Slam-dunk

In mathematics, particularly low-dimensional topology, the slam-dunk is a particular modification of a given surgery diagram in the 3-sphere for a 3-manifold. The name, but not the move, is due to Tim Cochran. Let K be a component of the link in the diagram and J be a component that circles K as a meridian. Suppose K has integer coefficient n and J has coefficient a rational number r. Then we can obtain a new diagram by deleting J and changing the coefficient of K to n-1/r. This is the slam-dunk.

The name of the move is suggested by the proof that these diagrams give the same 3-manifold. First, do the surgery on K, replacing a tubular neighborhood of K by another solid torus T according to the surgery coefficient n. Since J is a meridian, it can be pushed, or "slam dunked", into T. Since n is an integer, J intersects the meridian of T once, and so J must be isotopic to a longitude of T. Thus when we now do surgery on J, we can think of it as replacing T by another solid torus. This replacement, as shown by a simple calculation, is given by coefficient n - 1/r.

Slam dunk

A slam dunk, also dunk or dunk shot, is a type of basketball shot that is performed when a player jumps in the air, controls the ball(s) above the horizontal plane of the rim, and scores by putting the ball directly through the basket with one or both hands. This is considered a normal field goal attempt; if successful it is worth two points. Such a shot was known as a "dunk shot" until the term "slam dunk" was coined by former Los Angeles Lakers announcer Chick Hearn.

The slam dunk is the most efficient basketball shot. Moreover, it is a crowd-pleaser. Thus, the maneuver is often extracted from the basketball game and showcased in slam dunk contests. Perhaps the most popular is the NBA Slam Dunk Contest held during the annual NBA All-Star Weekend. The seminal incarnation of the NBA Slam Dunk Contest was held during the half-time of the 1976 American Basketball Association All-Star Game.

Dunking was banned in the NCAA from 1967 to 1976. Many people have attributed this to the dominance of the then-college phenomenon Lew Alcindor (now known as Kareem Abdul-Jabbar); the no-dunking rule is sometimes referred to as the "Lew Alcindor rule."

Slam Dunk (manga)

Slam Dunk (Japanese: スラムダンク, Hepburn: Suramu Danku) is a sports-themed manga series written and illustrated by Takehiko Inoue about a basketball team from Shōhoku High School. It was serialized in Weekly Shōnen Jump from 1990 to 1996, with the chapters collected into 31 tankōbon volumes by Shueisha. It was adapted into an anime series by Toei Animation which has been broadcast worldwide, enjoying much popularity particularly in Japan, several other Asian countries and Europe. As of 2012, Slam Dunk had sold 120 million copies in Japan alone, making it one of the best-selling manga series in history. Inoue later used basketball as a central theme in two subsequent manga titles: Buzzer Beater and Real. In 2010, Inoue received special commendations from the Japan Basketball Association for helping popularize basketball in Japan.

Plot

Hanamichi Sakuragi is a delinquent and the leader of a gang. Sakuragi is very unpopular with girls, having been rejected an astonishing fifty times. In his first year at Shohoku High School, he meets Haruko Akagi, the girl of his dreams, and is overjoyed when she is not repulsed or scared of him like all the other girls he has asked out.