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N-curve
We take the functional theoretic algebra ''C'' , 1of curves. For each loop ''γ'' at 1, and each positive integer ''n'', we define a curve \gamma_n called ''n''-curve. The ''n''-curves are interesting in two ways. #Their f-products, sums and differences give rise to many beautiful curves. #Using the ''n''-curves, we can define a transformation of curves, called ''n''-curving. Multiplicative inverse of a curve A curve ''γ'' in the functional theoretic algebra ''C'' , 1 is invertible, i.e. : \gamma^ \, exists if : \gamma(0)\gamma(1) \neq 0. \, If \gamma^=(\gamma(0)+\gamma(1))e - \gamma , where e(t)=1, \forall t \in , 1/math>, then : \gamma^= \frac. The set ''G'' of invertible curves is a non-commutative group under multiplication. Also the set ''H'' of loops at 1 is an Abelian subgroup of ''G.'' If \gamma \in H, then the mapping \alpha \to \gamma^\cdot \alpha\cdot\gamma is an inner automorphism of the group ''G.'' We use these concepts to define ''n''-curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-curve
We take the functional theoretic algebra ''C'' , 1of curves. For each loop ''γ'' at 1, and each positive integer ''n'', we define a curve \gamma_n called ''n''-curve. The ''n''-curves are interesting in two ways. #Their f-products, sums and differences give rise to many beautiful curves. #Using the ''n''-curves, we can define a transformation of curves, called ''n''-curving. Multiplicative inverse of a curve A curve ''γ'' in the functional theoretic algebra ''C'' , 1 is invertible, i.e. : \gamma^ \, exists if : \gamma(0)\gamma(1) \neq 0. \, If \gamma^=(\gamma(0)+\gamma(1))e - \gamma , where e(t)=1, \forall t \in , 1/math>, then : \gamma^= \frac. The set ''G'' of invertible curves is a non-commutative group under multiplication. Also the set ''H'' of loops at 1 is an Abelian subgroup of ''G.'' If \gamma \in H, then the mapping \alpha \to \gamma^\cdot \alpha\cdot\gamma is an inner automorphism of the group ''G.'' We use these concepts to define ''n''-curves ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Theoretic Algebra
Any vector space can be made into a unital associative algebra, called functional-theoretic algebra, by defining products in terms of two linear functionals. In general, it is a non-commutative algebra. It becomes commutative when the two functionals are the same. Definition Let ''AF'' be a vector space over a field ''F'', and let ''L''1 and ''L''2 be two linear functionals on AF with the property ''L''1(''e'') = ''L''2(''e'') = 1''F'' for some ''e'' in ''AF''. We define multiplication of two elements ''x'', ''y'' in ''AF'' by : x \cdot y = L_1(x)y + L_2(y)x - L_1(x) L_2(y) e. It can be verified that the above multiplication is associative and that ''e'' is the identity of this multiplication. So, AF forms an associative algebra with unit ''e'' and is called a ''functional theoretic algebra''(FTA). Suppose the two linear functionals ''L''1 and ''L''2 are the same, say ''L.'' Then ''AF'' becomes a commutative algebra with multiplication defined by : x \cdot y = L(x)y + L( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astroid
In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle as it rolls inside a fixed circle with four times the radius. By double generation, it is also the locus of a point on a circle as it rolls inside a fixed circle with 4/3 times the radius. It can also be defined as the envelope of a line segment of fixed length that moves while keeping an end point on each of the axes. It is therefore the envelope of the moving bar in the Trammel of Archimedes. Its modern name comes from the Greek word for "star". It was proposed, originally in the form of "Astrois", by Joseph Johann von Littrow in 1838. The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle. It is nearly identical in form to the evolute of an ellipse. Equations If the radius of the fixed circle is ''a'' then the equation is given by :x^ + y^ = a^. \, This implies that an astroid is al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Circle With N-Circle
Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * ''Unit'' (album), 1997 album by the Australian band Regurgitator * The Units, a synthpunk band Television * '' The Unit'', an American television series * '' The Unit: Idol Rebooting Project'', South Korean reality TV survival show Business * Stock keeping unit, a discrete inventory management construct * Strategic business unit, a profit center which focuses on product offering and market segment * Unit of account, a monetary unit of measurement * Unit coin, a small coin or medallion (usually military), bearing an organization's insignia or emblem * Work unit, the name given to a place of employment in the People's Republic of China Science and technology Science and medicine * Unit, a vessel or section of a chemical plant * Blood unit, a meas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhodonea Curve
In mathematics, a rose or rhodonea curve is a sinusoid specified by either the cosine or sine functions with no phase angle that is plotted in polar coordinates. Rose curves or "rhodonea" were named by the Italian mathematician who studied them, Guido Grandi, between the years 1723 and 1728. General overview Specification A rose is the set of points in polar coordinates specified by the polar equation :r=a\cos(k\theta) or in Cartesian coordinates using the parametric equations :x=r\cos(\theta)=a\cos(k\theta)\cos(\theta) :y=r\sin(\theta)=a\cos(k\theta)\sin(\theta). Roses can also be specified using the sine function. Since :\sin(k \theta) = \cos\left( k \theta - \frac \right) = \cos\left( k \left( \theta-\frac \right) \right). Thus, the rose specified by \,r=a\sin(k\theta) is identical to that specified by \,r = a\cos(k\theta) rotated counter-clockwise by \pi/2k radians, which is one-quarter the period of either sinusoid. Since they are specified using the cosine or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhodonea Curve
In mathematics, a rose or rhodonea curve is a sinusoid specified by either the cosine or sine functions with no phase angle that is plotted in polar coordinates. Rose curves or "rhodonea" were named by the Italian mathematician who studied them, Guido Grandi, between the years 1723 and 1728. General overview Specification A rose is the set of points in polar coordinates specified by the polar equation :r=a\cos(k\theta) or in Cartesian coordinates using the parametric equations :x=r\cos(\theta)=a\cos(k\theta)\cos(\theta) :y=r\sin(\theta)=a\cos(k\theta)\sin(\theta). Roses can also be specified using the sine function. Since :\sin(k \theta) = \cos\left( k \theta - \frac \right) = \cos\left( k \left( \theta-\frac \right) \right). Thus, the rose specified by \,r=a\sin(k\theta) is identical to that specified by \,r = a\cos(k\theta) rotated counter-clockwise by \pi/2k radians, which is one-quarter the period of either sinusoid. Since they are specified using the cosine or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crooked Egg
Crooked may refer to: * Crooked Creek (other) * Crooked Island (other) * Crooked Lake (other) * Crooked River (other) * Crooked Harbour, Hong Kong * Crooked Forest, West Pomerania, Poland * Crooked Bridge, a railroad bridge in Saskatchewan, Canada * Crooked Media, an American left-wing political media company * The Crooked Castle, part of the Vilnius Castle Complex, Vilnius, Lithuania * ''Crooked'' (album), by Kristin Hersh * "Crocked", a 2006 film directed by Art Camacho * "Crooked", a 2008 song by Evil Nine * ''Crooked'', original title of ''Game'' (2011 film), a Hindi action thriller * " Crooked", a 2013 song by G-Dragon * ''Crooked'', a 2015 novel by Austin Grossman See also * Crooked I Dominick Antron Wickliffe (born September 23, 1976), better known by his stage names Crooked I and Kxng Crooked, (stylised as KXNG Crooked and pronounced "King Crooked") is an American rapper from Long Beach, California. He is best known as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
