Data structure.
Data structure is both a programming language construct that unifies several
related attributes and a basic data type. Realization of the utility of
data structures in programming led eventually to the modern object oriented
trend. Among the basic data types are the stack, list, queue, tree.
Equation.
An equation is a statement that two mathematical object, e.g. algebraic
expressions, are equal under certain conditions. Equations are usually
and sometimes tacitly accompanied by the requirement to establish these
conditions. In the case where mathematical objects contain arbitrary variables,
such a requirement may mean finding those values of the variables that
turn the equation into equality. Equations are written as two mathematical
objects connected by the equality sign "=". Equations are sometimes
called more explicitly as conditional equations.
Equality.
An equality is a statement of two mathematical objects being equal. Like
equations, equalities are written as two mathematical objects connected
by the equality sign "=". The meaning of two objects being equal
depends very much on the nature of the objects. E.g., two matrices are
equal iff they have identical dimensions and all their corresponding elements
are equal. Two triangles are equal if there exists a distance preserving
transformation that maps one on the other (Nowadays equal triangles more
often than not are called congruent.) Equalities are sometimes called
unconditional equations.
Edge
The line segment where two faces of a polyhedron meet.
Equation
A mathematical sentence containing an equal sign.
Equiangular or equilateral triangle
See regular polygon regular polygon.
Estimation
Determining an approximate amount, value or size of something.
Quantitative estimation is determining the approximate number of items
in a group.
Computational estimation is determining the approximate result to an arithmetic
calculation.
Measurement estimation is determining the approximate length, perimeter,
area, volume or other measurement of a geometric figure.
Extreme value, local or global.
A function f:A->B is numeric if B is a set of numbers. For a numeric
function it's possible to compare its values at different points aA. Extreme
is a value which, in some sense is either maximum or minimum. If f(a)
exceeds all other values of f then we say it's a global extreme, maximum.
If it's only larger than values of f for points near a, the maximum is
local.
Exterior angle of a polygon
The
angle outside a polygon formed by extending one of its sides.
Field.
A field is a ring in which multiplication is a group operation. In France
(and sometimes elsewhere in Europe), the multiplicative group need not
be commutative. In the US and Russia it must be.
Floor.
For a real number r, its floor value [r] is defined as the largest integer
no greater than r. Thus [5]=[5.1]=5 and [-5]=-5 while [-5.1]=-6.
Fractional Part.
For a real number r, its fractional part is defined as {r}=r-[r], where
[r] is the floor value of r.
Free group.
Groups have generators, such elements that all other elements of a group
could be obtained from generators and their inverses using the group operation.
A group is said to be free if no relation exists between its generators
other than between an element and its inverse. The additive group of integers
is free with a single generator 1. The multiplicative group of all positive
rational numbers has prime numbers as its generators. From the Fundamental
Theorem of Arithmetic representation of integers in the form paqb...rc
where p, q, ..., r are all different primes, is unique. Therefore the
group is free. The group of sliding motions in the sliders puzzle is not
free. Indeed, for the sequence Sj+S+iSj-S-i we obviously have the following
identity (Sj+S+iSj-S-i)3=Id, where Id is the unit element of the group,
i.e. the element that leaves all the counters unchanged. |