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.

Sepak takraw (Sport)

Sepak takraw , or kick volleyball, is a sport native to the Malay-Thai Peninsula. Sepak takraw differs from the similar sport of volleyball in its use of a rattan ball and only allowing players to use their feet, knee, chest and head to touch the ball. It is a popular sport in Southeast Asia.

Sepak takraw

Quran (Islamic)

The Quran, also transliterated Qur'an, Koran, Al-Coran, Coran, Kuran, and Al-Qur'an, is the central religious text of Islam, which Muslims believe to be the verbatim word of God (Arabic: الله‎, Allah). It is regarded widely as the finest piece of literature in the Arabic language.

Al-Qurʾān - (القرآن)

Five Pillars of Islam (Islamic)

The Five Pillars of Islam (arkān-al-Islām أركان الإسلام; also arkān ad-dīn أركان الدين "pillars of the religion") are five basic acts in Islam, considered obligatory by believers and are the foundation of Muslim life. These are summarized in the famous hadith of Gabriel.

Islam

Islam (Islamic)

Islam (English  /ˈɪzlɑːm/; Arabic: الإسلام‎ al-ʾislām  IPA: [ʔɪsˈlæːm] is a monotheistic and Abrahamic religion articulated by the Qur'an, a text considered by its adherents to be the verbatim word of God (Arabic: الله‎ Allāh) and by the teachings and normative example (called the Sunnah and composed of Hadith) of Muhammad, considered by them to be the last prophet of God. An adherent of Islam is called a Muslim.

The Kaaba, in Mecca, Saudi Arabia, is the center of Islam. Muslims
from all over the world gather there to pray in unity.

Kung fu/Kungfu (Sport)

Kung fu/Kungfu or Gung fu/Gongfu (功夫, Pinyin: gōngfu) is a Chinese term referring to any study, learning, or practice that requires patience, energy, and time to complete, often used in the West to refer to Chinese martial arts, also known as Wushu. It is only in the late twentieth century, that this term was used in relation to Chinese Martial Arts by the Chinese community. The Oxford English Dictionary defines the term "Kung-fu" as "a primarily unarmed Chinese martial art resembling karate." This illustrates how this term has been misused in English. The origin of this misuse can be attributed to the misunderstanding or mistranslation of the term through movie subtitles or dubbing.

Chinese martial arts

Pencak Silat (Sport)

Pencak silat demonstration in Jakarta.

Pencak silat (also spelled penchak silat and pentjak silat) is an umbrella term for the indigenous martial arts created in Indonesia. The leading organization of pencak silat in Indonesia is IPSI (Ikatan Pencak Silat Indonesia, literally: Pencak Silat Association of Indonesia). The liaison body for international pencak silat is the International Pencak Silat Association or PERSILAT (Persekutuan Pencak Silat Antara Bangsa).

Portrait painting (Art)

The official Chinese court portrait painting of Empress Cao (wife of Emperor Renzong) of Song Dynasty

Portrait painting is a genre in painting, where the intent is to depict the visual appearance of the subject. Beside human beings, animals, pets and even inanimate objects can be chosen as the subject for a portrait. In addition to portrait painting, portraits can also be made in other media such as, etching, lithography, photography, even video and digital media.

Landscape painting (Art)

Themistokles von Eckenbrecher (German, 1842–1921), View of Laerdalsoren, on the Sognefjord, 1901

Hasegawa Tōhaku, Pine Trees, one of a pair of folding screens, Japan, 1593. 156.8 × 356 cm (61.73 × 140.16 in)

Landscape art is a term that covers the depiction of natural scenery such as mountains, valleys, trees, rivers, and forests, and especially art where the main subject is a wide view, with its elements arranged into a coherent composition. In other works landscape backgrounds for figures can still form an important part of the work. Sky is almost always included in the view, and weather is often an element of the composition. Detailed landscapes as a distinct subject are not found in all artistic traditions, and develop when there is already a sophisticated tradition of representing other subjects. The two main traditions spring from Western painting and Chinese art, going back well over a thousand years in both cases. Landscape photography has been very important since the 19th century, and is covered by its own article.

Persian miniature (Art)

Advice of the Ascetic (c. 1500-1550). As in Western illuminated manuscripts, exquisitely decorated borders were an integral part of the work of art.

A Persian miniature is a small painting on paper, whether a book illustration or a separate work of art intended to be kept in an album of such works called a muraqqa. The techniques are broadly comparable to the Western and Byzantine traditions of miniatures in illuminated manuscripts. Although there is an equally well-established Persian tradition of wall-painting, the survival rate and state of preservation of miniatures is better, and miniatures are much the best-known form of Persian painting in the West, and many of the most important examples are in Western, or Turkish, museums. Miniature painting became a significant Persian genre in the 13th century, receiving Chinese influence after the Mongol conquests, and the highest point in the tradition was reached in the 15th and 16th centuries. The tradition continued, under some Western influence, after this, and has many modern exponents. The Persian miniature was the dominant influence on other Islamic miniature traditions, principally the Ottoman miniature in Turkey, and the Mughal miniature in the Indian sub-continent.

History of art (Art)

Venus of Willendorf, circa 24,000–22,000 BP

Sculptures, cave paintings, rock paintings and petroglyphs from the Upper Paleolithic dating to roughly 40,000 years ago have been found, but the precise meaning of such art is often disputed because so little is known about the cultures that produced them. The oldest art objects in the world—a series of tiny, drilled snail shells about 75,000 years old—were discovered in a South African cave. Containers that may have been used to hold paints have been found dating as far back as 100,000 years.

Cave painting of a horse from the Lascaux caves, circa 16,000 BP

Sketch - drawing (Art)

Jesus and the Adulteress. A sketched figure composition by Rembrandt van Rijn

Charcoal sketch of willows by Thomas Gainsborough

A sketch (ultimately from Greek σχέδιος – schedios, "done extempore") is a rapidly executed freehand drawing that is not usually intended as a finished work. A sketch may serve a number of purposes: it might record something that the artist sees, it might record or develop an idea for later use or it might be used as a quick way of graphically demonstrating an image, idea or principle. Sketching is generally a prescribed part of the studies of art students.
The term "sketch" has most often been applied to graphic work executed in a dry media such as graphite pencil, charcoal or pastel. It may also apply to drawings executed in pen and ink, ballpoint pen, water colour and oil paint. The latter two are generally referred to as "water colour sketches" and "oil sketches". A sculptor might model three-dimensional sketches in clay or plasticine.
The term "sketchbook" refers to a book of blank paper on which an artist can, (or has already) drawn sketches. The book might be purchased bound or might comprise loose leaves of sketches assembled or bound together.
Most visual artists use, to a greater or lesser degree, the sketch as a method of recording or working out ideas. The sketchbooks of some individual artists have become very well known, including those of Leonardo da Vinci and Edgar Degas which have become art objects in their own right, with many pages showing finished studies as well as sketches.
The ability to quickly record impressions through sketching has found varied purposes in today's culture. Courtroom artists are usually sketchers. Sketches drawn to help authorities find or identify wanted people are called composite sketches. Street performers in popular tourist areas often include artists who sketch portraits within minutes.

Idioms of painting (Art)

Allegory

Allegory is a figurative mode of representation conveying meaning other than the literal. Allegory communicates its message by means of symbolic figures, actions or symbolic representation. Allegory is generally treated as a figure of rhetoric, but an allegory does not have to be expressed in language: it may be addressed to the eye, and is often found in realistic painting. An example of a simple visual allegory is the image of the grim reaper. Viewers understand that the image of the grim reaper is a symbolic representation of death.

Painting media (Art)

Honoré Daumier (1808–79), The Painter

Different types of paint are usually identified by the medium that the pigment is suspended or embedded in, which determines the general working characteristics of the paint, such as viscosity, miscibility, solubility, drying time, etc.