Arithmetic with fractions (Mathematics)

Like whole numbers, fractions obey the commutative, associative, and distributive laws, and the rule against division by zero.

Equivalent fractions

Multiplying the numerator and denominator of a fraction by the same (non-zero) number results in a fraction that is equivalent to the original fraction. This is true because for any non-zero number , the fraction . Therefore, multiplying by is equivalent to multiplying by one, and any number multiplied by one has the same value as the original number. By way of an example, start with the fraction .

Definitions (Mathematics)

Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All are controversial.

Survey of leading definitions

Early definitions

Aristotle defined mathematics as:

The science of quantity.

In Aristotle's classification of the sciences, discrete quantities were studied by arithmetic, continuous quantities by geometry.
Auguste Comte's definition tried to explain the role of mathematics in coordinating phenomena in all other fields:

Mathematical beauty (Mathematics)

An example of "beauty in method"—a simple and elegant proof of the Pythagorean theorem.

Many mathematicians derive aesthetic pleasure from their work, and from mathematics in general. They express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. Sometimes mathematicians describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry. Bertrand Russell expressed his sense of mathematical beauty in these words:

Wushu (Sport)

The sport of wushu is both an exhibition and a full-contact sport derived from traditional Chinese martial arts. It was developed in China after 1949, in an effort to standardize the practice of traditional Chinese martial arts, although attempts to structure the various decentralized martial arts traditions date back earlier, when the Central Guoshu Institute was established at Nanking in 1928. The term wushu is Chinese for "martial arts" (武 "Wu" = military or martial, 术 "Shu" = art). In contemporary times, wushu has become an international sport through the International Wushu Federation (IWUF), which holds the World Wushu Championships every two years; the first World Championships were held in 1991 in Beijing and won by Yuan Wen Qing.

A typical wushu competition, here represented by the 10th All-China Games.

Chinese martial arts training (Sport)

Chinese martial arts training consists of the following components: basics, forms, applications and weapons; different styles place varying emphasis on each component. In addition, philosophy, ethics and even medical practice are highly regarded by most Chinese martial arts. A complete training system should also provide insight into Chinese attitudes and culture.

Depiction of fighting monks demonstrating their skills to visiting dignitaries
(early 19th-century mural in the Shaolin Monastery).

History of tennis (Sport)

Jeu de paume in Paris, France, 1622.

Most historians believe that tennis originated in France in the 12th century, but the ball was then struck with the palm of the hand. It was not until the 16th century that rackets came into use, and the game began to be called "tennis." It was popular in England and France, although the game was only played indoors where the ball could be hit off the wall. This later created much controversy between many people who thought that it was unfair for the opposing team. They claimed that the other team was able to hit the ball in a certain way for it to hit the wall and come back to them. Henry VIII of England was a big fan of this game, which historians now refer to as real tennis.

American football rules (Sport)

Game play in American football consists of a series of downs, individual plays of short duration, outside of which the ball is dead or not in play. These can be plays from scrimmage—passes, runs, punts, or field goal attempts—or free kicks such as kickoffs. Substitutions can be made between downs, which allows for a great deal of specialization as coaches choose the players best suited for each particular situation. During a play, each team should have no more than 11 players on the field, and each of them has specific tasks assigned for that specific play.

The Tennessee Titans and the Houston Texans in formation before a play.