Stirling

Coordinates: 56°07′02″N 3°56′23″W / 56.117222°N 3.939722°W / 56.117222; -3.939722

Stirling (/ˈstɜːrlɪŋ/; Scots: Stirlin; Scottish Gaelic: Sruighlea [ˈs̪t̪ruʝlə]) is a city in central Scotland. The city is clustered around a large fortress and medieval old town. Stirling is the administrative centre for the Stirling council area, and is traditionally the county town of Stirlingshire. The city is located several miles to the west of the mouth of the River Forth. Historically it was strategically important as the "Gateway to the Highlands", with its position near the Highland Boundary Fault between the Scottish Lowlands and Highlands and has been described as the brooch which clasps the Highlands and the Lowlands together.

Its historical position as the nearest crossing of the Forth to the river mouth meant that it attracted invaders. The beast of Stirling is the wolf, which it shares with Rome. According to legend, when Stirling was under attack from Viking invaders, a wolf howled, alerting the townspeople in time to save the town.

Stirling (Reading, Pennsylvania)

Stirling is a historic mansion located at Reading, Berks County, Pennsylvania. It was built between 1890 and 1892, and is a three-story, 24-room, Châteauesque style dwelling. It was designed by noted Philadelphia architect Theophilus Parsons Chandler, Jr. (1845-1928) and built for industrialist James Hervey Sternbergh. It is constructed of squared granite ashlar and features a number of eclectic decorative elements including tall chimneys with decorated caps, a balustraded verandah, steeply pitched gable roofs, and roof dormers. It is now occupied by a bed and breakfast.

It was listed on the National Register of Historic Places in 1980.

References

Stirling (UK Parliament constituency)

Coordinates: 56°07′08″N 4°04′55″W / 56.119°N 4.082°W / 56.119; -4.082

Stirling is a county constituency of the House of Commons of the Parliament of the United Kingdom. It elects one Member of Parliament (MP) by the first past the post system of election.

Boundaries

1983-1997: Stirling District except the electoral division of Carseland.

1997-2005: The Stirling District electoral divisions of Bannockburn, Castle, Dounebraes, Menteith, Queensland, St Ninians, Strathendrick, Viewforth, and Wallace.

2005–present: The Stirling council area.

The constituency covers the whole of the Stirling council area. Most of the area is rural, which has tended to vote Conservative, but there are some large towns in the East, most notably Stirling itself, which used to vote Labour, but has now moved towards SNP. A similar constituency, also called Stirling, is used by the Scottish Parliament.

History

The area covered by the modern constituency was first represented in the British House of Commons in consequence of the Act of Union 1707 in 1708. The county town of Stirling was represented as part of Stirling Burghs and the county was represented by Stirlingshire, each returning one member.

Stirling's approximation

In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a very powerful approximation, leading to accurate results even for small values of n. It is named after James Stirling, though it was first stated by Abraham de Moivre.

The formula as typically used in applications is

(in big O notation). The next term in the O(ln(n)) is 1/2ln(2πn); a more precise variant of the formula is therefore

It is also possible to give a version of Stirling's formula with bounds valid for all positive integers n, rather than asymptotics: one has

for all positive integers n. Thus the ratio is always between √2π = 2.5066… and e = 2.71828….

As an asymptotic formula, Stirling's approximation has the property that the ratio

approaches 1 as n grows to infinity.

Derivation

The formula, together with precise estimates of its error, can be derived as follows. Instead of approximating n!, one considers its natural logarithm as this is a slowly varying function: