A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a prolate spheroid, shaped like an American football or rugby ball. If the ellipse is rotated about its minor axis, the result is an oblate spheroid, shaped like a lentil. If the generating ellipse is a circle, the result is a sphere. Due to the combined effects of gravity and rotation, the figure of the Earth is not quite a sphere, but instead is flattened in the direction of its axis of rotation. For that reason, in cartography the Earth is approximated by an oblate spheroid instead of a sphere; the current World Geodetic System model uses a spheroid whose radius is 6,378.137 km at the Equator and 6,356.752 km at the poles. The word spheroid meant "an spherical body", admitting irregularities beyond the bi- or tri-axial ellipsoidal shape, and, how the term is used in some older papers on geodesy.
The equation of a tri-axial ellipsoid centred at the origin with semi-axes a, b and c aligned along the coordinate axes is x 2 a 2 + y 2 b 2 + z 2 c 2 = 1. The equation of a spheroid with z as the symmetry axis is given by setting a = b: x 2 + y 2 a 2 + z 2 c 2 = 1; the semi-axis a is the equatorial radius of the spheroid, c is the distance from centre to pole along the symmetry axis. There are two possible cases: c < a: oblate spheroid c > a: prolate spheroidThe case of a = c reduces to a sphere. An oblate spheroid with c < a has surface area S o b l a t e = 2 π a 2 = 2 π a 2 + π c 2 e ln where e 2 = 1 − c 2 a 2. The oblate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis a and semi-minor axis c, therefore e may be identified as the eccentricity. A prolate spheroid with c > a has surface area S p r o l a t e = 2 π a 2 where e 2 = 1 − a 2 c 2. The prolate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis c and semi-minor axis a.
These formulas are identical in the sense that the formula for Soblate can be used to calculate the surface area of a prolate spheroid and vice versa. However, e becomes imaginary and can no longer directly be identified with the eccentricity. Both of these results may be cast into many other forms using standard mathematical identities and relations between parameters of the ellipse; the volume inside a spheroid is 4 π 3 a 2 c ≈ 4.19 a 2 c. If A = 2 a is the equatorial diameter, C = 2 c is the polar diameter, the volume is π 6 A 2 C ≈ 0.523 A 2 C. If a spheroid is parameterized as σ → =.
Grzegorz Lindenberg is a Polish journalist and sociologist. He is one of the co-founders of Gazeta Wyborcza, former General Director of Agora and first editor-in-chief of Super Express, one of founders of a right-wing antiimmigration website Euroislam.pl. He was the president of two online businesses. In 1979 he obtained a degree in sociology. In 1985 he obtained a PhD Degree at the Institute of Sociology at the University of Warsaw. In the years 1985–1987 he was a researcher working at the Russian Research Center at Harvard University as part of a scholarship from the Kościuszko Foundation and a lecturer at the University of Boston. From 1996 to 2004, he was a board member of the Stefan Batory Foundation in Warsaw. Since 2001, he is an independent consultant. Lindenberg organized the social movement of the amendment to the Animal Protection Act and unsuccessfully tried to make it adopted by the Sejm. Zmiana społeczna a świadomość polityczna, Warsaw 1986 Świadomość społeczna wobec kryzysu i konfliktu społecznego, Warsaw 1987 Anna Maria Goławska, Toskania i okolice: przewodnik subiektywny, Warsaw 2006 ISBN 9788373863279 Goławska, Anna Maria, Grzegorz Lindenberg.
Włochy: podróż na południe. Warszawa: Wydawnictwo Nowy Świat, 2010. ISBN 9788373863934 Ludzkość poprawiona. Jak najbliższe lata zmienią świat w którym żyjemy, Wydawnictwo Otwarte, Warsaw 2018 ISBN 9788375155457 Grzegorz Lindenberg personal website
Verrado High School is a high school in the Verrado community of Buckeye, United States under the jurisdiction of the Agua Fria Union High School District. The school started construction in early 2005 and opened in late 2006; the school is 220,000 square feet in size, designed for an enrollment of 1,600 students. It is built for the smaller learning communities format, with five "wings", it was built in 2006 with $36 million in funding. The school is LEED Silver-certified; the Orcutt/Winslow-built structure won the Education Design Showcase 2007 Project of Distinction Award. The classrooms have only three walls, no doors; the rooms with doors and four walls have windows to be able to see into the classroom. The three wall classrooms help students focus in class as they become immune to outside noises and distractions; the open hallways and friendly students and staff reflect One Verrado. In addition and Desert Edge High School have received solar panel installations, which will be forthcoming to the other high schools in the district by September 2011.
It is estimated that some 40 percent of the entire district's energy needs will come from these solar panels upon completion. The Verrado Vipers are part of the Arizona Interscholastic Association's Div II/III. Verrado competes in all AIA-sanctioned sports save for boys' badminton. Newsweek placed the school No. 1,586 in its 2013 list of America's Best High Schools, one of America's Most Challenging High Schools by the Washington Post