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Candido's Identity
__notoc__ Candido's identity, named after the Italian mathematician Giacomo Candido, is an identity for real numbers. It states that for two arbitrary real numbers x and y the following equality holds:Claudi Alsina, Roger B. Nelsen: "On Candido's Identity". In: ''Mathematics Magazine'', Volume 80, no. 3 (June, 2007), pp. 226-228 :\left[x^2+y^2+(x+y)^2\right]^2=2[x^4+y^4+(x+y)^4] The identity however is not restricted to real numbers but holds in every commutative ring. Candido originally devised the identity to prove the following identity for Fibonacci numbers: Thomas Koshy: ''Fibonacci and Lucas Numbers with Applications''. Wiley, 2001, , pp. 92, 299-300 :(f_n^2+f_^2+f_^2)^2=2(f_n^4+f_^4+f_^4) Proof A straightforward algebraic proof can be attained by simply completely expanding both sides of the equation. The identity however can also be interpreted geometrically. In this case it states that the area of square with side length x^2+y^2+(x+y)^2 equals twice the sum of areas o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Candido Identity
Candido is both a given name and a surname. Notable people with the name include: Given name * Candido Amantini (1914–1992), Italian Roman Catholic priest * Candido Camero known simply as "Candido" (1921-2020), Cuban percussionist * Candido Jacuzzi (1903–1986), Italian-American inventor * Candido Portinari (1903–1962), Brazilian painter * Candido Tirona (1863–1896), Filipino Revolutionary Surname * Antonio Candido (1918–2017), writer, professor, and literary critic * Candy Candido (1913–1999), American actor and bass player * Chris Candido (1972–2005), American professional wrestler * Giacomo Candido (1871–1941), Italian mathematician * Johnny Candido (born 1982), American professional wrestler Pseudonym * Jose Martinez Ruiz (1873-1967) Spanish essayist See also * ''Candido (magazine)'' (1945–1961), Italian weekly monarchist satirical magazine, funded by Giovannino Guareschi * Cándido * Cândido {{given name, type=both ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giacomo Candido
Giacomo Candido (10 July 1871, in Guagnano – 30 December 1941, in Galatina) was an Italian mathematician and historian of mathematics. Education and career In 1897 Candido received his ''Laurea'' (teaching degree) from the University of Pisa and started to teach mathematics: first, at the Liceo of Galatina, then at the Liceo of Campobasso and from 1927 at the Liceo of Brindisi. He was an editor and contributor for the ''Periodico di Matematica per l'Insegnamento secondario'' and was one of the founders of the journal ''La Matematica elementare'' (an intermediate-level journal for teachers, engineers and students). He was an Invited Speaker of the ICM in 1928 in Bologna and in 1932 in Zürich. In 1934 he founded the Apulian branch of ''Mathesis'', an Italian association of mathematics teachers. He is also remembered for his work on the history of mathematics. Candido's identity Candido devised his eponymous identity to prove that (F_n^2 +F_^2 +F_^2 )^2= 2(F_n^4 +F_^4 +F_^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutative Ring
In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings. Definition and first examples Definition A ''ring'' is a set R equipped with two binary operations, i.e. operations combining any two elements of the ring to a third. They are called ''addition'' and ''multiplication'' and commonly denoted by "+" and "\cdot"; e.g. a+b and a \cdot b. To form a ring these two operations have to satisfy a number of properties: the ring has to be an abelian group under addition as well as a monoid under multiplication, where multiplication distributes over addition; i.e., a \cdot \left(b + c\right) = \left(a \cdot b\right) + \left(a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci numbers, commonly denoted , form a integer sequence, sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Applications of Fibonacci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Candido Identity Proof C
Candido is both a given name and a surname. Notable people with the name include: Given name * Candido Amantini (1914–1992), Italian Roman Catholic priest * Candido Camero known simply as "Candido" (1921-2020), Cuban percussionist * Candido Jacuzzi (1903–1986), Italian-American inventor * Candido Portinari (1903–1962), Brazilian painter * Candido Tirona (1863–1896), Filipino Revolutionary Surname * Antonio Candido (1918–2017), writer, professor, and literary critic * Candy Candido (1913–1999), American actor and bass player * Chris Candido (1972–2005), American professional wrestler * Giacomo Candido (1871–1941), Italian mathematician * Johnny Candido (born 1982), American professional wrestler Pseudonym * Jose Martinez Ruiz (1873-1967) Spanish essayist See also * ''Candido (magazine)'' (1945–1961), Italian weekly monarchist satirical magazine, funded by Giovannino Guareschi * Cándido * Cândido Cândido is a Portuguese masculine given name, equivale ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Identities
In mathematics, an identity is an equality relating one mathematical expression ''A'' to another mathematical expression ''B'', such that ''A'' and ''B'' (which might contain some variables) produce the same value for all values of the variables within a certain range of validity. In other words, ''A'' = ''B'' is an identity if ''A'' and ''B'' define the same functions, and an identity is an equality between functions that are differently defined. For example, (a+b)^2 = a^2 + 2ab + b^2 and \cos^2\theta + \sin^2\theta =1 are identities. Identities are sometimes indicated by the triple bar symbol instead of , the equals sign. Common identities Algebraic identities Certain identities, such as a+0=a and a+(-a)=0, form the basis of algebra, while other identities, such as (a+b)^2 = a^2 + 2ab +b^2 and a^2 - b^2 = (a+b)(a-b), can be useful in simplifying algebraic expressions and expanding them. Trigonometric identities Geometrically, trigonometri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Numbers
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book '' Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the '' Fibonacci Quarterly''. Applications of Fibonacci numbers includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
