carbons that together form a five-membered ring.

History and etymology
Proline was first isolated in 1900 by Richard Willstätter who obtained the amino acid while studying N-methylproline, and synthesized proline by the reaction of sodium salt of diethyl malonate with 1,3-dibromopropane. The next year, Emil Fischer isolated proline from casein and the decomposition products of γ-phthalimido-propylmalonic ester, and published the synthesis of proline from phthalimide propylmalonic ester.

The name proline comes from pyrrolidine, one of its constituents.

Biosynthesis
Proline is biosynthetically derived from the amino acid L -glutamate. Glutamate-5-semialdehyde is first formed by glutamate 5-kinase (ATP-dependent) and glutamate-5-semialdehyde dehydrogenase (which requires NADH or NADPH). This can then either spontaneously cyclize to form 1-pyrroline-5-carboxylic acid, which is reduced to proline by pyrroline-5-carboxylate reductase (using NADH or NADPH), or turned into ornithine by ornithine aminotransferase, followed by cyclisation by ornithine cyclodeaminase to form proline.

Biological activity
L -Proline has been found to act as a weak agonist of the glycine receptor and of both NMDA and non-NMDA (AMPA/kainate) ionotropic glutamate receptors. It has been proposed to be a potential endogenous excitotoxin. In plants, proline accumulation is a common physiological response to various stresses but is also part of the developmental program in generative tissues (e.g. pollen).

A diet rich in proline was linked to an increased risk of depression in humans in a study from 2022 that was tested on a limited pre-clinical trial on humans and primarily in other organisms. Results were significant in the other organisms.

Properties in protein structure
The distinctive cyclic structure of proline's side chain gives proline an exceptional conformational rigidity compared to other amino acids. It also affects the rate of peptide bond formation between proline and other amino acids. When proline is bound as an amide in a peptide bond, its nitrogen is not bound to any hydrogen, meaning it cannot act as a hydrogen bond donor, but can be a hydrogen bond acceptor.

Peptide bond formation with incoming Pro-tRNAPro in the ribosome is considerably slower than with any other tRNAs, which is a general feature of N-alkylamino acids. Peptide bond formation is also slow between an incoming tRNA and a chain ending in proline; with the creation of proline-proline bonds slowest of all.

The exceptional conformational rigidity of proline affects the secondary structure of proteins near a proline residue and may account for proline's higher prevalence in the proteins of thermophilic organisms. Protein secondary structure can be described in terms of the dihedral angles φ, ψ and ω of the protein backbone. The cyclic structure of proline's side chain locks the angle φ at approximately −65°.

Proline acts as a structural disruptor in the middle of regular secondary structure elements such as alpha helices and beta sheets; however, proline is commonly found as the first residue of an alpha helix and also in the edge strands of beta sheets. Proline is also commonly found in turns (another kind of secondary structure), and aids in the formation of beta turns. This may account for the curious fact that proline is usually solvent-exposed, despite having a completely aliphatic side chain.

Multiple prolines and/or hydroxyprolines in a row can create a polyproline helix, the predominant secondary structure in collagen. The hydroxylation of proline by prolyl hydroxylase (or other additions of electron-withdrawing substituents such as fluorine) increases the conformational stability of collagen significantly. Hence, the hydroxylation of proline is a critical biochemical process for maintaining the connective tissue of higher organisms. Severe diseases such as scurvy can result from defects in this hydroxylation, e.g., mutations in the enzyme prolyl hydroxylase or lack of the necessary ascorbate (vitamin C) cofactor.

Cis–trans isomerization
Peptide bonds to proline, and to other N-substituted amino acids (such as sarcosine), are able to populate both the cis and trans isomers. Most peptide bonds overwhelmingly adopt the trans isomer (typically 99.9% under unstrained conditions), chiefly because the amide hydrogen (trans isomer) offers less steric repulsion to the preceding Cα atom than does the following Cα atom (cis isomer). By contrast, the cis and trans isomers of the X-Pro peptide bond (where X represents any amino acid) both experience steric clashes with the neighboring substitution and have a much lower energy difference. Hence, the fraction of X-Pro peptide bonds in the cis isomer under unstrained conditions is significantly elevated, with cis fractions typically in the range of 3-10%. However, these values depend on the preceding amino acid, with Gly and aromatic residues yielding increased fractions of the cis isomer. Cis fractions up to 40% have been identified for aromatic–proline peptide bonds.

From a kinetic standpoint, cis–trans proline isomerization is a very slow process that can impede the progress of protein folding by trapping one or more proline residues crucial for folding in the non-native isomer, especially when the native protein requires the cis isomer. This is because proline residues are exclusively synthesized in the ribosome as the trans isomer form. All organisms possess prolyl isomerase enzymes to catalyze this isomerization, and some bacteria have specialized prolyl isomerases associated with the ribosome. However, not all prolines are essential for folding, and protein folding may proceed at a normal rate despite having non-native conformers of many X–Pro peptide bonds.

Uses
Proline and its derivatives are often used as asymmetric catalysts in proline organocatalysis reactions. The CBS reduction and proline catalysed aldol condensation are prominent examples.

In brewing, proteins rich in proline combine with polyphenols to produce haze (turbidity).

L -Proline is an osmoprotectant and therefore is used in many pharmaceutical and biotechnological applications.

The growth medium used in plant tissue culture may be supplemented with proline. This can increase growth, perhaps because it helps the plant tolerate the stresses of tissue culture. For proline's role in the stress response of plants, see.

Specialties
Proline is one of the two amino acids that do not follow along with the typical Ramachandran plot, along with glycine. Due to the ring formation connected to the beta carbon, the ψ and φ angles about the peptide bond have fewer allowable degrees of rotation. As a result, it is often found in "turns" of proteins as its free entropy (ΔS) is not as comparatively large to other amino acids and thus in a folded form vs. unfolded form, the change in entropy is smaller. Furthermore, proline is rarely found in α and β structures as it would reduce the stability of such structures, because its side chain α-nitrogen can only form one nitrogen bond.

Additionally, proline is the only amino acid that does not form a red-purple colour when developed by spraying with ninhydrin for uses in chromatography. Proline, instead, produces an orange-yellow colour.

Synthesis
Racemic proline can be synthesized from diethyl malonate and acrylonitrile:
 * DL-Proline synth.png

title: Proline


text:
Coven

A coven is a group or gathering of witches. The word "coven" (from Anglo-Norman covent, cuvent, from Old French covent, from Latin conventum = convention) remained largely unused in English until 1921 when Margaret Murray promoted the idea that all witches across Europe met in groups of thirteen which they called "covens".

Modern paganism
In Wicca and other similar forms of modern pagan witchcraft, such as Stregheria and Feri, a coven is a gathering or community of witches, like an affinity group, engagement group, or small covenant group. It is composed of a group of practitioners who gather together for rituals such as Drawing Down the Moon, or celebrating the Sabbats. The place at which they generally meet is called a covenstead.

The number of people involved may vary. Although some consider thirteen to be ideal (probably in deference to Murray's theories), any group of at least three can be a coven. A group of two is usually called a "working couple" (regardless of their gender). It can also unofficially be called an "Obaven" by some members of the community, derived from the Scottish Gaelic word "obair" meaning work, a tribute to the more official term "working couple", a portmanteau with the word "coven". Thus creating the word, "Obaven". Within the community, many believe that a coven larger than thirteen is unwieldy, citing unwieldy group dynamics and an unfair burden on the leadership. When a coven has grown too large to be manageable, it may split, or "hive". In Wicca, this may also occur when a newly made High Priest or High Priestess, also called 3rd Degree initiation, leaves to start their own coven.

Wiccan covens are usually jointly led by a High Priestess and a High Priest, although some are led by only one or the other, and some by a same-sex couple. In more recent forms of modern pagan witchcraft, covens are sometimes run as democracies with a rotating leadership.

Online covens
With the rise of the Internet as a platform for collaborative discussion and media dissemination, it became popular for adherents and practitioners of Wicca to establish "online covens" which remotely teach tradition-specific crafts to students in a similar method of education as non-religious virtual online schools. One of the first online covens to take this route is the Coven of the Far Flung Net (CFFN), which was established in 1997 as the online arm of the Church of Universal Eclectic Wicca.

However, because of potentially-unwieldy membership sizes, many online covens limit their memberships to anywhere between 10 and 100 students. The CFFN, in particular, tried to devolve its structure into a system of sub-coven clans (which governed their own application processes), a system which ended in 2003 due to fears by the CFFN leadership that the clans were becoming communities in their own right.

Other contemporary forms
The Urban Coven is a group founded on Facebook by Becca Gordon for women in Los Angeles to gather, hike, and howl at the Moon. It meets monthly and is estimated to have almost 3,500 members. A January 2016 gathering at Griffith Park drew nearly 1,000 women, and was described as follows:

"A lot of the women ... were there in groups — mothers and daughters, friends, colleagues. Some arrived solo and struck up conversations with other women or hiked in solitude."

In popular culture
In popular culture, a coven is a group or gathering of witches who work spells in tandem. Such imagery can be traced back to Renaissance prints depicting witches and to the three "weird sisters" in Shakespeare's Macbeth (1606).

Orgiastic meetings of witches are depicted in the Robert Burns poem "Tam o' Shanter" (1791) and in the Goethe play Faust (1832).

Films featuring covens include Rosemary's Baby (1968), Crowhaven Farm (1970), Suspiria (1977) and its 2018 remake, The Witches of Eastwick (1987), Four Rooms (1995), The Craft (1996), Coven (1997), Underworld (2003), Underworld: Evolution (2006), The Covenant (2006), Paranormal Activity 3 (2011), The Witch (2015) and Hereditary (2018).

In television, covens have been portrayed in the U.S. in supernatural dramas such as Charmed, Witches of East End, The Vampire Diaries, The Originals, The Secret Circle, True Blood, Once Upon a Time and Chilling Adventures of Sabrina. The third season of American Horror Story is entitled Coven, and focuses on witches. The animated series The Owl House (2020–2023) also focuses on witches, and interprets covens as required organizations of witches with specialized magic.

In vampire novels such as The Vampire Chronicles by Anne Rice and the Twilight series by Stephenie Meyer, covens are families or unrelated groups of vampires who live together.

title: Coven


text:
Talk:Wenceslas IV Holy Roman Emperor

 * 1) We don't use the word 'acceed' nearly as often as it appears on the wikipedia. One reason is that there are better words, like 'succeed', that can be used to impart more information in a complex sentence structure.

 * 1) I'm not sure if this guy is King Wnceslaus the fourth, Emperor W the 4th, or duke W the 4th. It is not clear from the badly entitled article.

 * 1) The article makes it appear that W was able to help elect himself Emperor, since he was an imperial Elector -- whose title, by the way, in English would be Margrave of Brandenburg, Imperial Elector (or something more like that than the non-existent elector of Brandenburg.

 * 1) I am soooo tired of fixing space.

Could an intelligent and informed person please help?? Thanks! User:JHK

 * He was Wenceslaus IV of Bohemia and just plain Wenceslaus of the other territories because they never had a second. He held two electorates in succession - first as margrave of Brandenburg (1373-76) and then as king of Bohemia (1378-1419) - presumably he voted for himself as king of the Germans on the first occasion, though I don't know if this is recorded. - The usually intelligent and sometimes informed DP

 * Argh -- then is he Emperor W IV, or Emperor W...These entries are killing me! User:JHK

 * Remember the Imperial and Bohemian crowns are two entirely distinct entities though one is suzerain to the other: he was Bohemia's fourth Vaclav but the only Wenzel ever to be Emperor. If he'd been succeeded on both thrones by a later Wenceslas, he's become (posthumously) the Emperor Wenceslas I while remaining King Wenceslas IV of Bohemia. The subsequent Wenceslas would be the Emperor Wenceslas II and King Wenceslas V of Bohemia.

 * Anyway, if you think this one was bad you should have seen the entry for Rupert of Germany - she had a Wittelsbach who died in 1410 marrying the daughter of a Hohenzollern born in 1460! DP

 * I have no problem with the distinction -- it's just that I know he was the somethingth of one, and then the other somethingth of the other!. And why is this guy (whom I've always thought of as "good" King Wenceslas) the Drunkard -- was he really that bad? User:JHK

 * I think the "good" Wenceslas was a few centuries earlier: apparently Wenceslas IV was fond of the odd tipple and had a bit of a temper. But he seems to have been avoided needless military adventures and to have kept religious tensions in check until the end of his reign, which isn't bad. DP

title: Talk:Wenceslas IV Holy Roman Emperor