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  2. How to Solve It - Wikipedia

    en.wikipedia.org/wiki/How_to_Solve_It

    How to Solve It suggests the following steps when solving a mathematical problem: . First, you have to understand the problem. [2]After understanding, make a plan. [3]Carry out the plan.

  3. Sextic equation - Wikipedia

    en.wikipedia.org/wiki/Sextic_equation

    Watt's curve, which arose in the context of early work on the steam engine, is a sextic in two variables.. One method of solving the cubic equation involves transforming variables to obtain a sextic equation having terms only of degrees 6, 3, and 0, which can be solved as a quadratic equation in the cube of the variable.

  4. Basel problem - Wikipedia

    en.wikipedia.org/wiki/Basel_problem

    The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]

  5. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    One particular solution is x = 0, y = 0, z = 0. Two other solutions are x = 3, y = 6, z = 1, and x = 8, y = 9, z = 2. There is a unique plane in three-dimensional space which passes through the three points with these coordinates, and this plane is the set of all points whose coordinates are solutions of the equation.

  6. Horner's method - Wikipedia

    en.wikipedia.org/wiki/Horner's_method

    Horner's method can be used to convert between different positional numeral systems – in which case x is the base of the number system, and the a i coefficients are the digits of the base-x representation of a given number – and can also be used if x is a matrix, in which case the gain in computational efficiency is even greater.

  7. Transcendental equation - Wikipedia

    en.wikipedia.org/wiki/Transcendental_equation

    Graphical solution of sin(x)=ln(x) Approximate numerical solutions to transcendental equations can be found using numerical, analytical approximations, or graphical methods. Numerical methods for solving arbitrary equations are called root-finding algorithms. In some cases, the equation can be well approximated using Taylor series near the zero.

  8. Birch and Swinnerton-Dyer conjecture - Wikipedia

    en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer...

    This statement, due to Tunnell's theorem (Tunnell 1983), is related to the fact that n is a congruent number if and only if the elliptic curve y 2 = x 3 − n 2 x has a rational point of infinite order (thus, under the Birch and Swinnerton-Dyer conjecture, its L-function has a zero at 1). The interest in this statement is that the condition is ...

  9. Binomial approximation - Wikipedia

    en.wikipedia.org/wiki/Binomial_approximation

    The binomial approximation for the square root, + + /, can be applied for the following expression, + where and are real but .. The mathematical form for the binomial approximation can be recovered by factoring out the large term and recalling that a square root is the same as a power of one half.

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