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Pigeon-hole Principle
In mathematics, the pigeonhole principle states that if items are put into containers, with , then at least one container must contain more than one item. For example, of three gloves, at least two must be right-handed or at least two must be left-handed, because there are three objects but only two categories of handedness to put them into. This seemingly obvious statement, a type of counting argument, can be used to demonstrate possibly unexpected results. For example, given that the population of London is more than one unit greater than the maximum number of hairs that can be on a human's head, the principle requires that there must be at least two people in London who have the same number of hairs on their heads. Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Drawer
A drawer ( ) is a box-shaped container inside a piece of furniture that can be pulled out horizontally to access its contents. Drawers are built into numerous types of furniture, including cabinets, chests of drawers (bureaus), desks, and the like. Construction Drawers can be built in various ways using a variety of materials, including wood, various wood composites, sheet metal, and plastic. Wooden drawers are often crafted with a seamless front face, concealing the end grain from the side panels. The corners may feature dovetail joints for added strength or aesthetic appeal, with half-blind dovetail joints commonly used at the front corners to conceal the joint. To secure the bottom piece, a groove is typically cut into the four vertical sides to hold the drawer bottom in place. Handles and locks One or two handles or drawer pulls are commonly attached to the front face of the drawer to facilitate pulling it out from its enclosure. In some cases, drawers may have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Persian Language
Persian ( ), also known by its endonym and exonym, endonym Farsi (, Fārsī ), is a Western Iranian languages, Western Iranian language belonging to the Iranian languages, Iranian branch of the Indo-Iranian languages, Indo-Iranian subdivision of the Indo-European languages. Persian is a pluricentric language predominantly spoken and used officially within Iran, Afghanistan, and Tajikistan in three mutual intelligibility, mutually intelligible standard language, standard varieties, respectively Iranian Persian (officially known as ''Persian''), Dari, Dari Persian (officially known as ''Dari'' since 1964), and Tajik language, Tajiki Persian (officially known as ''Tajik'' since 1999).Siddikzoda, S. "Tajik Language: Farsi or not Farsi?" in ''Media Insight Central Asia #27'', August 2002. It is also spoken natively in the Tajik variety by a significant population within Uzbekistan, as well as within other regions with a Persianate society, Persianate history in the cultural sphere o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Japanese Language
is the principal language of the Japonic languages, Japonic language family spoken by the Japanese people. It has around 123 million speakers, primarily in Japan, the only country where it is the national language, and within the Japanese diaspora worldwide. The Japonic family also includes the Ryukyuan languages and the variously classified Hachijō language. There have been many Classification of the Japonic languages, attempts to group the Japonic languages with other families such as Ainu languages, Ainu, Austronesian languages, Austronesian, Koreanic languages, Koreanic, and the now discredited Altaic languages, Altaic, but none of these proposals have gained any widespread acceptance. Little is known of the language's prehistory, or when it first appeared in Japan. Chinese documents from the 3rd century AD recorded a few Japanese words, but substantial Old Japanese texts did not appear until the 8th century. From the Heian period (794–1185), extensive waves of Sino-Ja ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Italian Language
Italian (, , or , ) is a Romance language of the Indo-European language family. It evolved from the colloquial Latin of the Roman Empire. Italian is the least divergent language from Latin, together with Sardinian language, Sardinian. It is spoken by about 68 million people, including 64 million native speakers as of 2024. Italian is an official language in Languages of Italy, Italy, Languages of San Marino, San Marino, Languages of Switzerland, Switzerland (Ticino and the Grisons), and Languages of Vatican City, Vatican City; it has official Minority language, minority status in Minority languages of Croatia, Croatia, Slovene Istria, Romania, Bosnia and Herzegovina, and the municipalities of Santa Teresa, Espírito Santo, Santa Tereza, Encantado, Rio Grande do Sul, Encantado, and Venda Nova do Imigrante in Languages of Brazil#Language co-officialization, Brazil. Italian is also spoken by large Italian diaspora, immigrant and expatriate communities in the Americas and Austral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hungarian Language
Hungarian, or Magyar (, ), is an Ugric language of the Uralic language family spoken in Hungary and parts of several neighboring countries. It is the official language of Hungary and one of the 24 official languages of the European Union. Outside Hungary, it is also spoken by Hungarians, Hungarian communities in southern Slovakia, western Ukraine (Zakarpattia Oblast, Transcarpathia), central and western Romania (Transylvania), northern Serbia (Vojvodina), northern Croatia, northeastern Slovenia (Prekmurje), and eastern Austria (Burgenland). It is also spoken by Hungarian diaspora communities worldwide, especially in North America (particularly the Hungarian Americans, United States and Canada) and Israel. With 14 million speakers, it is the Uralic family's most widely spoken language. Classification Hungarian is a member of the Uralic language family. Linguistic connections between Hungarian and other Uralic languages were noticed in the 1670s, and the family's existenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dutch Language
Dutch ( ) is a West Germanic languages, West Germanic language of the Indo-European language family, spoken by about 25 million people as a first language and 5 million as a second language and is the List of languages by total number of speakers, third most spoken Germanic language. In Europe, Dutch is the native language of most of the population of the Netherlands and Flanders (which includes 60% of the population of Belgium). "1% of the EU population claims to speak Dutch well enough in order to have a conversation." (page 153). Dutch was one of the official languages of South Africa until 1925, when it was replaced by Afrikaans, a separate but partially Mutual intelligibility, mutually intelligible daughter language of Dutch. Afrikaans, depending on the definition used, may be considered a sister language, spoken, to some degree, by at least 16 million people, mainly in South Africa and Namibia, and evolving from Cape Dutch dialects. In South America, Dutch is the native l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Danish Language
Danish (, ; , ) is a North Germanic languages, North Germanic language from the Indo-European languages, Indo-European language family spoken by about six million people, principally in and around Denmark. Communities of Danish speakers are also found in Greenland, the Faroe Islands, and the northern Germany, German region of Southern Schleswig, where it has minority language status. Minor Danish-speaking communities are also found in Norway, Sweden, the United States, Canada, Brazil, and Argentina. Along with the other North Germanic languages, Danish is a descendant of Old Norse, the common language of the Germanic peoples who lived in Scandinavia during the Viking Age, Viking Era. Danish, together with Swedish, derives from the ''East Norse'' dialect group, while the Middle Norwegian language (before the influence of Danish) and Bokmål, Norwegian Bokmål are classified as ''West Norse'' along with Faroese language, Faroese and Icelandic language, Icelandic. A more recent c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chinese Language
Chinese ( or ) is a group of languages spoken natively by the ethnic Han Chinese majority and List of ethnic groups in China, many minority ethnic groups in China, as well as by various communities of the Chinese diaspora. Approximately 1.39 billion people, or 17% of the global population, speak a variety of Chinese as their first language. Chinese languages form the Sinitic languages, Sinitic branch of the Sino-Tibetan language family. The spoken varieties of Chinese are usually considered by native speakers to be dialects of a single language. However, their lack of mutual intelligibility means they are sometimes considered to be separate languages in a Language family, family. Investigation of the historical relationships among the varieties of Chinese is ongoing. Currently, most classifications posit 7 to 13 main regional groups based on phonetic developments from Middle Chinese, of which the most spoken by far is Mandarin Chinese, Mandarin with 66%, or around 800&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bulgarian Language
Bulgarian (; , ) is an Eastern South Slavic, Eastern South Slavic language spoken in Southeast Europe, primarily in Bulgaria. It is the language of the Bulgarians. Along with the closely related Macedonian language (collectively forming the East South Slavic languages), it is a member of the Balkan sprachbund and South Slavic languages, South Slavic dialect continuum of the Indo-European language family. The two languages have several characteristics that set them apart from all other Slavic languages, including the elimination of grammatical case, case declension, the development of a suffixed definite article, and the lack of a verb infinitive. They retain and have further developed the Proto-Slavic language, Proto-Slavic verb system (albeit analytically). One such major development is the innovation of evidentiality, evidential verb forms to encode for the source of information: witnessed, inferred, or reported. It is the official Languages of Bulgaria, language of Bulgar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Arabic Language
Arabic (, , or , ) is a Central Semitic languages, Central Semitic language of the Afroasiatic languages, Afroasiatic language family spoken primarily in the Arab world. The International Organization for Standardization (ISO) assigns language codes to 32 varieties of Arabic, including its standard form of Literary Arabic, known as Modern Standard Arabic, which is derived from Classical Arabic. This distinction exists primarily among Western linguists; Arabic speakers themselves generally do not distinguish between Modern Standard Arabic and Classical Arabic, but rather refer to both as ( "the eloquent Arabic") or simply ' (). Arabic is the List of languages by the number of countries in which they are recognized as an official language, third most widespread official language after English and French, one of six official languages of the United Nations, and the Sacred language, liturgical language of Islam. Arabic is widely taught in schools and universities around the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
French Language
French ( or ) is a Romance languages, Romance language of the Indo-European languages, Indo-European family. Like all other Romance languages, it descended from the Vulgar Latin of the Roman Empire. French evolved from Northern Old Gallo-Romance, a descendant of the Latin spoken in Northern Gaul. Its closest relatives are the other langues d'oïl—languages historically spoken in northern France and in southern Belgium, which French (Francien language, Francien) largely supplanted. It was also substratum (linguistics), influenced by native Celtic languages of Northern Roman Gaul and by the Germanic languages, Germanic Frankish language of the post-Roman Franks, Frankish invaders. As a result of French and Belgian colonialism from the 16th century onward, it was introduced to new territories in the Americas, Africa, and Asia, and numerous French-based creole languages, most notably Haitian Creole, were established. A French-speaking person or nation may be referred to as Fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
