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In mathematics, a Carlyle circle is a certain circle in a coordinate plane associated with a quadratic equation; it is named after Thomas Carlyle.The circle has the property that the solutions of the quadratic equation are the horizontal coordinates of the intersections of the circle with the horizontal axis.
[a] The constant satisfies the quadratic equation = + and is an irrational number with a value of [1] φ = 1 + 5 2 = {\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}=} 1.618 033 988 749 .... The golden ratio was called the extreme and mean ratio by Euclid , [ 2 ] and the divine proportion by Luca Pacioli , [ 3 ] and also goes by several other ...
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. [ 1 ]
Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, Al-Jabr. [40]
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
This quadratic equation has two solutions: = and = But if 0 {\displaystyle 0} is substituted for x {\displaystyle x} in the original equation, the result is the invalid equation 2 = 0 {\displaystyle 2=0} .
The equation = + (+) = is of the form + + =, and such an equation can be transformed into an equation solvable by the function (see an example of such a transformation here). Some algebra shows that the total time of flight, in closed form, is given as [ 7 ]
In mathematics, a spline is a ... while the polynomial piece 2t is not quadratic, the result is still called a quadratic spline. This demonstrates that the degree of ...