Tangle (mathematics)

In mathematics, the word tangle usually refers to one of two related concepts:

In link theory, a tangle is an embedding of n arcs and m circles into – the difference from the previous definition is that it includes circles as well as arcs, and partitions the boundary into two (isomorphic) pieces, which is algebraically more convenient – it allows one to add tangles by stacking them, for instance.

(A quite different use of 'tangle' appears in Graph minors X. Obstructions to tree-decomposition by N. Robertson and P. D. Seymour, J. Combinatorial Theory B 59 (1991) 153--190, who used it to describe separation in graphs. This usage has been extended to matroids.)

The balance of this article discusses Conway's sense of tangles; for the link theory sense, see that article.

Two n-tangles are considered equivalent if there is an ambient isotopy of one tangle to the other keeping the boundary of the 3-ball fixed. Tangle theory can be considered analogous to knot theory except instead of closed loops we use strings whose ends are nailed down. See also braid theory.

Tangle (series 3)

The third series of Tangle, an Australian drama television series, was confirmed in December 2010, and production began in June 2011 and ended in August. Series three will contain six episodes, and is written by Fiona Seres and Tony McNamara, and directed by Emma Freeman and Michael James Rowland.

Cast

Episodes

References

Tangle (TV series)

Tangle is an Australian drama series for the Showcase subscription television channel. It focuses on the tangled lives of two generations of two families. Tangle is filmed in Melbourne and first screened on 1 October 2009. It is written by Fiona Seres, Tony McNamara and Judi McCrossin, and directed by Jessica Hobbs, Matthew Saville and Stuart McDonald. There have so far been three seasons.

Plot

Season 1

Tangle revolves around the intertwined lives of the Kovac and Williams families and their network of friends and extended family. Nat Manning (Kat Stewart) returned to her home town of Melbourne after ten years in England on the minor celebrity circuit. She created ripples and then waves in the lives of two clans already struggling under the weight of their myriad secrets. Ally (Justine Clarke) is the devoted wife of builder Vince (Ben Mendelsohn), mother of Romeo and Gigi (Lincoln Younes and Eva Lazarro), who is happy to have her sister Nat back. Politician Tim (Joel Tobeck) had an affair 15 years ago with Nat, and as a result, Nat became pregnant. Tim and his wife Christine (Catherine McClements) patched up their marriage and fought hard for custody of the child, Max (Blake Davis). Divorcee Em is having an affair with married man Vince and doctor Gabriel (Matt Day) has a secret lust for married Ally.

Flare (acrobatic move)

The flare is an acrobatic move in which the performer alternates balancing the torso between either arm while swinging the legs beneath in continuous circles. It is a fundamental b-boying power move, and in gymnastics it may be performed on a pommel horse or during the floor exercise. The move is commonly spelled flair in gymnastics and further may be called a "Thomas flair" after its originator, Kurt Thomas.

Step-by-step

The left leg begins about 10 inches behind the right (not lined up). If the breaker already has momentum, he/she quickly puts down his left hand close to the left leg facing the fingers away from the body, towards the left. Next, the left leg is swung around as hard as possible while doing a jump. The breaker is prepared to put down the right hand. All of the breaker's weight shifts to the right arm, and he/she kicks the left leg up as high as possible. The right leg swings under the left and then the left hand comes down in front, such that both hands are now in front. Arching his/her back and without touching the ground, the breaker kicks the right leg up again and swings the left leg around low for another rotation.

Landing flare

The landing flare is a maneuver or stage during the landing of an aircraft.

The flare follows the final approach phase and precedes the touchdown and roll-out phases of landing. In the flare the nose of the plane is raised, slowing the descent rate, and the proper attitude is set for touchdown. In the case of conventional landing gear-equipped aircraft the attitude is set to touch down on all three wheels simultaneously or on just the main landing gear. In the case of tricycle gear-equipped aircraft the attitude is set to touchdown on the main landing gear. In the case of monowheel gear-equipped gliders, the flare consists only of leveling the aircraft.

In parachuting, the flare is the part of the parachute landing fall preceding ground contact, and is executed about 15 feet (5 m) above ground.

During a helicopter landing, a flare is used to reduce both vertical and horizontal speed to allow a near zero-speed touchdown.

References

External links

Flare (ship)

Flare is the angle at which a ship's hull plate or planking departs from the vertical in an outward direction with increasing height. A flared hull typically has a deck area larger than its cross-sectional area at the waterline. Most vessels have some degree of flare above the waterline. Advantages of hull flare can include improvements in stability, splash and wash suppression, and dockside utility.

Tumblehome is the inverse of flare, where the hull becomes narrower with increasing height.

See also

References