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).