A perimeter is a path that surrounds a two-dimensional shape. The term may be used either for the path itself or its length—it can be thought of as the length of the outline of a shape; the perimeter of a circle or ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a garden; the perimeter of a wheel describes. The amount of string wound around a spool is related to the spool's perimeter; the perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with ∫ 0 L d s, where L is the length of the path and d s is an infinitesimal line element. Both of these must be replaced with by algebraic forms in order to be calculated. If the perimeter is given as a closed piecewise smooth plane curve γ: → R 2 with γ = its length L can be computed as follows: L = ∫ a b x ′ 2 + y ′ 2 d t A generalized notion of perimeter, which includes hypersurfaces bounding volumes in n -dimensional Euclidean spaces, is described by the theory of Caccioppoli sets.
Polygons are fundamental to determining perimeters, not only because they are the simplest shapes but because the perimeters of many shapes are calculated by approximating them with sequences of polygons tending to these shapes. The first mathematician known to have used this kind of reasoning is Archimedes, who approximated the perimeter of a circle by surrounding it with regular polygons; the perimeter of a polygon equals the sum of the lengths of its sides. In particular, the perimeter of a rectangle of width w and length ℓ equals 2 w + 2 ℓ. An equilateral polygon is a polygon. To calculate the perimeter of an equilateral polygon, one must multiply the common length of the sides by the number of sides. A regular polygon may be characterized by the number of its sides and by its circumradius, to say, the constant distance between its centre and each of its vertices; the length of its sides can be calculated using trigonometry. If R is a regular polygon's radius and n is the number of its sides its perimeter is 2 n R sin .
A splitter of a triangle is a cevian that divides the perimeter into two equal lengths, this common length being called the semiperimeter of the triangle. The three splitters of a triangle all intersect each other at the Nagel point of the triangle. A cleaver of a triangle is a segment from the midpoint of a side of a triangle to the opposite side such that the perimeter is divided into two equal lengths; the three cleavers of a triangle all intersect each other at the triangle's Spieker center. The perimeter of a circle called the circumference, is proportional to its diameter and its radius; that is to say, there exists a constant number pi, π, such that if P is the circle's perimeter and D its diameter P = π ⋅ D. In terms of the radius r of the circle, this formula becomes, P = 2 π ⋅ r. To calculate a circle's perimeter, knowledge of its radius or diameter and the number π suffices; the problem is that π is not rational, nor is it algebraic. So, obtaining an accurate approximation of π is important in the calculation.
The computation of the digits of π is relevant to many fields, such as mathematical analysis and computer science. The perimeter and the area are two main measures of geometric figures. Confusing them is a common error, as well as believing that the greater one of them is, the greater the other must be. Indeed, a commonplace observation is that an enlargement of a shape make its area grow as well as its perimeter. For example, if a field is drawn on a 1/10,000 scale map, the actual field perimeter can be calculated multiplying the drawing perimeter by 10,000; the real area is 10,0002 times the area of the shape on the map. There is no relation between the area and the perimeter of an ordinary shape. F
2004 United States presidential election in Montana
The 2004 United States presidential election in Montana took place on November 2, 2004, was part of the 2004 United States presidential election. Voters chose 3 representatives, or electors to the Electoral College, who voted for president and vice president. Montana was won by incumbent President George W. Bush by a 20.5% margin of victory. Prior to the election, all 12 news organizations considered this a state Bush would win, or otherwise considered as a safe red state; the state votes for Democrats at the state level, having two Democratic senators: Max Baucus and Jon Tester, as well as a popular governor Brian Schweitzer. Montana has voted for the Republican presidential nominee in every election since 1964 except in 1992, when the state preferred Democrat Bill Clinton to Republican incumbent George H. W. Bush. Montana Democratic primary, 2004 There were 12 news organizations who made state-by-state predictions of the election. Here are their last predictions before election day. D. C. Political Report: Solid Republican Associated Press: Solid Bush CNN: Bush Cook Political Report: Solid Republican Newsweek: Solid Bush New York Times: Solid Bush Rasmussen Reports: Bush Research 2000: Solid Bush Washington Post: Bush Washington Times: Solid Bush Zogby International: Bush Washington Dispatch: Bush Only a few pre-election polls were taken here.
Bush won each one of them with at least 54 % of the vote. The final 3 polling average showed him leading 55% to 35%. Bush raised $385,635. Kerry raised $145,679. Neither campaign visited this state during the fall campaign. Bush's key to victory was winning the populated Yellowstone County with 60% along with the majority of other counties. Kerry only won 5 counties in the state, including swinging Missoula County and his best performance in the Democratic stronghold of Deer Lodge County. Due to the state's low population, only one congressional district is allocated; this district, called the At-Large district, because it covers the entire state, thus is equivalent to the statewide election results. Technically the voters of Montana cast their ballots for electors: representatives to the Electoral College. Montana is allocated 3 electors because it has 2 senators. All candidates who appear on the ballot or qualify to receive write-in votes must submit a list of 3 electors, who pledge to vote for their candidate and his or her running mate.
Whoever wins the majority of votes in the state is awarded all 3 electoral votes. Their chosen electors vote for president and vice president. Although electors are pledged to their candidate and running mate, they are not obligated to vote for them. An elector who votes for someone other than his or her candidate is known as a faithless elector; the electors of each state and the District of Columbia met on December 13, 2004, to cast their votes for president and vice president. The Electoral College itself never meets as one body. Instead the electors from each state and the District of Columbia met in their respective capitols; the following were the members of the Electoral College from the state. All 3 were pledged for Bush/Cheney. Jack Galt Thelma Baker John Brenden
Ravalli County, Montana
Ravalli County is a county in the southwestern part of the U. S. state of Montana. As of the 2010 United States Census, the population was 40,212, its county seat is Hamilton. Ravalli County is part of a north/south mountain valley bordered by the Sapphire Mountains on the East and the Bitterroot Mountains on the West, it is referred to as the Bitterroot Valley, named for the Bitterroot Flower. The county is on the Pacific Ocean side of the Continental Divide, which follows the Idaho-Montana border from Wyoming until Ravalli County. Here, it turns east into Montana, between Chief Joseph Pass and Lost Trail Pass, follows the Ravalli County-Beaverhead County border. Ravalli County was once home to the Bitterroot Salish tribe; the tribe was first encountered in 1805 by the Lewis and Clark Expedition, which noted their friendly nature. The Catholic Church took an interest in creating a mission in the area, in 1841, Stevensville was founded. In 1891, the Salish tribe moved to the current Flathead Reservation under the Treaty of Hellgate.
In 1877, Chief Joseph and his Wallowa band of Nez Perce passed through Ravalli County in their attempt to escape confinement to a reservation. Ravalli County was created in 1893 by the Montana Legislature, annexing a portion of Missoula County, it is named for the Italian Jesuit priest Antony Ravalli, who came to the Bitterroot Valley in 1845. According to the US Census Bureau, the county has an area of 2,400 square miles, of which 2,391 square miles is land and 9.4 square miles is water. U. S. Highway 93 Montana Highway 38 Bitterroot National Forest Lee Metcalf National Wildlife Refuge Lolo National Forest As of the 2000 United States Census, there were 36,070 people, 14,289 households, 10,188 families in the county; the population density was 15 people per square mile. There were 15,946 housing units at an average density of 7 per square mile; the racial makeup of the county was 96.71% White, 0.14% Black or African American, 0.88% Native American, 0.30% Asian, 0.10% Pacific Islander, 0.44% from other races, 1.44% from two or more races.
1.88% of the population were Hispanic or Latino of any race. 22.1% were of German, 14.1% English, 11.1% Irish, 7.9% American and 6.3% Norwegian ancestry. There were 14,289 households out of which 30.20% had children under the age of 18 living with them, 60.30% were married couples living together, 7.50% had a female householder with no husband present, 28.70% were non-families. 24.10% of all households were made up of individuals and 9.80% had someone living alone, 65 years of age or older. The average household size was 2.48 and the average family size was 2.94. The county population contained 25.60% under the age of 18, 6.20% from 18 to 24, 24.70% from 25 to 44, 28.00% from 45 to 64, 15.50% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 98.60 males. For every 100 females age 18 and over, there were 95.40 males. The median income for a household in the county was $31,992, the median income for a family was $38,397. Males had a median income of $30,994 versus $19,987 for females.
The per capita income for the county was $17,935. About 9.60% of families and 13.80% of the population were below the poverty line, including 20.10% of those under age 18 and 6.30% of those age 65 or over. As of the 2010 United States Census, there were 40,212 people, 16,933 households, 11,380 families in the county; the population density was 16.8 inhabitants per square mile. There were 19,583 housing units at an average density of 8.2 per square mile. The racial makeup of the county was 95.9% white, 0.9% American Indian, 0.5% Asian, 0.2% black or African American, 0.1% Pacific islander, 0.6% from other races, 1.9% from two or more races. Those of Hispanic or Latino origin made up 3.0% of the population. In terms of ancestry, 28.8% were German, 17.4% were English, 15.9% were Irish, 8.3% were American, 5.7% were Italian, 5.5% were Norwegian. Of the 16,933 households, 26.5% had children under the age of 18 living with them, 55.5% were married couples living together, 7.7% had a female householder with no husband present, 32.8% were non-families, 27.1% of all households were made up of individuals.
The average household size was 2.35 and the average family size was 2.83. The median age was 46.0 years. The median income for a household in the county was $43,000 and the median income for a family was $53,004. Males had a median income of $42,065 versus $27,629 for females; the per capita income for the county was $23,908. About 9.6% of families and 15.0% of the population were below the poverty line, including 23.5% of those under age 18 and 6.3% of those age 65 or over. Agriculture and timber form the bulk of Ravalli County economic activity. Marcus Daly, one of three Butte copper kings, funded logging operations in the Bitterroot Valley; the lumber was necessary for the Butte copper operation. More of Ravalli County's economy stems from tourism; the valley borders the Selway-Bitterroot Wilderness and offers a wide variety of wildlife, including some of the few remaining wolverine and wolf populations in the contiguous states. The Lost Trail Powder Mountain ski area is at Lost Trail Pass on the Idaho border on US-93.
Ravalli County voters have been reliably Republican, opting only one time for the Democratic Party candidate in national elections since 1940. Hamilton Darby Pinesdale Stevensville Henry L. Myers, Ravalli County prosecuting attorney, US Senator from Montana List of cemeteries in Ravalli County, Montana List of lakes in Ravalli County, Montana List of mountains in Ravalli County, Montana National Register of Historic Places listings in Ravalli County MT Officia
Idaho is a state in the northwestern region of the United States. It borders the state of Montana to the east and northeast, Wyoming to the east and Utah to the south, Washington and Oregon to the west. To the north, it shares a small portion of the Canadian border with the province of British Columbia. With a population of 1.7 million and an area of 83,569 square miles, Idaho is the 14th largest, the 12th least populous and the 7th least densely populated of the 50 U. S. states. The state's capital and largest city is Boise. Idaho prior to European settlement was inhabited by Native American peoples, some of whom still live in the area. In the early 19th century, Idaho was considered part of the Oregon Country, an area disputed between the U. S. and the United Kingdom. It became U. S. territory with the signing of the Oregon Treaty of 1846, but a separate Idaho Territory was not organized until 1863, instead being included for periods in Oregon Territory and Washington Territory. Idaho was admitted to the Union on July 3, 1890, becoming the 43rd state.
Forming part of the Pacific Northwest, Idaho is divided into several distinct geographic and climatic regions. In the state's north, the isolated Idaho Panhandle is linked with Eastern Washington, with which it shares the Pacific Time Zone – the rest of the state uses the Mountain Time Zone; the state's south includes the Snake River Plain, while the south-east incorporates part of the Great Basin. Idaho is quite mountainous, contains several stretches of the Rocky Mountains; the United States Forest Service holds about 38 % of the most of any state. Industries significant for the state economy include manufacturing, mining and tourism. A number of science and technology firms are either headquartered in Idaho or have factories there, the state contains the Idaho National Laboratory, the country's largest Department of Energy facility. Idaho's agricultural sector supplies many products, but the state is best known for its potato crop, which comprises around one-third of the nationwide yield; the official state nickname is the "Gem State".
The name's origin remains a mystery. In the early 1860s, when the United States Congress was considering organizing a new territory in the Rocky Mountains, eccentric lobbyist George M. Willing suggested the name "Idaho", which he claimed was derived from a Shoshone language term meaning "the sun comes from the mountains" or "gem of the mountains". Willing claimed he had invented the name. Congress decided to name the area Colorado Territory when it was created in February 1861. Thinking they would get a jump on the name, locals named a community in Colorado "Idaho Springs". However, the name "Idaho" did not fall into obscurity; the same year Congress created Colorado Territory, a county called Idaho County was created in eastern Washington Territory. The county was named after a steamship named Idaho, launched on the Columbia River in 1860, it is unclear after Willing's claim was revealed. Regardless, part of Washington Territory, including Idaho County, was used to create Idaho Territory in 1863.
Despite this lack of evidence for the origin of the name, many textbooks well into the 20th century repeated as fact Willing's account the name "Idaho" derived from the Shoshone term "ee-da-how". A 1956 Idaho history textbook says:"Idaho" is a Shoshoni Indian exclamation; the word consists of three parts. The first is "Ee", which in English conveys the idea of "coming down"; the second is "dah", the Shoshoni stem or root for both "sun" and "mountain". The third syllable, "how", denotes the exclamation and stands for the same thing in Shoshoni that the exclamation mark does in the English language; the Shoshoni word is "Ee-dah-how", the Indian thought thus conveyed when translated into English means, "Behold! the sun coming down the mountain. An alternative etymology attributes the name to the Plains Apache word "ídaahę́", used in reference to The Comanche. Idaho borders six U. S. states and one Canadian province. The states of Washington and Oregon are to the west and Utah are to the south, Montana and Wyoming are to the east.
Idaho shares a short border with the Canadian province of British Columbia to the north. The landscape is rugged with some of the largest unspoiled natural areas in the United States. For example, at 2.3 million acres, the Frank Church-River of No Return Wilderness Area is the largest contiguous area of protected wilderness in the continental United States. Idaho is a Rocky Mountain state with scenic areas; the state has snow-capped mountain ranges, vast lakes and steep canyons. The waters of the Snake River rush through the deepest gorge in the United States. Shoshone Falls plunges down rugged cliffs from a height greater than Niagara Falls; the major rivers in Idaho are the Snake River, the Clark Fork/Pend Oreille River, the Clearwater River, the Salmon River. Other significant rivers include the Coeur d'Alene River, the Spokane River, the Boise River, the Payette River; the Salmon River empties into the Snake in Hells Canyon and forms the southern boundary of Nez Perce County on its north shore, of which Lewiston is the county seat.
The Port of Lewiston, at the confluence of the Clearwater and the Snake Rivers is the farthest inland seaport on the West Coast at 465 river miles from the Pacific at Astoria, Oregon. Idaho's highest point is 12,662 ft, in the Lost River Range north of Mackay. Idaho's lowest poi
1968 United States presidential election in Montana
The 1968 United States presidential election in Montana took place on November 5, 1968, was part of the 1968 United States presidential election. Voters chose four representatives, or electors to the Electoral College, who voted for president and vice president. Montana voted for the Republican nominee, former Vice President Richard Nixon, over the Democratic nominee, Vice President Hubert Humphrey. Nixon won Montana by a large margin of 9.01 percent. A third-party candidate, former Alabama Governor George Wallace, won 7.29 per of the vote, not insubstantial for a third-party candidate. Wallace was most successful in the mountain regions, which have a tradition of hostility to Washington D. C. interference, to Northeastern big business. Wallace possessed little appeal in German and Scandinavian Plains regions; as of the 2016 presidential election, this remains the last occasion the Democratic presidential nominee has carried Jefferson County, where Humphrey won a 22-vote plurality
A county seat is an administrative center, seat of government, or capital city of a county or civil parish. The term is used in Canada, Romania and the United States. County towns have a similar function in the United Kingdom and Republic of Ireland, in Jamaica. In most of the United States, counties are the political subdivisions of a state; the city, town, or populated place that houses county government is known as the seat of its respective county. The county legislature, county courthouse, sheriff's department headquarters, hall of records and correctional facility are located in the county seat though some functions may be located or conducted in other parts of the county if it is geographically large. A county seat is but not always, an incorporated municipality; the exceptions include the county seats of counties that have no incorporated municipalities within their borders, such as Arlington County, Virginia. Ellicott City, the county seat of Howard County, is the largest unincorporated county seat in the United States, followed by Towson, the county seat of Baltimore County, Maryland.
Some county seats may not be incorporated in their own right, but are located within incorporated municipalities. For example, Cape May Court House, New Jersey, though unincorporated, is a section of Middle Township, an incorporated municipality. In some of the colonial states, county seats include or included "Court House" as part of their name. In the Canadian provinces of Prince Edward Island, New Brunswick, Nova Scotia, the term "shire town" is used in place of county seat. County seats in Taiwan are the administrative centers of the counties. There are 13 county seats in Taiwan, which are in the forms of county-administered city, urban township or rural township. Most counties have only one county seat. However, some counties in Alabama, Georgia, Kentucky, Mississippi, New Hampshire, New York, Vermont have two or more county seats located on opposite sides of the county. An example is Harrison County, which lists both Biloxi and Gulfport as county seats; the practice of multiple county seat towns dates from the days.
There have been few efforts to eliminate the two-seat arrangement, since a county seat is a source of pride for the towns involved. There are 36 counties with multiple county seats in 11 states: Coffee County, Alabama St. Clair County, Alabama Arkansas County, Arkansas Carroll County, Arkansas Clay County, Arkansas Craighead County, Arkansas Franklin County, Arkansas Logan County, Arkansas Mississippi County, Arkansas Prairie County, Arkansas Sebastian County, Arkansas Yell County, Arkansas Columbia County, Georgia Lee County, Iowa Campbell County, Kentucky Kenton County, Kentucky Essex County, Massachusetts Middlesex County, Massachusetts Plymouth County, Massachusetts Bolivar County, Mississippi Carroll County, Mississippi Chickasaw County, Mississippi Harrison County, Mississippi Hinds County, Mississippi Jasper County, Mississippi Jones County, Mississippi Panola County, Mississippi Tallahatchie County, Mississippi Yalobusha County, Mississippi Jackson County, Missouri Hillsborough County, New Hampshire Seneca County, New York Bennington County, Vermont In New England, the town, not the county, is the primary division of local government.
Counties in this region have served as dividing lines for the states' judicial systems. Connecticut and Rhode Island have no county level of thus no county seats. In Vermont and Maine the county seats are designated shire towns. County government consists only of a Superior Court and Sheriff, both located in the respective shire town. Bennington County has two shire towns. In Massachusetts, most government functions which would otherwise be performed by county governments in other states are performed by town or city governments; as such, Massachusetts has dissolved many of its county governments, the state government now operates the registries of deeds and sheriff's offices in those counties. In Virginia, a county seat may be an independent city surrounded by, but not part of, the county of which it is the administrative center. Two counties in South Dakota have their county seat and government services centered in a neighboring county, their county-level services are provided by Fall River Tripp County, respectively.
In Louisiana, divided into parishes rather than counties, county seats are referred to as parish seats. Alaska is divided into boroughs rather than counties; the Unorganized Borough, which covers 49 % of Alaska's area, has equivalent. The state with the most counties is Texas, with 254, the state with the fewest counties is Delaware, with 3. County seat war Administrative center County town, administrative centres in Ireland and the UK Chef-lieu, administrative centres in Algeria, Luxembourg, France and Tunisia Municipality, equivalent to county in many c
The beaver is a large nocturnal, semiaquatic rodent. Castor includes the North American beaver and Eurasian beaver. Beavers are known for building dams and lodges, they are the second-largest rodent in the world. Their colonies create one or more dams to provide still, deep water to protect against predators, to float food and building material; the North American beaver population as of 1988 was 6 -- 12 million. This population decline is the result of extensive hunting for fur, for glands used as medicine and perfume, because the beavers' harvesting of trees and flooding of waterways may interfere with other land uses. Beavers, along with pocket gophers and kangaroo rats, are castorimorph rodents, a suborder of rodents restricted to North America. Although just two related species exist today, beavers have a long fossil history in the Northern Hemisphere beginning in the Eocene, many species of giant beaver existed until quite such as Trogontherium in Europe, Castoroides in North America. Beavers are known for their natural trait of building dams on rivers and streams, building their homes in the resulting pond.
Beavers build canals to float building materials that are difficult to haul over land. They use powerful front teeth to cut trees and other plants that they use both for building and for food. In the absence of existing ponds, beavers must construct dams before building their lodges. First they place vertical poles fill between the poles with a crisscross of horizontally placed branches, they fill in the gaps between the branches with a combination of weeds and mud until the dam impounds sufficient water to surround the lodge. They are known for their alarm signal: when startled or frightened, a swimming beaver will dive while forcefully slapping the water with its broad tail, audible over great distances above and below water; this serves as a warning to beavers in the area. Once a beaver has sounded the alarm, nearby beavers may not reemerge for some time. Beavers are slow on land, but are good swimmers, can stay under water for as long as 15 minutes. Beavers do not hibernate; some of the pile is above water and accumulates snow in the winter.
This insulation of snow keeps the water from freezing in and around the food pile, providing a location where beavers can breathe when outside their lodge. Beavers have webbed hind-feet, a broad, scaly tail, they have poor eyesight, but keen senses of hearing and touch. A beaver's teeth grow continuously, their four incisors are composed of hard orange enamel on a softer dentin on the back. The chisel-like ends of incisors are maintained by their self-sharpening wear pattern; the enamel in a beaver's incisors contains iron and is more resistant to acid than enamel in the teeth of other mammals. Beavers continue to grow throughout their lives. Adult specimens weighing over 25 kg are not uncommon. Females are as large as or larger than males of the same age, uncommon among mammals. Beavers live up to 24 years of age in the wild; the English word "beaver" comes from the Old English word beofor or befer, which in turn sprang from the Proto-Germanic root *bebruz. Cognates in other Germanic languages include the Old Saxon bibar, the Old Norse bjorr, the Middle Dutch and Dutch bever, the Low German bever, the Old High German bibar and the Modern German Biber.
The Proto-Germanic word in turn came from the Proto-Indo-European word *bhebhrus, a reduplication of the PIE root *bher-, meaning "brown" or "bright", whose own descendants now include the Lithuanian bebras and the Czech bobr, as well as the Germanic forms. The North American and Eurasian beavers are the only extant members of the family Castoridae, contained in a single genus, Castor. Genetic research has shown the modern European and North American beaver populations to be distinct species and that hybridization is unlikely. Although superficially similar to each other, there are several important differences between the two species. Eurasian beavers tend to be larger, with larger, less rounded heads, narrower muzzles, thinner and lighter underfur, less oval-shaped tails and shorter shin bones, making them less capable of bipedal locomotion than the North American species. Eurasian beavers have longer nasal bones than their North American cousins, with the widest point being at the end of the snout for the former, in the middle for the latter.
The nasal opening for the Eurasian species is triangular, unlike that of the North American race, square. The foramen magnum is rounded in the Eurasian triangular in the North American; the anal glands of the Eurasian beaver are larger and thin-walled with a large internal volume compared to that of the North American species. The guard hairs of the Eurasian beaver have a longer hollow medulla at their tips. Fur colour is different. Overall, 66% of Eurasian beavers have pale brown or beige fur, 20% have reddish brown, nearly 8% are brown and only 4% have blackish coats. In North American beavers, 50% have pale brown fur, 25% are reddish brown, 20% are brown and 6% are blackish; the two species are not genetically compatible. North American beavers have 40 chromosomes, while Eurasian beavers have 48. More than 27 attempts were made in Russia to hybridize the two species, with one breeding between a male North American beaver and a female European resulting in a single stillborn kit. Thes