What is a Manifold?
The branch of science is concerned with control systems,
especially about the comparisons between those of machines and those
of man and other animals. In a series of operations, information gained at one
stage can be used to modify later performances of that operation. This is known as
feedback and enables a control system to check and possibly adjust its actions
when required.
What is a cyclic polygon?
A cyclic polygon is a
polygon with all its vertices on the circumference of a circle. All triangles
are cyclic, squares and rectangles are cyclic quadrilaterals, and all regular
polygons are cyclic.
What is the Impossibility Theorem?
Any theorem asserting the impossibility of some much sought-after is often intuitively plausible.
What is Locus?
The path is traced out by a point constrained to move by given conditions. The locus may be a point, line, curve, plane, surface, or solid. For example, the locus of a point that moves in such a
way that its distance from a fixed point is always equal to its distance from a
fixed straight line is a parabola.
What is a Manifold?
Manifold is a class with subclasses. For example, a plane is a two-dimensional manifold of points as each point is specified by two
coordinates, the abscissa and the ordinate. Similarly, Euclidean space is a
three-dimensional manifold of points.
What is Meridian?
Meridian is a great circle passing through the north and
south poles. A local meridian of a point on the earth’s surface is the great circle
passing through the north and south poles and that point.
What is Orthocenter?
An orthocenter is a point that is the common point of
intersection of the three altitudes of a triangle. The altitudes of a triangle are
the lines from each vertex drawn perpendicular to the opposite sides. The triangle
formed by joining the feet of the altitudes is called a peal triangle.
What is Osborne’s rule?
The rule that states that trigonometric identities can be
transformed into the corresponding identities for hyperbolic functions by
multiplying out fully, replacing all trigonometric functions with their
hyperbolic analogues, and then changing the signs of any terms involving the
product of two signs, for instance,
Cos (x-y) = cos x cos y + sin x + sin y
Osborne’s rule permits
us to infer
Cosh(x-y) = cosh x cosh y – sinh x sinh y
What is Perimeter?
Perimeter is the length of a plane figure around its edge. For
example, the perimeter of a square is four times the length of its side. The length of
a closed curve is its perimeter, so that the perimeter of a circle is its
circumference.
What is the Pivotal Function?
A function of data, derived from an experiment and the parameter
of interest, is regarded as a random variable with probability distribution independent
of any unknown parameter.
What is Platonism?
The philosophical theory that mathematical objects exist in
advance of and independently of our knowledge of them and of any physical
instantiation of them, and therefore that mathematical truth does not consist
in, but is the aim of the construction of proofs.
What is a Polyhedron?
A polyhedron is a solid figure bounded by several faces
each of which is a polygon. The point of intersection of three or more faces is
called a vertex of the polyhedron; the line of intersection of two plane faces
is called an edge of the polyhedron. A regular polyhedron is one in which all
the faces are congruent regular polygons. There are only five regular
polyhedrons with the number of faces as 4, 6, 8, 12 and 20.
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