127-445: Silverknowes / ˌ s ɪ l v ər ˈ n aʊ z / is a district of Edinburgh , Scotland . Silverknowes lies to the northwest of the city. The district contains over 2000 homes, ranging in size from bungalow to semi-detached housing, much of it built during the mid-twentieth century. It holds the EH4 postcode. Silverknowes is surrounded by Davidson's Mains (former village) to
254-657: A = cos B tan c , (R3) sin b = sin B sin c , (R8) cos A = sin B cos a , (R4) tan a = tan A sin b , (R9) cos B = sin A cos b , (R5) tan b = tan B sin
381-523: A = sin b cos A , (Q4) tan A = tan a sin B , (Q9) cos b = sin a cos B , (Q5) tan B = tan b sin A , (Q10) cos C = − cot
508-803: A cot b . {\displaystyle {\begin{alignedat}{4}&{\text{(Q1)}}&\qquad \cos C&=-\cos A\,\cos B,&\qquad \qquad &{\text{(Q6)}}&\qquad \tan B&=-\cos a\,\tan C,\\&{\text{(Q2)}}&\sin A&;=\sin a\,\sin C,&&{\text{(Q7)}}&\tan A&=-\cos b\,\tan C,\\&{\text{(Q3)}}&\sin B&;=\sin b\,\sin C,&&{\text{(Q8)}}&\cos a&=\sin b\,\cos A,\\&{\text{(Q4)}}&\tan A&=\tan a\,\sin B,&&{\text{(Q9)}}&\cos b&=\sin a\,\cos B,\\&{\text{(Q5)}}&\tan B&=\tan b\,\sin A,&&{\text{(Q10)}}&\cos C&=-\cot a\,\cot b.\end{alignedat}}} Logarithm Given
635-446: A tan C , (Q2) sin A = sin a sin C , (Q7) tan A = − cos b tan C , (Q3) sin B = sin b sin C , (Q8) cos
762-892: A , (R10) cos c = cot A cot B . {\displaystyle {\begin{alignedat}{4}&{\text{(R1)}}&\qquad \cos c&=\cos a\,\cos b,&\qquad \qquad &{\text{(R6)}}&\qquad \tan b&=\cos A\,\tan c,\\&{\text{(R2)}}&\sin a&=\sin A\,\sin c,&&{\text{(R7)}}&\tan a&=\cos B\,\tan c,\\&{\text{(R3)}}&\sin b&=\sin B\,\sin c,&&{\text{(R8)}}&\cos A&=\sin B\,\cos a,\\&{\text{(R4)}}&\tan a&=\tan A\,\sin b,&&{\text{(R9)}}&\cos B&=\sin A\,\cos b,\\&{\text{(R5)}}&\tan b&=\tan B\,\sin a,&&{\text{(R10)}}&\cos c&=\cot A\,\cot B.\end{alignedat}}} A quadrantal spherical triangle
889-479: A port several miles away (respectively, Leith and Piraeus ). Intellectually, the Scottish Enlightenment , with its humanist and rationalist outlook, was influenced by Ancient Greek philosophy . In 1822, artist Hugh William Williams organized an exhibition that showed his paintings of Athens alongside views of Edinburgh, and the idea of a direct parallel between both cities quickly caught
1016-465: A royal charter , c. 1124–1127 , by King David I granting a toft in burgo meo de Edenesburg to the Priory of Dunfermline . The shire of Edinburgh seems to have also been created in the reign of David I, possibly covering all of Lothian at first, but by 1305 the eastern and western parts of Lothian had become Haddingtonshire and Linlithgowshire , leaving Edinburgh as the county town of
1143-399: A , b , c , A , B . Napier provided an elegant mnemonic aid for the ten independent equations: the mnemonic is called Napier's circle or Napier's pentagon (when the circle in the above figure, right, is replaced by a pentagon). First, write the six parts of the triangle (three vertex angles, three arc angles for the sides) in the order they occur around any circuit of the triangle: for
1270-619: A Dutch translation, and this reached a second edition in 1607. In 1602 the work appeared at La Rochelle in a French version, by Georges Thomson , revised by Napier, and that also went through several editions (1603, 1605, and 1607). A new edition of the English original was called for in 1611, when it was revised and corrected by the author, and enlarged by the addition of With a resolution of certain doubts, moved by some well affected brethren. ; this appeared simultaneously at Edinburgh and London. The author stated that he still intended to publish
1397-450: A Latin edition, but it never appeared. A German translation, by Leo de Dromna , of the first part of Napier's work appeared at Gera in 1611, and of the whole by Wolfgang Meyer at Frankfurt-am-Main , in 1615. Among Napier's followers was Matthew Cotterius ( Matthieu Cottière ). In addition to his mathematical and religious interests, Napier was often perceived as a magician, and is thought to have dabbled in alchemy and necromancy . It
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#17327809247961524-419: A Restaurant, selling out to Whitbread in the late 1980s. In the early 1990s, Lauriston Farm Restaurant became a Whitbread Brewer's Fayre (1993) before being taken over by Mitchell and Butler, relaunching as The Lauriston Farm Restaurant, which was refurbished in 2019. The area of Silverknowes, Davidson's Mains, Muirhouse (former home to Irvine Welsh, author of Trainspotting), Granton, Cramond & Cammo boasts
1651-538: A centre of education, particularly in the fields of medicine, Scottish law , literature, philosophy, the sciences and engineering. The University of Edinburgh , founded in 1582 and now one of three in the city, is considered one of the best research institutions in the world. The financial centre of Scotland, Edinburgh is the second-largest financial centre in the United Kingdom, the fourth largest in Europe, and
1778-409: A darkened room and pet the cockerel, claiming the bird would crow if they were the one who stole his property. Unbeknownst to the servants, Napier had covered the bird with soot and when the servants emerged from the room, Napier inspected their hands to find the one who had been too afraid to touch the rooster. Another act which Napier is reported to have carried out, which may have seemed mystical to
1905-480: A former Four Star Stakis Hotel, before its current life as a Two Star Hotel come Homeless Hostel, Almond House Lodge Hotel); Granton House (destroyed by fire in 1954 after becoming a Home for the Homeless); Granton Tower; Craigroyston House; Royston House; Cammo House (destroyed by fire in 1978) and Cammo Estate. Silverknowes includes Silverknowes Beach and Promenade which stretches for 3 miles from Cramond Village in
2032-435: A large power of 10 rounded to an integer) was a practical difficulty. Neither Napier nor Briggs actually discovered the constant e ; that discovery was made decades later by Jacob Bernoulli . Napier delegated to Briggs the computation of a revised table. The computational advance available via logarithms, the inverse of powered numbers or exponential notation , was such that it made calculations by hand much quicker. The way
2159-523: A population in 2014 of 1,339,380. Like most of Scotland, Edinburgh has a cool temperate maritime climate ( Cfb ) which, despite its northerly latitude, is milder than places which lie at similar latitudes such as Moscow and Labrador . The city's proximity to the sea mitigates any large variations in temperature or extremes of climate. Winter daytime temperatures rarely fall below freezing while summer temperatures are moderate, rarely exceeding 22 °C (72 °F). The highest temperature recorded in
2286-789: A population of 912,490 in the same year. Recognised as the capital of Scotland since at least the 15th century, Edinburgh is the seat of the Scottish Government , the Scottish Parliament , the highest courts in Scotland , and the Palace of Holyroodhouse , the official residence of the monarch in Scotland. It is also the annual venue of the General Assembly of the Church of Scotland . The city has long been
2413-499: A positive real number b such that b ≠ 1, the logarithm of a positive real number x with respect to base b is the exponent by which b must be raised to yield x . In other words, the logarithm of x to base b is the unique real number y such that b = x . The logarithm is denoted "log b x " (pronounced as "the logarithm of x to base b ", "the base- b logarithm of x ", or most commonly "the log, base b , of x "). An equivalent and more succinct definition
2540-634: A series of small summits to the south of the city centre that command expansive views looking northwards over the urban area to the Firth of Forth. Edinburgh is drained by the river named the Water of Leith , which rises at the Colzium Springs in the Pentland Hills and runs for 18 miles (29 km) through the south and west of the city, emptying into the Firth of Forth at Leith. The nearest
2667-410: A set of numbered rods. Napier may have worked largely in isolation, but he had contact with Tycho Brahe who corresponded with his friend John Craig . Craig certainly announced the discovery of logarithms to Brahe in the 1590s (the name itself came later); there is a story from Anthony à Wood , perhaps not well substantiated, that Napier had a hint from Craig that Longomontanus , a follower of Brahe,
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#17327809247962794-585: A shire covering the central part of Lothian, which was called Edinburghshire or Midlothian (the latter name being an informal, but commonly used, alternative until the county's name was legally changed in 1947). Edinburgh was largely under English control from 1291 to 1314 and from 1333 to 1341, during the Wars of Scottish Independence . When the English invaded Scotland in 1298 , Edward I of England chose not to enter Edinburgh but passed by it with his army. In
2921-492: A trigonometric context so it would be even more relevant. His work Mirifici Logarithmorum Canonis Descriptio (1614) contained fifty-seven pages of explanatory matter and ninety pages of tables listing the natural logarithms of trigonometric functions . The book also has a discussion of theorems in spherical trigonometry , usually known as Napier's Rules of Circular Parts. Modern English translations of both Napier's books on logarithms and their description can be found on
3048-655: A war band from across the Brittonic world who gathered in Eidyn before a fateful raid; this may describe a historical event around AD 600. In 638, the Gododdin stronghold was besieged by forces loyal to King Oswald of Northumbria , and around this time control of Lothian passed to the Angles . Their influence continued for the next three centuries until around 950, when, during the reign of Indulf , son of Constantine II ,
3175-488: Is a memorial to him at St Cuthbert's at the west side of Edinburgh. Napier's father was Sir Archibald Napier of Merchiston Castle, and his mother was Janet Bothwell, daughter of the politician and judge Francis Bothwell , and a sister of Adam Bothwell who became the Bishop of Orkney . Archibald Napier was 16 years old when John Napier was born. There are no records of Napier's early learning, but many believe that he
3302-439: Is affectionately nicknamed Auld Reekie , Scots for Old Smoky , for the views from the country of the smoke-covered Old Town. A note in a collection of the works of the poet, Allan Ramsay , explains, "Auld Reeky...A name the country people give Edinburgh, from the cloud of smoke or reek that is always impending over it." In Walter Scott 's 1820 novel The Abbot , a character observes that "yonder stands Auld Reekie—you may see
3429-570: Is almost entirely within the City of Edinburgh Council boundary, merging with Musselburgh in East Lothian. Towns within easy reach of the city boundary include Inverkeithing , Haddington , Tranent , Prestonpans , Dalkeith , Bonnyrigg , Loanhead , Penicuik , Broxburn , Livingston and Dunfermline . Edinburgh lies at the heart of the Edinburgh & South East Scotland City region with
3556-419: Is believed he left Scotland to further his education in mainland Europe, following the advice given by his uncle Adam Bothwell in a letter written to John Napier's father on 5 December 1560, saying, "I pray you, sir, to send John to the schools either to France or Flanders , for he can learn no good at home". It is not known which university Napier attended in Europe, but when he returned to Scotland in 1571 he
3683-593: Is cloudier and somewhat wetter, but differences are minor. Temperature and rainfall records have been kept at the Royal Observatory since 1764. The most recent official population estimates (2020) are 506,520 for the locality (includes Currie ), 530,990 for the Edinburgh settlement (includes Musselburgh ). John Napier John Napier of Merchiston ( / ˈ n eɪ p i ər / NAY -pee-ər ; Latinized as Ioannes Neper ; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston ,
3810-400: Is defined to be a spherical triangle in which one of the sides subtends an angle of π /2 radians at the centre of the sphere: on the unit sphere the side has length π /2. In the case that the side c has length π /2 on the unit sphere the equations governing the remaining sides and angles may be obtained by applying the rules for the right spherical triangle of the previous section to
3937-426: Is encircled by a green belt , designated in 1957, which stretches from Dalmeny in the west to Prestongrange in the east. With an average width of 3.2 km (2 mi) the principal objectives of the green belt were to contain the outward expansion of the city and to prevent the agglomeration of urban areas. Expansion affecting the green belt is strictly controlled but developments such as Edinburgh Airport and
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4064-468: Is given credit as the largest single factor in the general adoption of decimal arithmetic . The Trissotetras (1645) of Thomas Urquhart builds on Napier's work, in trigonometry . Henry Briggs was an early adopter of the Napierian logarithm. He later computed a new table of logarithms to base 10, accurate to 14 decimal places. An alternative unit to the decibel used in electrical engineering ,
4191-482: Is governed by the City of Edinburgh Council , a unitary authority. The City of Edinburgh council area had an estimated population of 514,990 in mid-2021, and includes outlying towns and villages which are not part of Edinburgh proper. The city is in the Lothian region and was historically part of the shire of Midlothian (also called Edinburghshire). "Edin", the root of the city's name, derives from Eidyn ,
4318-556: Is stated that Napier should "do his utmost diligence to search and seek out, and by all craft and ingine to find out the same, or make it sure that no such thing has been there." This contract was never fulfilled by Napier, and no gold was found when the Edinburgh Archaeological Field society excavated the castle between 1971 and 1986. Among Napier's early followers were the instrument makers Edmund Gunter and John Speidell . The development of logarithms
4445-483: Is that the function f : x → l o g b x {\displaystyle f\colon x\to log_{b}x} is the inverse function to the function f : x → b x . {\displaystyle f\colon x\to b^{x}.} Napier had an interest in the Book of Revelation , from his student days at St Salvator's College, St Andrews . Under
4572-588: Is the capital city of Scotland and one of its 32 council areas . The city is located in southeast Scotland and is bounded to the north by the Firth of Forth estuary and to the south by the Pentland Hills . Edinburgh had a population of 506,520 in mid-2020, making it the second-most populous city in Scotland and the seventh-most populous in the United Kingdom . The wider metropolitan area had
4699-440: Is typical of the old quarters of many Northern European cities. The New Town was an 18th-century solution to the problem of an increasingly crowded city which had been confined to the ridge sloping down from the castle. In 1766 a competition to design a "New Town" was won by James Craig , a 27-year-old architect. The plan was a rigid, ordered grid, which fitted in well with Enlightenment ideas of rationality. The principal street
4826-641: The Athens of the North since the early 19th century. References to Athens, such as Athens of Britain and Modern Athens , had been made as early as the 1760s. The similarities were seen to be topographical but also intellectual. Edinburgh's Castle Rock reminded returning grand tourists of the Athenian Acropolis , as did aspects of the neoclassical architecture and layout of New Town . Both cities had flatter, fertile agricultural land sloping down to
4953-590: The Book of Revelation to attempt to predict the date of the Apocalypse . Napier identified events in chronological order which he believed were parallels to events described in the Book of Revelation believing that Revelation 's structure implied that the prophecies would be fulfilled incrementally. In this work Napier dated the seventh trumpet to 1541, and predicted the end of the world would occur in either 1688 or 1700. Napier did not believe that people could know
5080-661: The George Square and Potterrow areas proved highly controversial. Since the 1990s a new "financial district", including the Edinburgh International Conference Centre , has grown mainly on demolished railway property to the west of the castle, stretching into Fountainbridge , a run-down 19th-century industrial suburb which has undergone radical change since the 1980s with the demise of industrial and brewery premises. This ongoing development has enabled Edinburgh to maintain its place as
5207-803: The Romans arrived in Lothian at the end of the 1st century AD, they found a Brittonic Celtic tribe whose name they recorded as the Votadini . The Votadini transitioned into the Gododdin kingdom in the Early Middle Ages , with Eidyn serving as one of the kingdom's districts. During this period, the Castle Rock site, thought to have been the stronghold of Din Eidyn, emerged as the kingdom's major centre. The medieval poem Y Gododdin describes
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5334-713: The Royal High School in Barnton, one of Scotland's most famous schools, the 28th oldest school in the world, dating back to 1128. Previously, one of the primary schools serving the area was known as Silverknowes Primary. After its merger with Muirhouse Primary, the land was developed as housing, and now has the address of Silverknowes Eastway. This newly developed area falls within the catchments of Craigroyston Primary & High schools. The following Lothian Buses link Silverknowes to Edinburgh city centre and beyond: In 2006, there were plans to place Silverknowes in
5461-668: The Royal Highland Showground at Ingliston lie within the zone. Similarly, suburbs such as Juniper Green and Balerno are situated on green belt land. One feature of the Edinburgh green belt is the inclusion of parcels of land within the city which are designated green belt, even though they do not connect with the peripheral ring. Examples of these independent wedges of green belt include Holyrood Park and Corstorphine Hill. Edinburgh includes former towns and villages that retain much of their original character as settlements in existence before they were absorbed into
5588-689: The Scotland Act , which came into force the following year, established a devolved Scottish Parliament and Scottish Executive (renamed the Scottish Government since September 2007 ). Both based in Edinburgh, they are responsible for governing Scotland while reserved matters such as defence, foreign affairs and some elements of income tax remain the responsibility of the Parliament of the United Kingdom in London. In 2022, Edinburgh
5715-739: The South Bridge in the 1780s. The Southside is particularly popular with families (many state and private schools are here), young professionals and students (the central University of Edinburgh campus is based around George Square just north of Marchmont and the Meadows ), and Napier University (with major campuses around Merchiston and Morningside). The area is also well provided with hotel and "bed and breakfast" accommodation for visiting festival-goers. These districts often feature in works of fiction. For example, Church Hill in Morningside,
5842-568: The neper , is named after Napier, as is Edinburgh Napier University in Edinburgh, Scotland. The crater Neper on the Moon is named after him. In French, Spanish and Portuguese, the natural logarithm is named after him (respectively, Logarithme Népérien and Logaritmos Neperianos for Spanish and Portuguese). In Finnish and Italian, the mathematical constant e is named after him ( Neperin luku and Numero di Nepero ). In 1572, Napier married 16-year-old Elizabeth, daughter of James Stirling,
5969-503: The "burh" (fortress), named in the 10th-century Pictish Chronicle as oppidum Eden , was abandoned to the Scots. It thenceforth remained, for the most part, under their jurisdiction. The royal burgh was founded by King David I in the early 12th century on land belonging to the Crown, though the date of its charter is unknown. The first documentary evidence of the medieval burgh is
6096-499: The 1860s began the transformation of the area into the predominantly Victorian Old Town seen today. More improvements followed in the early 20th century as a result of the work of Patrick Geddes , but relative economic stagnation during the two world wars and beyond saw the Old Town deteriorate further before major slum clearance in the 1960s and 1970s began to reverse the process. University building developments which transformed
6223-465: The 18th-century novel The Expedition of Humphry Clinker by Tobias Smollett one character describes Edinburgh as a "hotbed of genius". Edinburgh was also a major centre for the Scottish book trade. The highly successful London bookseller Andrew Millar was apprenticed there to James McEuen. From the 1770s onwards, the professional and business classes gradually deserted the Old Town in favour of
6350-520: The 19th century and joined by new industries such as rubber works , engineering works and others. By 1821, Edinburgh had been overtaken by Glasgow as Scotland's largest city. The city centre between Princes Street and George Street became a major commercial and shopping district, a development partly stimulated by the arrival of railways in the 1840s. The Old Town became an increasingly dilapidated, overcrowded slum with high mortality rates. Improvements carried out under Lord Provost William Chambers in
6477-607: The 4th Laird of Keir and of Cadder . They had two children. Elizabeth died in 1579, and Napier then married Agnes Chisholm, with whom he had ten more children. Napier's father-in-law, Sir James Chisholm of Cromlix, was one of many excommunicated by the General Assembly of the Presbyterian party following the Spanish blanks plot . Napier sat on the General Assembly that excommunicated the plotters, and petitioned
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#17327809247966604-411: The Castle Rock, giving rise to allusions to the seven hills of Rome . Occupying a narrow gap between the Firth of Forth to the north and the Pentland Hills and their outrunners to the south, the city sprawls over a landscape which is the product of early volcanic activity and later periods of intensive glaciation. Igneous activity between 350 and 400 million years ago, coupled with faulting , led to
6731-668: The English in 1544, Edinburgh continued to develop and grow, and was at the centre of events in the 16th-century Scottish Reformation and 17th-century Wars of the Covenant . In 1582, Edinburgh's town council was given a royal charter by King James VI permitting the establishment of a university; founded as Tounis College (Town's College), the institution developed into the University of Edinburgh , which contributed to Edinburgh's central intellectual role in subsequent centuries. In 1603, King James VI of Scotland succeeded to
6858-620: The English throne, uniting the crowns of Scotland and England in a personal union known as the Union of the Crowns , though Scotland remained, in all other respects, a separate kingdom. In 1638, King Charles I's attempt to introduce Anglican church forms in Scotland encountered stiff Presbyterian opposition culminating in the conflicts of the Wars of the Three Kingdoms . Subsequent Scottish support for Charles Stuart 's restoration to
6985-470: The Firth of Forth to Granton. The work was completed in 1947, at which point the construction of a parallel motor road, Marine Drive, was begun. The scheme originally included plans for a paddling pool, open-air swimming pool and model yacht basin, but these were never realised. In 1894, the Caledonian Railway opened a branch line from Craigleith to Barnton via Davidson's Mains, running through
7112-673: The Jacobite "Highland Army" before its march into England. After its eventual defeat at Culloden , there followed a period of reprisals and pacification, largely directed at the rebellious clans . In Edinburgh, the Town Council, keen to emulate London by initiating city improvements and expansion to the north of the castle, reaffirmed its belief in the Union and loyalty to the Hanoverian monarch George III by its choice of names for
7239-424: The North". Robert Louis Stevenson, also a son of the city, wrote that Edinburgh "is what Paris ought to be". The earliest known human habitation in the Edinburgh area was at Cramond , where evidence was found of a Mesolithic camp site dated to c. 8500 BC. Traces of later Bronze Age and Iron Age settlements have been found on Castle Rock, Arthur's Seat , Craiglockhart Hill and the Pentland Hills . When
7366-679: The Palace of Holyroodhouse, the churches of St. Giles , Greyfriars and the Canongate , and the extensive Georgian New Town built in the 18th/19th centuries. Edinburgh's Old Town and New Town together are listed as a UNESCO World Heritage Site , which has been managed by Edinburgh World Heritage since 1999. The city's historical and cultural attractions have made it the UK's second-most visited tourist destination, attracting 4.9 million visits, including 2.4 million from overseas in 2018. Edinburgh
7493-548: The Provost for the time as Sheriff, and by the Bailies for the time as Sheriffsdepute conjunctly and severally; with full power to hold Courts, to punish transgressors not only by banishment but by death, to appoint officers of Court, and to do everything else appertaining to the office of Sheriff; as also to apply to their own proper use the fines and escheats arising out of the exercise of the said office." Despite being burnt by
7620-505: The United Kingdom's second largest financial and administrative centre after London. Financial services now account for a third of all commercial office space in the city. The development of Edinburgh Park , a new business and technology park covering 38 acres (15 ha), 4 mi (6 km) west of the city centre, has also contributed to the District Council's strategy for the city's major economic regeneration. In 1998,
7747-707: The West through Silverknowes to Gypsy Brae Recreational Park and Granton in the East. Silverknowes Beach is tidal and overlooks Cramond Island, which can be accessed across the Drum Sands for four hours twice a day and via Cramond Causeway, built in 1939 by the War Department as part of World War Two Coastal Defences. To the west of Silverknowes is the Lauriston Castle and Estate. Open farmland lies between
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#17327809247967874-544: The adjectival forms Edinburgensis and Edinensis are used in educational and scientific contexts. Edina is a late 18th-century poetical form used by the Scots poets Robert Fergusson and Robert Burns . "Embra" or "Embro" are colloquialisms from the same time, as in Robert Garioch 's Embro to the Ploy . Ben Jonson described it as "Britaine's other eye", and Sir Walter Scott referred to it as "yon Empress of
8001-628: The architectural style of the New Town into the early 19th century. Bute House , the official residence of the First Minister of Scotland , is on the north side of Charlotte Square. The hollow between the Old and New Towns was formerly the Nor Loch , which was created for the town's defence but came to be used by the inhabitants for dumping their sewage . It was drained by the 1820s as part of
8128-543: The area. With the redevelopment, Edinburgh has gained the business of cruise liner companies which now provide cruises to Norway, Sweden, Denmark, Germany, and the Netherlands. The coastal suburb of Portobello is characterised by Georgian villas, Victorian tenements, a beach and promenade and cafés, bars, restaurants and independent shops. There are rowing and sailing clubs, a restored Victorian swimming pool, and Victorian Turkish baths . The urban area of Edinburgh
8255-543: The beginning of three centuries of Germanic influence in south east Scotland that laid the foundations for the development of Scots , before the town was ultimately subsumed in 954 by the kingdom known to the English as Scotland. As the language shifted from Cumbric to Northumbrian Old English and then Scots , the Brittonic din in Din Eidyn was replaced by burh , producing Edinburgh . In Scottish Gaelic din becomes dùn , producing modern Dùn Èideann . The city
8382-565: The city between October and April. Located slightly north of the city centre, the weather station at the Royal Botanic Garden Edinburgh (RBGE) has been an official weather station for the Met Office since 1956. The Met Office operates its own weather station at Gogarbank on the city's western outskirts, near Edinburgh Airport . This slightly inland station has a slightly wider temperature span between seasons,
8509-423: The city was 31.6 °C (88.9 °F) on 25 July 2019 at Gogarbank, beating the previous record of 31 °C (88 °F) on 4 August 1975 at Edinburgh Airport. The lowest temperature recorded in recent years was −14.6 °C (5.7 °F) during December 2010 at Gogarbank. Given Edinburgh's position between the coast and hills, it is renowned as "the windy city", with the prevailing wind direction coming from
8636-473: The city's northward expansion. Craig's original plan included an ornamental canal on the site of the loch, but this idea was abandoned. Soil excavated while laying the foundations of buildings in the New Town was dumped on the site of the loch to create the slope connecting the Old and New Towns known as The Mound . In the middle of the 19th century the National Gallery of Scotland and Royal Scottish Academy Building were built on The Mound, and tunnels for
8763-415: The creation of tough basalt volcanic plugs , which predominate over much of the area. One such example is the Castle Rock which forced the advancing ice sheet to divide, sheltering the softer rock and forming a 1 mi-long (1.6 km) tail of material to the east, thus creating a distinctive crag and tail formation. Glacial erosion on the north side of the crag gouged a deep valley later filled by
8890-567: The crest of a ridge from it terminating at Holyrood Palace. Minor streets (called closes or wynds ) lie on either side of the main spine forming a herringbone pattern. Due to space restrictions imposed by the narrowness of this landform, the Old Town became home to some of the earliest "high rise" residential buildings. Multi-storey dwellings known as lands were the norm from the 16th century onwards with ten and eleven storeys being typical and one even reaching fourteen or fifteen storeys. Numerous vaults below street level were inhabited to accommodate
9017-426: The effects of gout at home at Merchiston Castle at the age of 67. He was buried in the kirkyard of St Giles in Edinburgh. Following the loss of the kirkyard of St Giles to build Parliament House , his remains were transferred to an underground vault on the north side of St Cuthbert's Parish Church at the west side of Edinburgh. There is also a wall monument to Napier at St Cuthbert's. Many mathematicians at
9144-434: The expanding city of the nineteenth and twentieth centuries. Many areas, such as Dalry , contain residences that are multi-occupancy buildings known as tenements , although the more southern and western parts of the city have traditionally been less built-up with a greater number of detached and semi-detached villas. The historic centre of Edinburgh is divided in two by the broad green swathe of Princes Street Gardens . To
9271-477: The fact that the social classes shared the same urban space, even inhabiting the same tenement buildings; although here a form of social segregation did prevail, whereby shopkeepers and tradesmen tended to occupy the cheaper-to-rent cellars and garrets, while the more well-to-do professional classes occupied the more expensive middle storeys. During the Jacobite rising of 1745 , Edinburgh was briefly occupied by
9398-473: The infamous Mississippi Bubble; Barnton House (a.k.a. Cramond Regis), Former Hunting Estate of Kings of Scotland; Muirhouse (now Muirhouse Mansion, formerly known as Randalistoun), Grade A Listed Building, now a Homeless Hostel; Silverknowe House, formerly Silverknowe Hydro Convalescence Home (destroyed by fire in 1960 while being used as Silverknowes Golf Club House); Broomfield House owned by Earl Haig's Sister (which became The Commodore Hotel 1950s to early 2000s,
9525-698: The influence of the sermons of Christopher Goodman , he developed a strongly anti-papal reading, going as far as to say that the Pope was the Antichrist in some of his writings. Napier regarded A Plaine Discovery of the Whole Revelation of St. John (1593) as his most important work. It was written in English, unlike his other publications, in order to reach the widest audience and so that, according to Napier, "the simple of this island may be instructed". A Plaine Discovery used mathematical analysis of
9652-620: The influx of incomers, particularly Irish immigrants , during the Industrial Revolution . The street has several fine public buildings such as St Giles' Cathedral, the City Chambers and the Law Courts . Other places of historical interest nearby are Greyfriars Kirkyard and Mary King's Close . The Grassmarket , running deep below the castle is connected by the steep double terraced Victoria Street. The street layout
9779-532: The largest concentration of significant Country Houses in Scotland: Lauriston Castle, with its world-famous Blue John Glass and Furniture Collections, once Owned by John Napier , Inventor of Logarithms & former Home of John Law (economist) of Lauriston, World-Famous in the 18th & 19th Centuries, Chief Financier of France under King Louis XIV, Founder of the Bank of France and Creator of
9906-436: The locals, was when Napier removed the pigeons from his estate since they were eating his grain. Napier caught the pigeons by strewing grain laced with alcohol throughout the field and then capturing the pigeons once they were too drunk to fly away. A contract still exists for a treasure hunt , made between Napier and Robert Logan of Restalrig . Napier was to search Fast Castle for treasure allegedly hidden there, wherein it
10033-535: The middle of the 14th century, the French chronicler Jean Froissart described it as the capital of Scotland (c. 1365), and James III (1451–88) referred to it in the 15th century as "the principal burgh of our kingdom". In 1482 James III "granted and perpetually confirmed to the said Provost, Bailies, Clerk, Council, and Community, and their successors, the office of Sheriff within the Burgh for ever, to be exercised by
10160-623: The modern-day skyscraper. Most of these old structures were replaced by the predominantly Victorian buildings seen in today's Old Town. In 1611 an act of parliament created the High Constables of Edinburgh to keep order in the city, thought to be the oldest statutory police force in the world. Following the Treaty of Union in 1706, the Parliaments of England and Scotland passed Acts of Union in 1706 and 1707 respectively, uniting
10287-482: The more elegant "one-family" residences of the New Town, a migration that changed the city's social character. According to the foremost historian of this development, "Unity of social feeling was one of the most valuable heritages of old Edinburgh, and its disappearance was widely and properly lamented." Despite an enduring myth to the contrary, Edinburgh became an industrial centre with its traditional industries of printing, brewing and distilling continuing to grow in
10414-537: The name for the region in Cumbric , the Brittonic Celtic language formerly spoken there. The name's meaning is unknown. The district of Eidyn was centred on the stronghold of Din Eidyn, the dun or hillfort of Eidyn. This stronghold is believed to have been located at Castle Rock , now the site of Edinburgh Castle . A siege of Din Eidyn by Oswald , king of the Angles of Northumbria in 638 marked
10541-880: The new "Forth" local authority voting ward. This outraged residents, who felt it would lead to the breakup of Davidson's Mains as a community. Over 600 objections were sent by members of the community and various local establishments, and Silverknowes became part of "Almond" ward alongside Davidson's Mains, Barnton and Cramond. The area is served by the Davidson's Mains and Silverknowes Association and four City of Edinburgh Councillors, MSP for Edinburgh West and MP for Edinburgh West. 55°58′10.19″N 3°16′13.78″W / 55.9694972°N 3.2704944°W / 55.9694972; -3.2704944 Edinburgh Edinburgh ( / ˈ ɛ d ɪ n b ər ə / ED -in-bər-ə , Scots: [ˈɛdɪnbʌrə] ; Scottish Gaelic : Dùn Èideann [t̪un ˈeːtʲən̪ˠ] )
10668-734: The north. Silverknowes lies within the boundaries of the Almond local government ward (Ward 1), the Edinburgh West parliamentary constituency (UK parliament) and the Edinburgh Western parliamentary constituency (Scottish parliament). It is part of the area covered by the Davidson's Mains & Silverknowes Association and the Silverknowes Community Council. Until the 1930s, the Silverknowes area
10795-547: The northern fringes overlooking Cramond Island. Silverknowes Beach and Promenade are in sight of Lauriston Castle and stretches 3 miles from Granton in the East to Cramond village in the west, along the banks of the Firth of Forth . The Boardwalk Beach Club café lies about half-way along the Promenade. There is a frequent 29 Lothian Bus Service to Silverknowes Promenade from Edinburgh City Centre, taking 20 minutes direct from Edinburgh Waverley Station and 1 hour from Gorebridge, to
10922-475: The now drained Nor Loch . These features, along with another hollow on the rock's south side, formed an ideal natural strongpoint upon which Edinburgh Castle was built. Similarly, Arthur's Seat is the remains of a volcano dating from the Carboniferous period , which was eroded by a glacier moving west to east during the ice age. Erosive action such as plucking and abrasion exposed the rocky crags to
11049-415: The other two parts. The ten Napier's Rules are given by The key for remembering which trigonometric function goes with which part is to look at the first vowel of the kind of part: middle parts take the sine, adjacent parts take the tangent, and opposite parts take the cosine. For an example, starting with the sector containing a {\displaystyle a} we have: The full set of rules for
11176-400: The polar triangle A'B'C' with sides a',b',c' such that A' = π − a , a' = π − A etc. The results are: (Q1) cos C = − cos A cos B , (Q6) tan B = − cos
11303-567: The popular imagination. When plans were drawn up in the early 19th century to architecturally develop Calton Hill , the design of the National Monument directly copied Athens' Parthenon . Tom Stoppard 's character Archie of Jumpers said, perhaps playing on Reykjavík meaning "smoky bay", that the "Reykjavík of the South" would be more appropriate. The city has also been known by several Latin names , such as Edinburgum , while
11430-405: The potential of the recent developments in mathematics, particularly those of prosthaphaeresis , decimal fractions, and symbolic index arithmetic, to tackle the issue of reducing computation. He appreciated that, for the most part, practitioners who had laborious computations generally did them in the context of trigonometry. Therefore, as well as developing the logarithmic relation, Napier set it in
11557-522: The railway line between Haymarket and Waverley stations were driven through it. The Southside is a residential part of the city, which includes the districts of St Leonards , Marchmont , Morningside , Newington , Sciennes , the Grange and Blackford . The Southside is broadly analogous to the area covered formerly by the Burgh Muir , and was developed as a residential area after the opening of
11684-470: The remainder of his life. He had a property within Edinburgh city as well on Borthwick's Close off the Royal Mile . On 7 June 1596 Napier wrote a paper Secret inventions, profitable and necessary in these days for defence of this island . He describes two kinds of burning mirror for use against ships at a distance, a special kind of artillery shot, and a musket-proof metal chariot. Napier died from
11811-472: The right spherical triangle is (Todhunter, Art.62) (R1) cos c = cos a cos b , (R6) tan b = cos A tan c , (R2) sin a = sin A sin c , (R7) tan
11938-413: The river gets to the city centre is at Dean Village on the north-western edge of the New Town, where a deep gorge is spanned by Thomas Telford 's Dean Bridge , built in 1832 for the road to Queensferry . The Water of Leith Walkway is a mixed-use trail that follows the course of the river for 19.6 km (12.2 mi) from Balerno to Leith. Excepting the shoreline of the Firth of Forth, Edinburgh
12065-403: The second half of the century, the city was at the heart of the Scottish Enlightenment , when thinkers like David Hume, Adam Smith, James Hutton and Joseph Black were familiar figures in its streets. Edinburgh became a major intellectual centre, earning it the nickname "Athens of the North" because of its many neo-classical buildings and reputation for learning, recalling ancient Athens. In
12192-431: The smoke hover over her at twenty miles' distance". In 1898, Thomas Carlyle comments on the phenomenon: "Smoke cloud hangs over old Edinburgh, for, ever since Aeneas Silvius 's time and earlier, the people have the art, very strange to Aeneas, of burning a certain sort of black stones, and Edinburgh with its chimneys is called 'Auld Reekie' by the country people". The 19th-century historian Robert Chambers asserted that
12319-427: The sobriquet could not be traced before the reign of Charles II in the late 17th century. He attributed the name to a Fife laird, Durham of Largo, who regulated the bedtime of his children by the smoke rising above Edinburgh from the fires of the tenements. "It's time now bairns, to tak' the beuks, and gang to our beds, for yonder's Auld Reekie, I see, putting on her nicht -cap!". Edinburgh has been popularly called
12446-523: The south of Edinburgh. It is possible to reach the 18th century Cramond Village using this Silverknowes Promenade. To the east side of Silverknowes Road lies the Silverknowes Golf Club and 18 hole golf course, operated by Edinburgh Leisure. The golf course stretches to the beach. Along Silverknowes Parkway there are also well-used playing fields. Most of the neighbourhood lies in the catchment area for Davidson's Mains Primary School and
12573-499: The south of Silverknowes. The line closed to passengers in 1951 and to goods traffic in 1960. The surviving trackbed is now a footpath and cycle path, forming part of the National Cycle Network Route 1. During World War II, Silverknowes was the site of a heavy anti-aircraft battery, situated on the north side of Silverknowes Golf Course. A Starfish anti-aircraft decoy was located 700 metres (770 yd) to
12700-413: The south, Barnton , Lauriston to the west, and Muirhouse to the east. Silverknowes is located in the north west of Edinburgh, on the shores of the Firth of Forth . It lies approximately 5 kilometres (3 miles) from the city centre. The district is bounded by Cramond to the north and west, Davidson's Mains to the southwest, Blackhall to the south, Muirhouse to the east, and the Firth of Forth to
12827-548: The south, the view is dominated by Edinburgh Castle, built high on Castle Rock, and the long sweep of the Old Town descending towards Holyrood Palace. To the north lie Princes Street and the New Town. The West End includes the financial district, with insurance and banking offices as well as the Edinburgh International Conference Centre. Edinburgh's Old and New Towns were listed as a UNESCO World Heritage Site in 1995 in recognition of
12954-546: The south-west, which is often associated with warm, unstable air from the North Atlantic Current that can give rise to rainfall – although considerably less than cities to the west, such as Glasgow. Rainfall is distributed fairly evenly throughout the year. Winds from an easterly direction are usually drier but considerably colder, and may be accompanied by haar , a persistent coastal fog. Vigorous Atlantic depressions, known as European windstorms , can affect
13081-542: The south. The development was originally a mixture of private and council housing , but is now mainly owner-occupied, most of the council houses having been purchased by their tenants under the Right to Buy legislation of the 1980s. In the early 1930s, Edinburgh Corporation started developing the Silverknowes Esplanade, a 3.2 kilometres (2.0 mi) walkway running from Cramond along the south shore of
13208-553: The southern shore of the Firth of Forth. The city centre is 2 + 1 ⁄ 2 mi (4.0 km) southwest of the shoreline of Leith and 26 mi (42 km) inland, as the crow flies, from the east coast of Scotland and the North Sea at Dunbar . While the early burgh grew up near the prominent Castle Rock, the modern city is often said to be built on seven hills , namely Calton Hill , Corstorphine Hill , Craiglockhart Hill, Braid Hill , Blackford Hill , Arthur's Seat and
13335-456: The streets of the New Town: for example, Rose Street and Thistle Street; and for the royal family, George Street , Queen Street , Hanover Street, Frederick Street and Princes Street (in honour of George's two sons). The consistently geometric layout of the plan for the extension of Edinburgh was the result of a major competition in urban planning staged by the Town Council in 1766. In
13462-783: The thirteenth largest internationally. The city is a cultural centre, and is the home of institutions including the National Museum of Scotland , the National Library of Scotland and the Scottish National Gallery . The city is also known for the Edinburgh International Festival and the Fringe , the latter being the world's largest annual international arts festival. Historic sites in Edinburgh include Edinburgh Castle ,
13589-501: The throne of England resulted in Edinburgh's occupation by Oliver Cromwell 's Commonwealth of England forces – the New Model Army – in 1650. In the 17th century, Edinburgh's boundaries were still defined by the city's defensive town walls . As a result, the city's growing population was accommodated by increasing the height of the houses. Buildings of 11 storeys or more were common, and have been described as forerunners of
13716-419: The time were acutely aware of the issues of computation and were dedicated to relieving practitioners of the calculation burden. Napier was famous for his devices to assist with these issues of computation. He invented a well-known mathematical artefact, the ingenious numbering rods more quaintly known as "Napier's bones", that offered mechanical means for facilitating computation. In addition, Napier recognized
13843-456: The triangle shown above left, going clockwise starting with a gives aCbAcB . Next replace the parts that are not adjacent to C (that is A, c, B ) by their complements and then delete the angle C from the list. The remaining parts can then be drawn as five ordered, equal slices of a pentagram, or circle, as shown in the above figure (right). For any choice of three contiguous parts, one (the middle part) will be adjacent to two parts and opposite
13970-824: The true date of the Apocalypse, but claimed that since the Bible contained so many clues about the end, God wanted the Church to know when the end was coming. In his dedication of the Plaine Discovery to James VI , dated 29 Jan 1594, Napier urged the king to see "that justice be done against the enemies of God's church," and counselled the King "to reform the universal enormities of his country, and first to begin at his own house, family, and court." The volume includes nine pages of Napier's English verse. It met with success at home and abroad. In 1600 Michiel Panneel produced
14097-538: The two kingdoms in the Kingdom of Great Britain effective from 1 May 1707. As a consequence, the Parliament of Scotland merged with the Parliament of England to form the Parliament of Great Britain , which sat at Westminster in London. The Union was opposed by many Scots, resulting in riots in the city. By the first half of the 18th century, Edinburgh was described as one of Europe's most densely populated, overcrowded and unsanitary towns. Visitors were struck by
14224-415: The unique character of the Old Town with its medieval street layout and the planned Georgian New Town, including the adjoining Dean Village and Calton Hill areas. There are over 4,500 listed buildings within the city, a higher proportion relative to area than any other city in the United Kingdom. The castle is perched on top of a rocky crag (the remnant of an extinct volcano) and the Royal Mile runs down
14351-427: The web, as well as a discussion of Napier's bones and Promptuary (another early calculating device). His invention of logarithms was quickly taken up at Gresham College , and prominent English mathematician Henry Briggs visited Napier in 1615. Among the matters they discussed were a re-scaling of Napier's logarithms, in which the presence of the mathematical constant now known as e (more accurately, e times
14478-551: The west before leaving a tail of deposited glacial material swept to the east. This process formed the distinctive Salisbury Crags , a series of teschenite cliffs between Arthur's Seat and the location of the early burgh. The residential areas of Marchmont and Bruntsfield are built along a series of drumlin ridges south of the city centre, which were deposited as the glacier receded. Other prominent landforms such as Calton Hill and Corstorphine Hill are also products of glacial erosion. The Braid Hills and Blackford Hill are
14605-487: The west, at the west end of Marine Drive. This consisted of a group of 'fire-burning' boxes, designed to appear from the air as a burning town or city, thus diverting enemy aircraft from their intended targets. Lauriston Farm Buildings were used for Farming Purposes until the 1970s, when the Ross Family introduced a Market Garden followed by an Eatery. The Robertson Family then took over Lauriston Farm and turned it into
14732-499: Was a Scottish landowner known as a mathematician , physicist , and astronomer . He was the 8th Laird of Merchiston . John Napier is best known as the discoverer of logarithms . He also invented the so-called " Napier's bones " and made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, Merchiston Tower in Edinburgh , is now part of the facilities of Edinburgh Napier University . There
14859-514: Was a matter of great resentment when the two burghs merged in 1920 into the City of Edinburgh. Even today the parliamentary seat is known as "Edinburgh North and Leith". The loss of traditional industries and commerce (the last shipyard closed in 1983) resulted in economic decline. The Edinburgh Waterfront development has transformed old dockland areas from Leith to Granton into residential areas with shopping and leisure facilities and helped rejuvenate
14986-469: Was affected by the 2022 Scotland bin strikes . In 2023, Edinburgh became the first capital city in Europe to sign the global Plant Based Treaty , which was introduced at COP26 in 2021 in Glasgow. Green Party councillor Steve Burgess introduced the treaty. The Scottish Countryside Alliance and other farming groups called the treaty "anti-farming". Situated in Scotland's Central Belt , Edinburgh lies on
15113-587: Was fluent in Greek, a language that was not commonly taught in European universities at the time. There are also no records showing his enrollment in the premier universities in Paris or Geneva during this time. In 1571, Napier, aged 21, returned to Scotland, and bought a castle at Gartness in 1574. On the death of his father in 1608, Napier and his family moved into Merchiston Castle in Edinburgh, where he resided
15240-407: Was interrupted by World War II , but resumed in 1952 with the development of Silverknowes Bank, Brae, Court, Eastway, Gardens, Grove, Parkway and Place, these all being to the east of Silverknowes Road. Most of these roads form a series of concentric semi-circles on either side of Silverknowes Road. In 1960, Silverknowes Green, Midway, Southway and View were built on part of the former Drylaw Estate to
15367-551: Was open farmland. It was previously part of the Lauriston Estate, and was known as Randalston (spelled as Randalistoun on some maps), that name dating back to at least the 14th century. In 1934, most of the land was acquired by McTaggart & Mickel, a Glasgow-based firm of tenement builders. In 1936, the firm started building houses to the west of the existing Silverknowes Road, creating Silverknowes Avenue, Crescent, Drive, Hill (formerly Circus), Loan and Terrace. The work
15494-399: Was opened to later scientific advances, in astronomy , dynamics , and other areas of physics . Napier made further contributions. He improved Simon Stevin 's decimal notation, introducing the full stop (.) as the delimiter for the fractional part. Lattice multiplication , used by Fibonacci , was made more convenient by his introduction of Napier's bones , a multiplication tool using
15621-542: Was privately tutored during early childhood. At age 13, he was enrolled in St Salvator's College, St Andrews . Near the time of his matriculation the quality of the education provided by the university was poor, owing in part to the Reformation's causing strife between those of the old faith and the growing numbers of Protestants. There are no records showing that John Napier completed his education at St Andrews. It
15748-431: Was said that he would travel about with a black spider in a small box, and that his black cockerel was his familiar spirit . Some of Napier's neighbours accused him of being a sorcerer and in league with the devil, believing that all of the time he spent in his study was being used to learn the black art. These rumours were stoked when Napier used his black cockerel to catch a thief. Napier told his servants to go into
15875-572: Was the home of Muriel Spark 's Miss Jean Brodie, and Ian Rankin 's Inspector Rebus lives in Marchmont and works in St Leonards. Leith was historically the port of Edinburgh, an arrangement of unknown date that was confirmed by the royal charter Robert the Bruce granted to the city in 1329. The port developed a separate identity from Edinburgh, which to some extent it still retains, and it
16002-576: Was to be George Street , running along the natural ridge to the north of what became known as the "Old Town". To either side of it are two other main streets: Princes Street and Queen Street. Princes Street has become Edinburgh's main shopping street and now has few of its Georgian buildings in their original state. The three main streets are connected by a series of streets running perpendicular to them. The east and west ends of George Street are terminated by St Andrew Square and Charlotte Square respectively. The latter, designed by Robert Adam , influenced
16129-404: Was working in a similar direction. Craig had notes on a method of Paul Wittich that used trigonometric identities to reduce a multiplication formula for the sine function to additions. When one of the angles, say C , of a spherical triangle is equal to π /2 the various identities given above are considerably simplified. There are ten identities relating three elements chosen from the set
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