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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.

1271 Avenue of the Americas (formerly known as the Time & Life Building) is a 48-story skyscraper on Sixth Avenue (Avenue of the Americas), between 50th and 51st streets, in the Midtown Manhattan neighborhood of New York City. Designed by architect Wallace Harrison of Harrison, Abramovitz, and Harris, the building was developed between 1956 and 1960 as part of Rockefeller Center. The building's eight-story base partially wraps around its 48-story main tower. Both sections are surrounded by a plaza, which has white-and-gray pavement in a serpentine pattern, as well as water fountains. The facade consists of glass panels between limestone columns. The lobby contains serpentine floors, white-marble and stainless-steel walls, and reddish-burgundy glass ceilings, in addition to artwork by Josef Albers, Fritz Glarner, and Francis Brennan. The ground floor also includes storefronts and originally housed La Fonda del Sol, a Latin American–themed restaurant. Each of the upper floors covers 28,000 square feet (2,600 m2), with the offices arranged around the core. The 48th floor originally contained the Hemisphere Club, which operated as a members-only restaurant during the day and was open to the public during evenings. After the media firm Time Inc. expressed its intention to move from 1 Rockefeller Plaza in the 1950s, Rockefeller Center's owners proposed a skyscraper at 1271 Avenue of the Americas to accommodate the move. Construction started in May 1957; the building was topped out during November 1958, and occupants began moving into their offices in late 1959. The New York City Landmarks Preservation Commission designated the lobby as a city landmark in 2002. Time Inc. vacated 1271 Avenue of the Americas in 2015, and the building was subsequently renovated between 2015 and 2019.

The 13th Airborne Division was an airborne forces formation of division-size of the United States Army that was active during World War II. The division was commanded for most of its existence by Major General Elbridge G. Chapman. It was officially activated in the United States in August 1943 at Fort Bragg in North Carolina, remaining active until February 1946, however it never saw combat. After activation the division remained in the United States to complete its training. This training was completed by September 1944, but had to be extended by a further four months when the division provided replacements for the 82nd and 101st Airborne Divisions. The division also encountered delays in mounting large-scale training exercises due to a lack of transport aircraft in the United States. This shortage was caused by the 82nd and 101st Airborne Divisions taking priority over the 13th in terms of equipment due to the two divisions serving in combat in Europe. As a consequence of these delays the division was not fully trained and combat-ready until January 1945, and was transferred to France and the European Theater of Operations in February. When the division arrived in France, it came under the command of the First Allied Airborne Army, which controlled all Allied airborne formations. The division, along with two others, was selected to participate in Operation Varsity, the airborne operation to support the Anglo-Canadian 21st Army Group crossing the River Rhine, but was removed from the operation due to there being insufficient transport aircraft to carry all three divisions into combat. Several other operations were planned for the division after the end of Operation Varsity, but these operations were cancelled when their objectives were captured by the rapid advance of Allied ground forces and they became superfluous. After the end of the conflict in Europe, the 13th Airborne was shipped to the United States to stage there before it was to participate in the planned invasion of Japan, but the conflict in the Far East ended before it was required and it remained in the United States. The 13th Airborne Division was finally inactivated on 26 February 1946 and its combat personnel were transferred to the command of the 82nd Airborne Division.

The 13th Missouri Cavalry Regiment was a cavalry unit that served in the Confederate States Army during the American Civil War. In early April 1863, Captain Robert C. Wood, aide-de-camp to Confederate Major General Sterling Price, was detached to form an artillery unit from some of the men of Price's escort. Wood continued recruiting for the unit, which was armed with four Williams guns, and grew to 275 men by the end of September. The next month, the unit fought in the Battle of Pine Bluff, driving back Union Army troops into a barricaded defensive position, from which the Union soldiers could not be dislodged. By November, the unit, which was known as Wood's Missouri Cavalry Battalion, had grown to 400 men but no longer had the Williams guns. In April 1864, Wood's battalion, which was also known as the 14th Missouri Cavalry Battalion, played a minor role in the defeat of a Union foraging party in the Battle of Poison Spring, before spending the summer of 1864 at Princeton, Arkansas. In September, the unit joined Price's Raid into the state of Missouri, but their assault during the Battle of Pilot Knob failed to capture Fort Davidson. Wood's battalion fought at the Battle of Little Blue River on October 21 after having participated in some further fighting and operationed against railroads. Two days later, Price's army was defeated at the Battle of Westport, and began retreating through the state of Kansas. During the retreat, on October 25, Wood's battalion was part of the Confederate line when it was shattered at the Battle of Mine Creek. During that action, the unit suffered 72 casualties, 50 of them as prisoners of war and the rest as killed and wounded. It then accompanied Price's army to Laynesport, Arkansas, via the Indian Territory and Texas. At an unknown date, it was enlarged to regimental strength and renamed the 13th Missouri Cavalry Regiment. After Price's Raid, the unit spent the rest of the war serving outpost duty in Arkansas. The Confederate commander of the Trans-Mississippi Department surrendered on June 2, 1865, and the men of the 13th Missouri Cavalry Regiment were paroled six days later. Around 670 men served in the unit over the course of its existence, at least 67 of whom died during that time.

The 13th Waffen Mountain Division of the SS Handschar (1st Croatian) was a mountain infantry division of the Waffen-SS, an armed branch of the German Nazi Party that served alongside but was never formally part of the Wehrmacht during World War II. At the post-war Nuremberg trials, the Waffen-SS was declared to be a criminal organisation due to its major involvement in war crimes and crimes against humanity. From March to December 1944, the division fought a counter-insurgency campaign against communist-led Yugoslav Partisan resistance forces in the Independent State of Croatia, a fascist puppet state of Germany that encompassed almost all of modern-day Croatia, all of modern-day Bosnia and Herzegovina, and parts of Serbia. The division was named Handschar (Serbo-Croatian: Handžar), after a local fighting knife or scimitar carried by Ottoman policemen during the centuries that the region was part of the Ottoman Empire. It was the first non-Germanic Waffen-SS division, and its formation marked the expansion of the Waffen-SS into a multi-ethnic military force. Composed mainly of Bosnian Muslims with some Catholic Croats, and mostly German and Yugoslav Volksdeutsche officers and non-commissioned officers, the members of the division took an oath of allegiance to the German Führer Adolf Hitler and the Croatian Poglavnik Ante Pavelić. The division fought briefly in the Syrmia region north of the Sava river before crossing into northeastern Bosnia. After crossing the Sava, it established a designated "security zone" in northeastern Bosnia between the Sava, Bosna, Drina, and Spreča rivers. It also fought outside the security zone on several occasions, and earned a reputation for brutality and savagery, not only during combat operations but also for atrocities committed against Serb and Jewish civilians. In late 1944, parts of the division were transferred briefly to the Zagreb area, and non-German members began to desert in large numbers. Over the winter of 1944–45, the unit was sent to the Baranja region, where it fought against the Red Army and Bulgarians throughout southern Hungary, falling back via a series of defensive lines until they were inside the Reich frontier. Most of the remaining Bosnian Muslims left at this point and attempted to return to Bosnia. The rest retreated further west, hoping to surrender to the Western Allies. Most of the remaining members became prisoners of the British Army. Subsequently, 38 officers were extradited to Yugoslavia to face criminal charges, and ten were executed. Hundreds of former members of the division fought in the 1947–48 civil war in Mandatory Palestine and the 1948 Arab–Israeli War.

The 15th Tank Corps (Russian: 15-й танковый корпус, 15-y tankoviy korpus) was a tank corps of the Soviet Union's Red Army. It formed in 1938 from a mechanized corps and fought in the Soviet invasion of Poland, during which it participated in the capture of the Grodno and Augustów Forest from Poland. The corps was disbanded in January 1940 at Vilnius and Šalčininkai in Lithuania. In 1942, the corps was reformed under the command of Major General Vasily Koptsov and became part of the 3rd Tank Army. It first saw combat in the unsuccessful Kozelsk Offensive of late August and early September, a relatively small operation to encircle a German salient, which resulted in the corps taking heavy losses in proportion to the territory gained. After spending the rest of the year in reserve, receiving new supplies and equipment, the corps was transferred to the southern front in southwestern Russia to fight in the Ostrogozhsk–Rossosh Offensive during January 1943, in which it played a major role by forming part of the forces that encircled thousands of Axis troops on the middle reaches of the Don River. In February 1943, the unit fought in Operation Star, achieving its objective of recapturing the key city of Kharkov in eastern Ukraine. As the Soviet advance outran its supply lines, the corps was slowly worn down and was virtually destroyed after being surrounded by a German counteroffensive in the Third Battle of Kharkov during late February and early March. Koptsov was among those killed in the fighting. The corps was rebuilt in the following months and became part of the newly created 3rd Guards Tank Army, fighting in Operation Kutuzov, the Soviet counteroffensive during the Battle of Kursk, in late July. For its actions in the offensive, the corps was converted into the 7th Guards Tank Corps.

In a campaign that took place from August to December 1678 in Kediri (in modern-day East Java, Indonesia) during the Trunajaya rebellion, the forces of the Mataram Sultanate, led by Amangkurat II, and of the Dutch East India Company (VOC), led by Anthonio Hurdt, marched inland into eastern Java against Trunajaya's forces. After a series of marches beset by logistical difficulties and harassment by Trunajaya's forces, the Mataram–VOC army crossed the Brantas River on the night of 16–17 November. They then marched on Trunajaya's capital and stronghold at Kediri and took it by direct assault on 25 November. Kediri was plundered by the Dutch and Javanese victors, and the Mataram treasury—captured by Trunajaya after his victory at Plered—was completely lost in the looting. Trunajaya himself fled Kediri and continued his greatly weakened rebellion until his capture at the end of 1679. During the march to Kediri, the Mataram–VOC army purposefully split itself into three columns which took different, indirect routes to Kediri, as suggested by Amangkurat. This enabled the army to meet more factions and to win over those with wavering allegiance, swelling its forces. The army marched through areas previously unexplored by the Dutch. The Dutch account was recorded in a journal by Hurdt's secretary Johan Jurgen Briel. Accounts of the campaign also appear in the Javanese chronicles, known as babads.