One World Trade Center

One World Trade Center is the main building of the rebuilt World Trade Center complex in Lower Manhattan, New York City. One WTC is the tallest building in the United States, the tallest building in the Western Hemisphere, the seventh-tallest in the world; the supertall structure has the same name as the North Tower of the original World Trade Center, destroyed in the terrorist attacks of September 11, 2001. The new skyscraper stands on the northwest corner of the 16-acre World Trade Center site, on the site of the original 6 World Trade Center; the building is bounded by West Street to the west, Vesey Street to the north, Fulton Street to the south, Washington Street to the east. The building's architect is David Childs, whose firm Skidmore, Owings & Merrill designed the Burj Khalifa and the Willis Tower; the construction of below-ground utility relocations and foundations for the new building began on April 27, 2006. One World Trade Center became the tallest structure in New York City on April 30, 2012, when it surpassed the height of the Empire State Building.

The tower's steel structure was topped out on August 30, 2012. On May 10, 2013, the final component of the skyscraper's spire was installed, making the building, including its spire, reach a total height of 1,776 feet, its height in feet is a deliberate reference to the year when the United States Declaration of Independence was signed. The building opened on November 3, 2014. On March 26, 2009, the Port Authority of New York and New Jersey confirmed that the building would be known by its legal name of "One World Trade Center", rather than its colloquial name of "Freedom Tower"; the building is 104 standard floors high. The new World Trade Center complex will include five high-rise office buildings built along Greenwich Street, as well as the National September 11 Memorial & Museum, located just south of One World Trade Center where the original Twin Towers stood; the construction of the new building is part of an effort to memorialize and rebuild following the destruction of the original World Trade Center complex.

The construction of the World Trade Center, of which the Twin Towers were the centerpieces, was conceived as an urban renewal project and spearheaded by David Rockefeller. The project was intended to help revitalize Lower Manhattan; the project was planned by the Port Authority of New York and New Jersey, which hired architect Minoru Yamasaki. He came up with the idea of building twin towers. After extensive negotiations, the New Jersey and New York State governments, which supervise the Port Authority, consented to the construction of the World Trade Center at the Radio Row site, located in the lower-west area of Manhattan. To satisfy the New Jersey government, the Port Authority agreed to buy the bankrupt Hudson & Manhattan Railroad, which transported commuters from New Jersey to Lower Manhattan; the towers were designed as framed tube structures, giving tenants open floor plans, unobstructed by columns or walls. The framed tube design was introduced by Bangladeshi-American structural engineer Fazlur Rahman Khan in the 1960s.

The design was accomplished by using many spaced perimeter columns, providing much of the structure's strength, with the gravity load shared with the core columns. The elevator system, which made use of sky lobbies and a system of express and local elevators, allowed substantial floor space to be used for office purposes by making the structural core smaller; the design and construction of the towers involved many other innovative techniques, such as wind tunnel experiments and the slurry wall for digging the foundation. Yamasaki incorporated elements of Islamic architecture in the building's design, having designed Saudi Arabia's Dhahran International Airport with the Saudi Binladin Group. Construction of the North Tower began in August 1966; the first tenants moved into the North Tower in December 1970. In the 1970s, four other low-level buildings were built as part of the World Trade Center complex. A seventh building was built in the mid-1980s. After Seven World Trade Center was built in the 1980s, the World Trade Center complex had a total of seven buildings.

Each tower was over 1,350 feet high, occupied about 1 acre of the total 16 acres of the site's land. During a press conference in 1973, Yamasaki was asked, "Why two 110-story buildings? Why not one 220-story building?" His response was, "I didn't want to lose the human scale." When it was topped out on December 4, 1970, One World Trade Center became the tallest building in the world, surpassing the Empire State Building, which had held the record for 40 years. The North Tower was 1,368 feet tall, in 1978, a telecommunications antenna was added to the top of the roof. With the 360-foot -tall antenna, the highest point of the North Tower reached 1,728 ft. However, the tower only held its record until May 1973, when Chicago's Sears Tower, 1,450 feet tall at the rooftop, was completed. At 110 floors, the World Trade Center towers had more floors than any other building at that time; this number was not surpassed until the construction of the Burj Khalifa, which opened in 2010. Of the 110 stories, eight were s

Wrapped normal distribution

In probability theory and directional statistics, a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping" of the normal distribution around the unit circle. It finds application in the theory of Brownian motion and is a solution to the heat equation for periodic boundary conditions, it is approximated by the von Mises distribution, due to its mathematical simplicity and tractability, is the most used distribution in directional statistics. The probability density function of the wrapped normal distribution is f W N = 1 σ 2 π ∑ k = − ∞ ∞ exp ⁡, where μ and σ are the mean and standard deviation of the unwrapped distribution, respectively. Expressing the above density function in terms of the characteristic function of the normal distribution yields: f W N = 1 2 π ∑ n = − ∞ ∞ e − σ 2 n 2 / 2 + i n = 1 2 π ϑ, where ϑ is the Jacobi theta function, given by ϑ = ∑ n = − ∞ ∞ n q n 2 where w ≡ e i π θ and q ≡ e i π τ; the wrapped normal distribution may be expressed in terms of the Jacobi triple product: f W N = 1 2 π ∏ n = 1 ∞.

Where z = e i and q = e − σ 2. In terms of the circular variable z = e i θ the circular moments of the wrapped normal distribution are the characteristic function of the normal distribution evaluated at integer arguments: ⟨ z n ⟩ = ∫ Γ e i n θ f W N d θ = e i n μ − n 2 σ 2 / 2. Where Γ is some interval of length 2 π; the first moment is the average value of z known as the mean resultant, or mean resultant vector: ⟨ z ⟩ = e i μ − σ 2 / 2 The mean angle is θ μ = A r g ⟨ z ⟩ = μ {\displays

The Stoning of Saint Stephen

The Stoning of Saint Stephen is the first signed painting by Dutch artist Rembrandt, painted in 1625 at the age of 19. It is kept in the Musée des Beaux-Arts de Lyon; this work is inspired by the martyrdom of Saint Stephen, recounted in Acts 7. This young deacon in the Christian community of Jerusalem was sentenced to death by stoning; the painting was influenced by the art of Adam Elsheimer. It represents the moment when Stephen was stoned outside the city by his many tormentors, he utters his last words to Christ as the light around him shows that the heavens are open; the painting is divided into two distinct zones with a diagonal creating an effect of chiaroscuro: on the left, a man on horseback is in the shadow, on the right and his persecutors are in the light. Saul of Tarsus can be seen seated in the background holding in his lap the coats of the stoners; some inaccuracies in the drawing can be seen. The character behind Stephen seems to be a self-portrait done into a wider composition, as Spanish painter Diego Velázquez did in Las Meninas.

John Durham suggests that Rembrandt "presents himself as a somewhat alarmed presence, a participant who may be having second thoughts about what was taking place." At Musée des Beaux-Arts de Lyon