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  2. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized ...

  3. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    The axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z.The geometrical definition (sometimes referred to as static) begins by defining the line of nodes (N) as the intersection of the planes xy and XY (it can also be defined as the common perpendicular to the axes z and Z and then written as the vector product N = z × Z).

  4. Algebraic structure - Wikipedia

    en.wikipedia.org/wiki/Algebraic_structure

    Given a (countable) set of variables x, y, z, etc. the term algebra is the collection of all possible terms involving m, i, e and the variables; so for example, m(i(x), m(x, m(y,e))) would be an element of the term algebra. One of the axioms defining a group is the identity m(x, i(x)) = e; another is m(x,e) = x.

  5. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1] [2] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...

  6. Boolean algebra - Wikipedia

    en.wikipedia.org/wiki/Boolean_algebra

    A law of Boolean algebra is an identity such as x ∨ (yz) = (xy) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...

  7. Consensus theorem - Wikipedia

    en.wikipedia.org/wiki/Consensus_theorem

    In Boolean algebra, the consensus theorem or rule of consensus[ 1] is the identity: The consensus or resolvent of the terms and is . It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other. If includes a term that is negated in (or vice versa), the ...

  8. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.

  9. Coordinate system - Wikipedia

    en.wikipedia.org/wiki/Coordinate_system

    Coordinate system. The spherical coordinate system is commonly used in physics. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ ( theta ), and azimuthal angle φ ( phi ). The symbol ρ ( rho) is often used instead of r.

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