The Mathematics Portal
Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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- ... that an equivalence between algebraic and geometric definitions of constructible numbers helps prove the impossibility of squaring the circle?
- ... that museum director Alena Aladava rebuilt the Belarusian national art collection in the aftermath of the Second World War?
- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that the number of cannonballs in a square pyramid with cannonballs along each edge is ?
- ... that 100 years after Mary Emily Sinclair wrote a master's thesis in mathematics on the discriminants of quintic polynomials, Helaman Ferguson based a sculpture on her work?
- ... that mathematics professor Ari Nagel has fathered more than a hundred children?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that the 1914 Lubin vault fire in Philadelphia destroyed several thousand unique early silent films?
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- ...that there are different sizes of infinite sets in set theory? More precisely, not all infinite cardinal numbers are equal?
- ...that every natural number can be written as the sum of four squares?
- ...that the largest known prime number is nearly 25 million digits long?
- ...that the set of rational numbers is equal in size to the set of integers; that is, they can be put in one-to-one correspondence?
- ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
- ...that it is unknown whether π and e are algebraically independent?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
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The frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570 Image credit: |
Euclid's Elements (Greek: Στοιχεῖα) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Egypt during the early 3rd century BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems) and proofs thereof. Euclid's books are in the fields of Euclidean geometry, as well as the ancient Greek version of number theory. The Elements is one of the oldest extant axiomatic deductive treatments of geometry, and has proven instrumental in the development of logic and modern science.
It is considered one of the most successful textbooks ever written: the Elements was one of the very first books to go to press, and is second only to the Bible in number of editions published (well over 1000). For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students. Not until the 20th century did it cease to be considered something all educated people had read. It is still (though rarely) used as a basic introduction to geometry today. (Full article...)
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