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96-590: The Arbor Hill Historic District–Ten Broeck Triangle , originally the Ten Broeck Historic District , is a seven- block area located within the Arbor Hill neighborhood north of what is today downtown Albany , New York, United States. In 1979 its easternmost third, the Ten Broeck Triangle, the second oldest residential neighborhood in the city, was recognized as a historic district and listed on

192-398: A polygon ( / ˈ p ɒ l ɪ ɡ ɒ n / ) is a plane figure made up of line segments connected to form a closed polygonal chain . The segments of a closed polygonal chain are called its edges or sides . The points where two edges meet are the polygon's vertices or corners . An n -gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon

288-544: A central space that is semi-private. They may contain a mixture of uses, with commercial or retail functions on the ground floor. Perimeter blocks are a key component of many European cities and are an urban form that allows very high urban densities to be achieved without high-rise buildings. In North American English and Australian English , the word "block" is used as an informal unit of distance. For example, someone giving directions might say, "It's three blocks from here", meaning either literally three blocks distant (in

384-409: A city grid) or the equivalent of three blocks without a grid. Since there is no standard dimension for city blocks, and they are typically rectangular in shape, meaning a block and one direction is a different length than a block in another, colloquial directions involving blocks as proxies for measurements in feet or meters are obviously both imprecise and relative. Polygon In geometry ,

480-563: A committee to seek alternative uses for it. By that point the church needed extensive repairs estimated to cost at least $ 2 million. In 2000 St. Joseph's made the Historic Albany Foundation's list of "Seven to Save" in the city, and then the New York State Preservation League's similar list for the state two years later. A plan to rehabilitate it for use as a nightclub fell through, and when the building itself

576-400: A few residents and businessmen listing "Arbor Hill" as their address. During the 1830s, they built some of the first houses in the district after the mansion. A few from this period, such as 10 Ten Broeck Place and 31 Second Street, survive. Similarly, the mixed-use Greek Revival buildings around the intersection of Second and South Swan were built in the early 1840s. Intensive development of

672-494: A given perimeter, the one with the largest area is regular (and therefore cyclic). Many specialized formulas apply to the areas of regular polygons . The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p by This radius is also termed its apothem and is often represented as a . The area of a regular n -gon in terms of the radius R of its circumscribed circle can be expressed trigonometrically as: The area of

768-812: A high-crime area. He chose the design, "Mother Africa", from suggestions submitted by local youth, who also assisted on the painting. The project was cosponsored by the Ten Broeck Triangle Preservation League and the Social Capital Development Corporation. During the 2010s, St. Joseph's Academy was renovated into the Albany Barn, a 13,500-square-foot (1,250 m) space for 22 artists to live and work. In 2018 Albany mayor Kathy Sheehan and her husband bought 18 First Street for $ 77,000. "I've been talking about preserving these buildings, moving downtown," she said. "I need to walk

864-468: A later popularity with immigrants. The district occupies the southeastern portion of Albany's Arbor Hill neighborhood. Its southern corner is Sweet Pilgrim Baptist Church at the junction of Ten Broeck Street and Clinton Avenue (part of U.S. Route 9 ), a block west of the Palace Theatre and across from Albany's Family Court building. The district's boundary, at that point also the eastern boundary of

960-467: A long time after Albany was established as a city, the district remained undeveloped and outside city limits, a place where the city might expand in the future. When it was developed, after independence , this was limited. After the Erie Canal was built, the pace of development increased, requiring the removal of a cemetery. Most of the current stock of buildings date to the mid- and late 19th century when

1056-401: A regular n -gon inscribed in a unit-radius circle, with side s and interior angle α , {\displaystyle \alpha ,} can also be expressed trigonometrically as: The area of a self-intersecting polygon can be defined in two different ways, giving different answers: Using the same convention for vertex coordinates as in the previous section, the coordinates of

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1152-513: A series of cells or Superblocks, each containing a network of narrower streets.” Superblocks can also be retroactively superimposed on pre-existing grid plan by changing the traffic rules and streetscape of internal streets within the superblock, as in the case of Barcelona 's superilles ( Catalan for superblocks). Each superilla has nine city blocks, with speed limits on the internal roads slowed to 10–20 km/h (6.2–12.4 mph), through traffic disallowed, and through travel possible only on

1248-399: A simple formula for the polygon's area based on the numbers of interior and boundary grid points: the former number plus one-half the latter number, minus 1. In every polygon with perimeter p and area A , the isoperimetric inequality p 2 > 4 π A {\displaystyle p^{2}>4\pi A} holds. For any two simple polygons of equal area,

1344-471: A state of neglect and disrepair. That area also extended to St. Joseph's School, part of the church's complex. Accordingly, in 1984, the district was extended by 21 acres (8.5 ha) to its present size of 34 acres (14 ha). In addition to almost tripling its area, it more than doubled the amount of contributing properties to 220. The expanded district was renamed to reflect the area's wider scope and historic naming. St. Joseph's particularly struggled in

1440-459: Is a 2-dimensional example of the more general polytope in any number of dimensions. There are many more generalizations of polygons defined for different purposes. The word polygon derives from the Greek adjective πολύς ( polús ) 'much', 'many' and γωνία ( gōnía ) 'corner' or 'angle'. It has been suggested that γόνυ ( gónu ) 'knee' may be the origin of gon . Polygons are primarily classified by

1536-602: Is about 264 by 900 feet (80 m × 274 m). In Chicago , a typical city block is 330 by 660 feet (100 m × 200 m), meaning that 16 east-west blocks or 8 north-south blocks measure one mile, which has been adopted by other US cities. In much of the United States and Canada, the addresses follow a block and lot number system , in which each block of a street is allotted 100 building numbers. The blocks in central Melbourne, Australia , are also 330 by 660 feet (100 m × 200 m), formed by splitting

1632-464: Is an important informal unit of length equal to the distance between two streets of a street grid. In most cities of the New World that were planned rather than developing gradually over a long period of time, streets are typically laid out on a grid plan of square or rectangular city blocks. Using the perimeter block development principle, city blocks are developed so that buildings are located along

1728-439: Is commonly called the shoelace formula or surveyor's formula . The area A of a simple polygon can also be computed if the lengths of the sides, a 1 , a 2 , ..., a n and the exterior angles , θ 1 , θ 2 , ..., θ n are known, from: The formula was described by Lopshits in 1963. If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives

1824-459: Is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polygons and other self-intersecting polygons . Some sources also consider closed polygonal chains in Euclidean space to be a type of polygon (a skew polygon ), even when the chain does not lie in a single plane. A polygon

1920-451: Is large, this approaches one half. Or, each vertex inside the square mesh connects four edges (lines). The imaging system calls up the structure of polygons needed for the scene to be created from the database. This is transferred to active memory and finally, to the display system (screen, TV monitors etc.) so that the scene can be viewed. During this process, the imaging system renders polygons in correct perspective ready for transmission of

2016-429: Is one which does not intersect itself. More precisely, the only allowed intersections among the line segments that make up the polygon are the shared endpoints of consecutive segments in the polygonal chain. A simple polygon is the boundary of a region of the plane that is called a solid polygon . The interior of a solid polygon is its body , also known as a polygonal region or polygonal area . In contexts where one

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2112-401: The patroon of his family's lands to the north of the city in what was then the town of Watervliet , including the future district, began having them surveyed. As the city could now safely expand, he had streets and building lots laid out in what came to be called Colonie, largely along the lines they were actually built. He designated the land that is now the park named after his family to be

2208-526: The American Planning Association 's (APA) upstate New York chapter for excellence in implementing the plan. Four years later the national APA recognized the entirety of Arbor Hill as one of its 10 great neighborhoods in America, along with Washington, D.C. 's Adams Morgan , Savannah, Georgia 's Victorian District and Seattle 's Fremont . City block In a city with a grid system,

2304-461: The Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon. The lengths of the sides of a polygon do not in general determine its area. However, if the polygon is simple and cyclic then the sides do determine the area. Of all n -gons with given side lengths, the one with the largest area is cyclic. Of all n -gons with

2400-613: The Giant's Causeway in Northern Ireland , or at the Devil's Postpile in California . In biology , the surface of the wax honeycomb made by bees is an array of hexagons , and the sides and base of each cell are also polygons. In computer graphics , a polygon is a primitive used in modelling and rendering. They are defined in a database, containing arrays of vertices (the coordinates of

2496-633: The Lumber District , the yards down by the canal and river where they did their business. Another church, Sweet Pilgrim Baptist, was constructed in 1876 at the Clinton Avenue intersection, giving the district a distinctive southern gateway. At the north corner, the polygonal home at 105 Ten Broeck featured an iron mansard roof , a hallmark of the contemporary Second Empire style. Some of the existing houses, such as 8 Hall Place, also had mansard roofs added when they were expanded with third stories. There

2592-542: The National Register of Historic Places . Four years later, the district was increased to its current size and renamed to reflect its expansion to include some of the rest of Arbor Hill. The future district was first established by its oldest contributing property , the Ten Broeck Mansion , built at the end of the 18th century by a prominent local family. It lent its name to the Ten Broeck Triangle, established in

2688-483: The Romanesque Revival of the late 19th century. The brick rectory with stone trim built by St. Joseph's in 1892 at 12 St. Joseph's Terrace is the district's most prominent example. At 51 and 51 1 ⁄ 2 First, a pair of brick houses built in 1885, the intricate detailing includes terra cotta and stained glass windows. The Romanesque houses at 67 Ten Broeck Street and 3 and 5 St. Joseph's Terrace are clad in

2784-534: The Ten Broeck Mansion , is individually listed on the Register as well. Some others have distinctive characteristics within the district. In 2003 two planning firms hired by the city sought citizen input and created the Arbor Hill Citizen Advisory Committee, which developed a plan to improve life in Arbor Hill as a whole. Among the aspects considered was how the historic district could benefit

2880-456: The geometrical vertices , as well as other attributes of the polygon, such as color, shading and texture), connectivity information, and materials . Any surface is modelled as a tessellation called polygon mesh . If a square mesh has n + 1 points (vertices) per side, there are n squared squares in the mesh, or 2 n squared triangles since there are two triangles in a square. There are ( n + 1) / 2( n ) vertices per triangle. Where n

2976-488: The regular star pentagon is also known as the pentagram . To construct the name of a polygon with more than 20 and fewer than 100 edges, combine the prefixes as follows. The "kai" term applies to 13-gons and higher and was used by Kepler , and advocated by John H. Conway for clarity of concatenated prefix numbers in the naming of quasiregular polyhedra , though not all sources use it. Polygons have been known since ancient times. The regular polygons were known to

Arbor Hill Historic District–Ten Broeck Triangle - Misplaced Pages Continue

3072-431: The 1850s, when a third of the hundred houses in the Ten Broeck Triangle, the eastern portion of the district, were built. North Hawk and Hall streets were built almost completely during this period. The rowhouses from 2–38 First Street went up between 1854 and 1862. In 1855 St. Joseph's Church was built on Ten Broeck between First and Second to serve the growing Irish immigrant population, which generally did not live in

3168-590: The 1970s and serious, ongoing efforts at historic preservation and restoration. The settlement that became Albany was established by the Dutch in the early 17th century as Fort Orange . The development around it was known first as Wiltwyck, becoming Albany when the English assumed control of New Netherland in 1667. It formally became a city with the grant of the Dongan Charter in 1686. Then, and for many years after, it

3264-444: The 1990s the Ten Broeck Triangle had been almost completely restored and was home to a thriving community of young professionals and their families. However, the rest of the district, like the rest of Arbor Hill, had not been gentrified and continued to have the problems associated with poorer, predominantly minority urban neighborhoods. While there was tension between residents who continued to support those efforts and residents who felt

3360-483: The Albany Housing Authority a grant for a feasibility study on the former St. Joseph's School. It also reported on Historic Albany's progress in stabilizing and restoring St. Joseph's, possibly for future use as a branch library. The organization had helped the plan's cultural goals as well by organizing a walking tour of the Ten Broeck Triangle. In 2010 the city and the advisory committee shared an award from

3456-562: The Broadway portion of the Clinton Avenue Historic District follows the rear lot lines of all the houses on the east side of the street, past St. Joseph's Church and Van Rensselaer Park north to Livingston Avenue. There, the Ten Broeck Mansion , originally known as Arbor Hill, which later became the name for the district, occupies a large parcel at the intersection's southwest corner. The boundary then turns northwest along

3552-528: The Register). The Clinton Avenue Historic District on the south includes the city's densest concentration of 19th-century rowhouses , mostly brick. To the east, downhill to North Pearl Street ( New York State Route 32 ), are neighborhoods of mixed older and newer buildings and vacant lots, slowly being redeveloped, closer to the Hudson River . The district has passed through several distinct historical periods. For

3648-696: The Second Street intersection. Midway between First Street and Clinton the boundary turns southeast to follow the rear property line of the lots on First, again the boundary with the Clinton Avenue Historic District. This line becomes Ludlow Alley shortly before North Hawk Street. After a short southward jog to take in the two properties on that street north of Clinton, it returns to the alley and follows it back to Clinton at Ten Broeck. The irregular polygon within this boundary includes six large blocks covering 34 acres (14 ha). In addition to

3744-474: The Ten Broeck area began moving to the newer neighborhoods in the city's undeveloped western sections, which offered larger houses and larger lots in the newer suburban style of living. They rented the houses they left behind or sold them, with the result that many were subdivided into multiple units, making the Ten Broeck Triangle less exclusive than it had been for the previous 50 years. This increase in density

3840-501: The Ten Broeck neighborhood will greatly benefit and market values can be expected to escalate rapidly." Projects suggested specifically for the district include promoting the adaptive reuse of larger properties like St. Joseph's School, a tree-lined pathway from North Swan to the Ten Broeck Mansion, and improving the sidewalks along North Swan. The reuse of St. Joseph's Church was also considered, with low-impact uses preferred. It

3936-526: The ancient Greeks, with the pentagram , a non-convex regular polygon ( star polygon ), appearing as early as the 7th century B.C. on a krater by Aristophanes , found at Caere and now in the Capitoline Museum . The first known systematic study of non-convex polygons in general was made by Thomas Bradwardine in the 14th century. In 1952, Geoffrey Colin Shephard generalized the idea of polygons to

Arbor Hill Historic District–Ten Broeck Triangle - Misplaced Pages Continue

4032-404: The area with three auctions of foreclosed houses on Ten Broeck Street during that period. Starting prices were between $ 5–10,000; winning bidders received a $ 70,000 grant and a $ 80,000 loan at 3 percent interest. Priority went to former residents of Arbor Hill, families, and those who demonstrated an eagerness to participate in the community. All had to have a sufficient credit history to justify

4128-401: The basketball courts to the south. Mature trees are abundant throughout. Topographically the district rises almost a hundred feet (30 m) from its eastern and southern edges to level terrain along North Swan between Second and Third. This reflects the ravine there, one of the few remaining from when Albany was first settled as most were later partially filled in to facilitate development, now

4224-454: The beginning). He lived there until his death in 1810; Elizabeth survived him by three years. By that point a few other houses had likely been built nearby, but not enough to make the group a neighborhood, even after Colonie was annexed by the city in 1815. The mansion was sold to new owners who, over the next three decades, refurbished and expanded it with elements of the similar Greek Revival architectural style . The northward expansion of

4320-424: The block is the smallest group of buildings that is surrounded by streets . City blocks are the space for buildings within the street pattern of a city, and form the basic unit of a city's urban fabric. City blocks may be subdivided into any number of smaller land lots usually in private ownership, though in some cases, it may be other forms of tenure. City blocks are usually built-up to varying degrees and thus form

4416-649: The brick Federal style mansion on five acres (2 ha) that they leased from her brother, Stephen van Rensselaer III , he had served as a delegate to the Second Continental Congress in 1775, a general commanding New York's militia at the Battle of Saratoga and later Albany's mayor and a state senator . Ten Broeck named the mansion Prospect due to the commanding view it offered of the Hudson and its river traffic (some other accounts suggest he called it Arbor Hill from

4512-484: The burying ground for inhabitants of his Rensselaerwyck manor. Development was delayed because of the Revolutionary War , but by the late 18th century some houses had been built in the area. Foremost among them was what is now known as the Ten Broeck Mansion , built by another landed descendant of Dutch settlers, Abraham Ten Broeck , after his previous house burned down. By 1797, when he and his wife Elizabeth built

4608-453: The centroid of a solid simple polygon are In these formulas, the signed value of area A {\displaystyle A} must be used. For triangles ( n = 3 ), the centroids of the vertices and of the solid shape are the same, but, in general, this is not true for n > 3 . The centroid of the vertex set of a polygon with n vertices has the coordinates The idea of a polygon has been generalized in various ways. Some of

4704-409: The city envisioned by the elder van Rensselaer finally came to pass after 1825, when the Erie Canal was opened. Many new arrivals to the city, drawn by the canal and its economic opportunities, needed places to live and work. They looked north, along Broadway and North Pearl. Some found the mansion neighborhood and the blocks to its west to their liking, enough that city directories of the period show

4800-496: The city's affluent. As the 20th century began, it gradually became a more middle-class neighborhood, then, after the Great Migration , predominantly African American . As an effective racial ghetto , the neighborhood and its historic buildings suffered the effects of disinvestment and decline. The designation of the historic district, and other efforts by preservationists later in the century, have begun to reverse that trend. In

4896-466: The city. Residents of the Triangle continue to advocate for the church's restoration. Historic Albany also helped partially preserve 41 Ten Broeck Street. In 2000, after ownership had reverted to Albany County following a foreclosure for unpaid property taxes , the county began to demolish the building. A court ordered the work stopped after finding that the county had not gained the proper approvals. It

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4992-426: The complex plane, where each real dimension is accompanied by an imaginary one, to create complex polygons . Polygons appear in rock formations, most commonly as the flat facets of crystals , where the angles between the sides depend on the type of mineral from which the crystal is made. Regular hexagons can occur when the cooling of lava forms areas of tightly packed columns of basalt , which may be seen at

5088-402: The construction of two apartment buildings, at 7–8 and 9–10 St. Joseph's Terrace, in 1914. Both brick with stone trim, one three stories and the other four, they were the first buildings in the neighborhood designed as multiple dwellings. Together with the nearby house at 3 St. Joseph's, a one-story brick building with marble trim and a Spanish-style pantile roof, built that same year, they are

5184-612: The construction of what is now the State Department of Education Building in 1912 also resettled in Arbor Hill. As early as 1922 many of the city's prominent African-American institutions and organizations, such as churches and social clubs , were located in Arbor Hill. This growth led to the name being applied to the larger area it presently refers to, extending north to the railroad tracks, west to Northern Boulevard (now Henry Johnson Boulevard) and south to Sheridan Avenue. In 1948 came

5280-574: The district but near it, close to their jobs along the riverfront. It was designed by Brooklyn architect Patrick Keely , himself an Irish immigrant, who had previously designed the Cathedral of the Immaculate Conception on Eagle Street downtown. By 1870, much of the district had been developed. The lavish houses in particular that lined Ten Broeck Street gave it the nickname "Millionaire's Row." Many had been built by lumber merchants and overlooked

5376-425: The district was one of Albany's most desirable addresses. Later, as the affluent moved to the suburbs in the early 20th century, it became denser , and in the 1920s came to be identified more with the city's growing African-American population. Due to that racial stigma, the neighborhood declined in status over the course of the 20th century. That trend began to reverse with the formation of community organizations in

5472-458: The example of Philadelphia , New York City adopted the Commissioners' Plan of 1811 for a more extensive grid plan . Some variations of the interpretation of city blocks include superblocks, subblocks, and perimeter blocks. A superblock , or super-block , is an area of urban land that is bounded by arterial roads and the size of multiple typically sized city blocks. Within the superblock,

5568-540: The first suggestion that the neighborhood's future in the city lay with its own past. After a century of ownership, the descendants of James Olcott Worth formally transferred the Ten Broeck mansion from their family to the Albany County Historical Association. The ACHA began converting it into the historic house museum it is today; in 1971 it was listed on the National Register. The challenges

5664-530: The key to revitalizing the neighborhood, due to its proximity to downtown Albany and the growing service-sector jobs there. To further this goal, they worked with preservationists to have the triangle recognized as a historic district . That 13-acre (5.3 ha) area was duly listed on the Register in 1979 as the Ten Broeck Historic District. The city's urban renewal agency helped to repopulate

5760-491: The late 2010s Albany mayor Kathy Sheehan and her husband bought and rehabilitated one of the district's vacant townhouses to make their home. Over 200 buildings, mostly a mix of rowhouses and detached houses built between the 1840s and 1870s, are listed as contributing properties . The largest, the Ten Broeck Mansion, is also the only property in the district listed on the Register individually. The district also includes two churches, including St. Joseph's Church , reflecting

5856-589: The late 20th century. After being among the many historic locations in Albany used by the producers of the 1987 film Ironweed to recreate the city's appearance during the Great Depression , tight finances forced the Diocese of Albany to sell it to a congregant who in turn rented it back to them. That transaction did not prevent the church's outright closure in 1994; two years later the diocese bought it back and appointed

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5952-684: The latest-built contributing properties to the district. During the Great Migration of the 1920s, many of the African Americans who came north to Albany from the Southern states settled in Arbor Hill, an area that had been one of the first where their predecessors had settled in the city. It came to be regarded as more desirable among newcomers than their other destination, the South End . Residents of that neighborhood often moved to Arbor Hill after they had made some money. African Americans displaced by

6048-458: The loan. The AHCCA assisted the city in identifying bidders who met those qualifications. While only half the houses sold under the program were actually rehabilitated, the program was considered a success. Continuing historic surveys and inventories of the area found that the blocks between the Ten Broeck Triangle and North Swan also had many intact rowhouses from the same 19th century period with little modern intrusion, even if some of them were in

6144-457: The local road network, if any, is designed to serve only local needs. Superblocks can also contain an orthogonal internal road network, including those based on a grid plan or quasi-grid plan. That typology is prevalent in Japan and China, for example. Chen defines the supergrid and superblock urban morphology in that context as follows: “The Supergrid is a large-scale net of wide roads that defines

6240-430: The middle of the following century when successful businessmen, primarily lumber dealers, built large houses along Ten Broeck Avenue with the fortunes they had made from trade on the Erie Canal . It was one of the first neighborhoods to develop north of the city's downtown as it grew during the 19th century. Its fortunes began to slip as the city expanded westward to new neighborhoods like Washington Park which attracted

6336-549: The modern affordable housing that is there now. Similar projects targeted the blocks west of North Swan, leaving gaps and modern intrusions that also persist today. In 1975 several residents of the Ten Broeck Triangle formed the Arbor Hill Concerned Citizens Association (AHCCA) to lobby the city for improvements in neighborhood services. Many of them lived in the surviving townhouses, which they had often restored themselves. They saw gentrification as

6432-833: The more important include: The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek -derived numerical prefix with the suffix -gon , e.g. pentagon , dodecagon . The triangle , quadrilateral and nonagon are exceptions. Beyond decagons (10-sided) and dodecagons (12-sided), mathematicians generally use numerical notation, for example 17-gon and 257-gon. Exceptions exist for side counts that are easily expressed in verbal form (e.g. 20 and 30), or are used by non-mathematicians. Some special polygons also have their own names; for example

6528-494: The neighborhood faced in maintaining its historic properties were demonstrated later, in the 1960s. By that time the neighborhood, overwhelmingly African American, was considered one of the worst in Albany. Sweet Pilgrim's distinctive spire was removed, leaving St. Joseph's as the only church in the district with a presence in the city's skyline. Later in the decade, urban renewal efforts began to target Arbor Hill. The houses north of Livingston Avenue were demolished and replaced with

6624-459: The neighborhood of Sheridan Hollow , which separates Arbor Hill and the district from downtown Albany . To the north of the district are newer housing projects built during the urban renewal projects of the 1960s and 1970s. On the west of North Swan are similar neighborhoods but with newer, less coherent architecture (One building near the district, the Stephen and Harriet Myers House , is listed on

6720-412: The neighborhood regained some of its original prestige when Thomas Worth Olcott, a prominent banker, bought the Ten Broeck Mansion and formally renamed it Arbor Hill. He and his family expanded it over the next several years. The King Building, an elaborate Greek Revival duplex, was built over four years in the 1850s at 27–29 North Swan in front of the archway that provided access to the mansion's grounds on

6816-421: The neighborhood should focus on improving lower-end housing, as the 20th century ended the latter efforts became more acceptable as it was clearer that gentrification could not spread beyond the triangle. In 2002 local artist Yacob Williams painted the first of four murals in the Arbor Hill neighborhood on the house at the corner of North Swan and Livingston, a project intended to improve the quality of life in

6912-471: The neighborhood was the result of an 1845 change. The soil of the Rensselaerwyck cemetery was particularly sandy and loose. Since it sat on a slope above the streets, heavy rains would often wash away markers and expose the underlying coffins and remains. By the early 1840s, there were many calls to move the bodies elsewhere. One of the most vocal advocates for such a move, Joseph Hall, a gardener who lived on

7008-431: The neighborhood's future. The Ten Broeck Triangle, it noted, was one of three areas of Arbor Hill where property values did not suffer from the neighborhood's bad reputation. "It is not unusual to see an abandoned building next to a home in which a property owner has invested $ 300,000 or more," in the Triangle, the report said. "Clearly, to the extent that neighborhood-wide problems are alleviated or solved, property owners in

7104-461: The newer Washington Park , completed in 1882, and the lack of service from the city's new streetcar network. The neighborhood was home to Michael N. Nolan , an Irish immigrant who served as mayor and later, a member of the U.S. House of Representatives . Architecturally, the new construction largely reflected contemporary trends. There were still a few late Italianate structures like 96 North Swan Street, built in 1885. But most new housing followed

7200-552: The notation ( x n , y n ) = ( x 0 , y 0 ) will also be used. If the polygon is non-self-intersecting (that is, simple ), the signed area is or, using determinants where Q i , j {\displaystyle Q_{i,j}} is the squared distance between ( x i , y i ) {\displaystyle (x_{i},y_{i})} and ( x j , y j ) . {\displaystyle (x_{j},y_{j}).} The signed area depends on

7296-525: The number of sides. Polygons may be characterized by their convexity or type of non-convexity: The property of regularity may be defined in other ways: a polygon is regular if and only if it is both isogonal and isotoxal, or equivalently it is both cyclic and equilateral. A non-convex regular polygon is called a regular star polygon . Euclidean geometry is assumed throughout. Any polygon has as many corners as it has sides. Each corner has several angles. The two most important ones are: In this section,

7392-423: The ordering of the vertices and of the orientation of the plane. Commonly, the positive orientation is defined by the (counterclockwise) rotation that maps the positive x -axis to the positive y -axis. If the vertices are ordered counterclockwise (that is, according to positive orientation), the signed area is positive; otherwise, it is negative. In either case, the area formula is correct in absolute value . This

7488-533: The perimeter of the block, with entrances facing the street, and semi-private courtyards in the rear of the buildings. This historic arrangement reflects organic development of structures and land usage, adapted to urban planning. Since the spacing of streets in grid plans varies so widely among cities, or even within cities, it is difficult to generalize about the size of a city block. Oblong blocks range considerably in width and length. The standard block in Manhattan

7584-434: The perimeter roads. In a geoprocessing perspective there are two complementary ways of modeling city blocks: A block without sidewalks is always within a block with sidewalks . The geometric subtraction of a block without sidewalks from block with sidewalks , contains the sidewalk, the alley, and any other non-lot sub-structure. A perimeter block is a type of city block which is built up on all sides surrounding

7680-502: The physical containers or "streetwalls" of public space. Most cities are composed of a greater or lesser variety of sizes and shapes of urban block. For example, many pre-industrial cores of cities in Europe, Asia, and the Middle East tend to have irregularly shaped street patterns and urban blocks, while cities based on grids have much more regular arrangements. By extension, the word "block"

7776-426: The processed data to the display system. Although polygons are two-dimensional, through the system computer they are placed in a visual scene in the correct three-dimensional orientation. In computer graphics and computational geometry , it is often necessary to determine whether a given point P = ( x 0 , y 0 ) {\displaystyle P=(x_{0},y_{0})} lies inside

7872-423: The rear. In the blocks to the west, newer clusters such as 53, 55 and 57 First Street joined the scattered houses that already existed. At 23 and 25 Second Street, two brick houses were built in the late 1840s. These show a common architectural transition for that era, with their basic Greek Revival forms being overlaid with Italianate and Gothic Revival ornament . The Italianate style would become dominant in

7968-475: The section of Third now known as Ten Broeck Place, had Hall Street named for him when it was opened in 1849, four years after the cemetery was moved. While the former burying ground site was made into a park instead of being built on, construction on other parcels increased. The year the graves were moved, 41 Ten Broeck Street, the earliest dated house on that street after the mansion, was erected. The brick rowhouses at 15–23 and 35–39 Ten Broeck followed. In 1848,

8064-399: The south side of Livingston and follows it to North Swan Street, which it turns to follow south. A hundred feet (30 m) south of the intersection, it takes in the properties on the west side and continues to do so for the next three blocks . These include Bethany Baptist Church, St. Joseph's Youth Center and some commercial properties along the adjacent blocks and the public basketball courts at

8160-552: The square blocks in an original grid with a narrow street down the middle. Many Old World cities have grown by accretion over time rather than being planned, making rectangular city blocks uncommon in the innermost development among most European cities , for example. An exception is represented by those cities that were founded as Roman military settlements, and that often preserve the original grid layout around two main orthogonal axes (such as Turin, Italy ) and cities heavily damaged during World War II (like Frankfurt ). Following

8256-437: The streets already named, the entirety of St. Joseph's Terrace and Hall Place are within the district. It has 220 contributing resources , with only two non-contributing modern properties. One hundred of those properties are houses, primarily two- to three-story wood frame or brick structures built between the 1820s and the early 20th century. The remainder are either small commercial buildings or institutional structures such as

8352-533: The style's more common rusticated brownstone . In the new century, the neighborhood's growth slowed down as it was nearly built out. A few new houses were built, mostly architecturally sympathetic to their surroundings but experimenting slightly with their materials, such as local architect William Lee Woollett's brick houses with marble trim at 43 and 45 Ten Broeck Street in 1900. At 66 First Street another brick and stone house went up, sympathetic with its much older neighbors. The affluent families that had lived in

8448-423: The three churches in the district. Open space within the district is mostly planned, such as Van Rensselaer Park, the neighboring space around the church known as St. Joseph's park, and the large parcel at the district's northeast corner where the Ten Broeck Mansion and its gardens (and former carriage house ) are located. There are a few vacant lots and parking lots. The expansion added North Swan Street Park and

8544-417: The vertices of the polygon under consideration are taken to be ( x 0 , y 0 ) , ( x 1 , y 1 ) , … , ( x n − 1 , y n − 1 ) {\displaystyle (x_{0},y_{0}),(x_{1},y_{1}),\ldots ,(x_{n-1},y_{n-1})} in order. For convenience in some formulas,

8640-480: The walk." Restoring the house turned out to be more extensive than they expected, requiring replacing a side wall, the roof, the entire plumbing and electrical systems, and gutting the interior. "It stopped being much of a historic preservation because we couldn't preserve anything", she said. The couple moved in late in 2019. All but three of the 220 buildings in the district are contributing properties to its historic character. Almost all of those 217 are houses. One,

8736-417: Was also suggested that Ten Broeck Street itself be made more pedestrian-friendly, either with wider sidewalks, trees on the sidewalks or a tree-lined center median . Participants in the meetings rejected a proposal for a new "signature building" at North Swan and Livingston because they thought the area was dense enough already. In a 2005 progress report on the plan, the city noted that the state had awarded

8832-555: Was confined to the fort and the area around it enclosed by a stockade , corresponding roughly to its present downtown . The prominent ridge beyond Sheridan Hollow to the north was first referred to as Arbor Hill during that period. The stockade era reflected the threat that still existed to the frontier town from the French , which ended with the 1763 defeat of New France in the French and Indian War . The next year, Stephen van Rensselaer II ,

8928-421: Was enough demand for housing in the Ten Broeck Triangle that a new street was added in the ensuing decade. St. Joseph's Terrace was laid out in 1881 and formally subdivided for building ten years later. The houses built there in the 1890s were similar in form to those that had been built in the previous decades, reflecting the area's continuing status as a desirable neighborhood, despite increasing competition from

9024-750: Was eventually transferred to Historic Albany, which had brought the suit. Today only the facade remains, and Historic Albany is working to find a developer willing to restore it and rebuild the structure. The AHCCA founded a separate group called the Arbor Hill Improvement Corporation in the early 1980s to address housing issues that the private developers of the area were not. It assists residents in applying for financing and restoration grants, sometimes partnering with similar organizations in other neighborhoods in applying for grants. Another community group, St. Joseph Housing Corporation, has renovated some old buildings into affordable housing . By

9120-468: Was on the verge of collapse in the winter of 2001 the city had to shore it up and take possession under eminent domain . It was in turn deeded to Historic Albany, which was able to secure matching funds for the necessary work which continued to stage cultural events there to raise all the money for a more complete restoration . Its plans for the adaptive reuse of the building failed to meet with community approval, and in 2013 Historic Albany returned it to

9216-455: Was reflected in the most significant construction of the 20th century's first decade. St. Joseph's had housed its school in various other buildings, but finally had to construct one for the purpose. The four-story brick edifice with stone trim completed in 1905 was the largest building in the western blocks of the future district. Back on Ten Broeck Street, the church itself got a new spire in 1910. The trend toward increasing density culminated in

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