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The 1 Line, formerly Central Link, is a light rail line in Seattle, Washington, United States, and part of Sound Transit's Link light rail system. It serves 23 stations in King and Snohomish counties, traveling 33 miles (53 km) between Lynnwood City Center and Angle Lake stations. The line connects Lynnwood, Mountlake Terrace, Shoreline, the University District, Downtown Seattle, the Rainier Valley, and Seattle–Tacoma International Airport. The 1 Line carried over 26 million total passengers in 2023, with an average of nearly 80,000 daily passengers on weekdays. It runs for 20 hours per day on weekdays and Saturdays, with headways as low as six minutes during peak hours, and reduced 18-hour service on Sundays and holidays.
Trains are composed of three or more cars that each can carry 194 passengers, including 74 in seats, along with wheelchairs and bicycles. Fares are paid through the regional ORCA card, paper tickets, or a mobile app. Sound Transit uses proof-of-payment to verify passenger fares, employing fare ambassadors and transit police to conduct random inspections. Until August 2024, fares were calculated based on distance traveled. All stations have ticket vending machines, public art, bicycle parking, and bus connections, while several also have park-and-ride lots.
Voters approved Central Link in a 1996 ballot measure and construction began in 2003, after the project was reorganized under a new budget and truncated route in response to higher than expected costs. The light rail line, which followed decades of failed transit plans for the Seattle region, opened on July 18, 2009, terminating at Westlake in the Downtown Seattle Transit Tunnel and Tukwila International Boulevard near Sea–Tac Airport. It was extended south to SeaTac/Airport in December 2009, north to the University of Washington in March 2016, and south to Angle Lake in September 2016. The line was temporarily renamed the Red Line until its designation was changed to the 1 Line in 2021, coinciding with an extension to Northgate.
The first cross-county extension, north to Lynnwood, opened in August 2024. A further southern extension to Federal Way is planned to open in 2026. The 2 Line, planned to connect Seattle to the Eastside suburbs, will form a multi-line network via its connection with the 1 Line in 2025. Further expansion under Sound Transit 3 will divide the current corridor between two lines, the 1 Line from Ballard to Tacoma and the 3 Line from Everett to West Seattle.
1 Wall Street (also known as the Irving Trust Company Building, the Bank of New York Building, and the BNY Mellon Building) is a 654-foot-tall (199 m) Art Deco skyscraper in the Financial District of Lower Manhattan, New York City. The building, which occupies a full city block, consists of two sections. The original 50-story building was designed by Ralph Thomas Walker of the firm Voorhees, Gmelin and Walker and constructed between 1929 and 1931 for Irving Trust, an early-20th-century American bank. A 28-story annex to the south (later expanded to 36 stories) was designed by the successor firm Voorhees, Walker, Smith, Smith & Haines and built between 1963 and 1965.
The limestone facade consists of slight inwardly-curved bays with fluting to resemble curtains. On the lower stories are narrow windows and elaborate entrances. The massing of 1 Wall Street incorporates numerous small setbacks, and there are chamfers at the corners of the original building. The top of the original building consists of a freestanding tower with fluted windowless bays. The facade of the annex is crafted in a style reminiscent of the original structure. The original building has an ornate lobby, known as the Red Room, with colored mosaics. The 10th through 45th floors were originally rented to tenants, while the other floors contained offices, lounges, and other spaces for Irving Trust.
At the time of its construction, 1 Wall Street occupied what was one of the most valuable plots in the city. The building replaced three previous structures, including the Manhattan Life Insurance Building, which was once the world's tallest building. After Irving Trust was acquired by the Bank of New York (BNY) in 1988, 1 Wall Street served as the global headquarters of BNY and its successor BNY Mellon through 2015. After the developer Harry Macklowe purchased the building, he renovated it from 2018 to 2023, converting the interior into 566 condominium apartments with some commercial space. Sales of the condo units have been sluggish for Macklowe.
The building is one of New York City's Art Deco landmarks, although architectural critics initially ignored it in favor of such buildings as the Empire State Building and the Chrysler Building. The exterior of the building's original section was designated as a city landmark in 2001, and the Red Room was similarly designated in 2024. In addition, the structure is a contributing property to the Wall Street Historic District, a National Register of Historic Places district created in 2007.
In mathematics, 1 − 2 + 3 − 4 + ··· is an infinite series whose terms are the successive positive integers, given alternating signs. Using sigma summation notation the sum of the first m terms of the series can be expressed as
$$\sum_{n=1}^{m}n(-1)^{n-1}.$$
The infinite series diverges, meaning that its sequence of partial sums, (1, −1, 2, −2, 3, ...), does not tend towards any finite limit. Nonetheless, in the mid-18th century, Leonhard Euler wrote what he admitted to be a paradoxical equation:
$$1-2+3-4+\cdots =\frac{1}{4}.$$
A rigorous explanation of this equation would not arrive until much later. Starting in 1890, Ernesto Cesàro, Émile Borel and others investigated well-defined methods to assign generalized sums to divergent series—including new interpretations of Euler's attempts. Many of these summability methods easily assign to 1 − 2 + 3 − 4 + ... a "value" of 1/4. Cesàro summation is one of the few methods that do not sum 1 − 2 + 3 − 4 + ..., so the series is an example where a slightly stronger method, such as Abel summation, is required.
The series 1 − 2 + 3 − 4 + ... is closely related to Grandi's series 1 − 1 + 1 − 1 + .... Euler treated these two as special cases of the more general sequence 1 − 2n + 3n − 4n + ..., where n = 1 and n = 0 respectively. This line of research extended his work on the Basel problem and leading towards the functional equations of what are now known as the Dirichlet eta function and the Riemann zeta function.
1080° Snowboarding is a snowboarding video game developed and published by Nintendo for the Nintendo 64 in 1998. In the game, players control one of five snowboarders from a third-person perspective, using a combination of buttons to jump and perform tricks across eight levels.
1080° was announced in November 1997 and developed over nine months. It received critical acclaim and won an Interactive Achievement Award from the Academy of Interactive Arts & Sciences. The game sold over two million units. A sequel, 1080° Avalanche, was released for the GameCube in November 2003. The game was re-released for the Wii in 2008 and for the Wii U Virtual Console in 2016. It was also re-released on the Nintendo Classics service in 2023.