- published: 15 Nov 2015
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In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is a polygon that has eight sides. A regular octagon is represented by the Schläfli symbol {8}.
A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. The internal angle at each vertex of a regular octagon is 135° and the sum of all the internal angles is 1080° (as for any octagon). The area of a regular octagon of side length a is given by
In terms of R (circumradius), the area is
In terms of r (inradius), the area is
These last two coefficients bracket the value of pi, the area of the unit circle.
The area can also be derived as follows:
where S is the span of the octagon, or the second shortest diagonal; and a is the length of one of the sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside (making sure that four of the eight sides touch the four sides of the square) and then taking the corner triangles (these are 45–45–90 triangles) and placing them with right angles pointed inward, forming a square. The edges of this square are each the length of the base.
Miesha Tate (pronounced /ˈmiːʃə/; born August 18, 1986) is a professional mixed martial artist. She is the former Strikeforce Women's Bantamweight Champion and the current Freestyle Cage Fighting Women's Bantamweight Champion. She has also competed and won a silver medal in the FILA Grappling Championships.
Tate is currently the #6-ranked pound-for-pound female MMA fighter in the world by MMARising.com and the #3-ranked 135-pound female fighter according to the Unified Women's MMA Rankings.
Tate wrestled on the boys' wrestling team in high school. In 2005, she won the high school women's state championship and went on to win nationals at the World Team Trials in the 158 lb division.
While attending Central Washington University Miesha's colleague, Rosalia Watson, encouraged her to attend the mixed martial arts club with her. Soon after attending, Tate officially joined the mixed martial arts sport club at Central Washington University that was run by her current boyfriend and trainer, Bryan Caraway. She amassed a 5-1 amateur record in MMA before turning pro.
Thomas Jacob "Jack" Black (born August 28, 1969) is an American comedian, actor and musician. He makes up one half of the comedy and satirical rock duo Tenacious D. The group has three albums as well as a television series and a film. His acting career is extensive, starring primarily as bumbling, cocky, but internally self-conscious outsiders in comedy films. He was a member of the Frat Pack, a group of comedians who have appeared together in several Hollywood films, and has been nominated for a Golden Globe award. He has also won an MTV Movie Award, and a Nickelodeon Kids Choice Award as well as hosting the 2006, 2008, and 2011 Kids Choice Awards.
Black was born in Santa Monica, California, the son of two satellite engineers, Judith (née Cohen), who worked on the Hubble Space Telescope, and Thomas William Black. His mother is Jewish and his father converted to Judaism (Black attended Hebrew school). On The Tonight Show, he said his surname may have come from the occupational name Blacksmith. Black's parents divorced when he was 10; Black moved to Culver City with his father and frequently visited his mother’s home. As a child, Black appeared in a commercial for the Activision game Pitfall! in 1982, which was later shown during an appearance on Jimmy Kimmel Live and again on The Tonight Show with Conan O' Brien. When Black entered high school, his parents enrolled him at the Poseidon School, a private secondary school engineered specifically for students struggling in the traditional school system. Black also attended the Crossroads School, where he excelled in drama. He later attended UCLA but dropped out during his sophomore year to pursue a career in entertainment, at which point his father discontinued his financial support.[citation needed] Fellow UCLA alumnus Tim Robbins later cast Black in Bob Roberts. He also had recurring roles on the HBO sketch comedy series Mr. Show.
Actors: Tim Weske (miscellaneous crew), Tim Weske (miscellaneous crew), Deborah Dutch (actress), Vernon Wells (actor), Brad Mays (editor), Sophiah Koikas (actress), Sophiah Koikas (actress), Brian Danner (miscellaneous crew), Mark Bedell (actor), Mark Bedell (actor), Mark Bedell (miscellaneous crew), Kestrin Pantera (actress), Smokey Miles (actor), Jackeline Olivier (actress), Mitch Toles (producer),
Plot: Alvareen is the story of a quirky & confused young woman named Alice. Alice is trying to discover why she hears different 'voices' in her mind. Through the help of an earnest, devoted friend named Kevin, the guidance of a Tarot Reader and the manipulations of the scheming Dream Mistress, Alice finds herself in the strange & mysterious world of Castle Yesterday. At the Castle, a wicked wizard named Octagon confronts Alice. He magically splits Alice into two beings: her current self and her past self when she was a Warrior Goddess named Alvareen. Alvareen is a fierce, beautiful princess whose father, King Charles, was killed because of Octagon's quest for power. She is determined to avenge her name and is impatient with Alice's seeming weakness. She reluctantly teaches Alice fighting skills and together they battle both the Shadow Warriors and ultimately, each other. Throughout her journey, Alice meets a myriad of Pirates, Elves, Faeries, Trolls and many other magical and unusual creatures. At the end of the story, Alice must learn how to use her newfound powers wisely and to finally discover real love.
Genres: Fantasy,Actors: Jake Roberts (actor), Rob Kellum (actor), Octagon (actor), Asistencia Asesoría y Administración (director),
Genres: Sport,