three-dimensional space curve
51Quaternions and spatial rotation — Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to… …
52Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics …
53Projective transformation — A projective transformation is a transformation used in projective geometry: it is the composition of a pair of perspective projections. It describes what happens to the perceived positions of observed objects when the point of view of the… …
54Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th …
55Homogeneous coordinate system — A homogeneous coordinate system is a coordinate system in which there is an extra dimension, used most commonly in computer science to specify whether the given coordinates represent a vector (if the last coordinate is zero) or a point (if the… …
56Real projective plane — In mathematics, the real projective plane is the space of lines in R3 passing through the origin. It is a non orientable two dimensional manifold, that is, a surface, that has basic applications to geometry, but which cannot be embedded in our… …
57Homotopy groups of spheres — In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure… …
58quadratic equation — Math. an equation containing a single variable of degree 2. Its general form is ax2 + bx + c = 0, where x is the variable and a, b, and c are constants (a non zero). [1680 90] * * * Algebraic equation of particular importance in optimization. A… …
59Poincaré conjecture — In mathematics, the Poincaré conjecture (French, pronounced|pwɛ̃kaʀe) [cite encyclopedia | encyclopedia=The American Heritage Dictionary of the English Language | title=Poincaré, Jules Henri | url=http://www.bartleby.com/61/3/P0400300.html |… …
60Planar graph — Example graphs Planar Nonplanar Butterfly graph K5 The complete graph K4 …
