**Robotics in mathematical explanation**

A feedback controlled mechanical device. Robotics is the
study of the design, applications, and control and sensory systems of robots;
for example, the design of robot arms that can approach an object from any
orientation and grip it.

A robot’s control system may be simple and consist of only a
sequencing device so that the device moves in a repetitive pattern, or more
sophisticated so that the robot’s movements are generated by computer from data
about the environment. The robot’s sensory out of procedure, such as the rule
of three, or transformation rules.

**Theory of games in mathematical explanation**

The mathematical
study of the probabilities of each outcome in games. Although there is an
element of chance in who wins, there are often general rules for maximizing the
chances of one particular outcome. These are calculated from the rules of the
game and the number of players, using techniques of probability.

**Thomson lamp**

A paradoxical machine devised as a thought – experiment by British
philosopher James Thomson in 1970 to highlight the difficulty in zeno’s
paradoxes of deciding whether a super task, an infinite number of tasks in
finite time, has been completed.

The lamp is switched on, and after a minute switches off;
after a further half minute it comes on again, goes off after another quarter
minute, and so on, changing its state after each term of a convergent series of
time intervals.

Since this series of intervals has a sum of two minutes, the
process must have terminated after that time, so the lamp must be either on or
off; yet it cannot be either on or off, since each time it entered either state
is immediately switched again. This does not show, however, as Thomson argued,
that zeno’s paradoxes are unresolved by taking limits, since paradoxes concern
convergent rather than oscillating series of tasks.

**Topology**

A branch of modern mathematics rather of geometry, concerned
with the general properties of shapes and space. In topology we study the
properties that are not altered by continuous distortions such as stretching or
twisting.

For example, a sphere and an ellipsoid are though different
figures in geometry but are equivalent figure in topology since one can be
transformed into the other by a continuous deformation.

**Weak topology**

The topology imposed on the underlying vector space by taking
as sub-base all open half spaces-containing zero. This gives the weakest
topology in which ass the norm continuous linear functional are continuous. A space
is reflexive if the unit ball is weakly compact or equivalently, by the
eberlein-Smulian theorem, if it is weakly sequentially compact.

Some mathematical explanations of science concepts
Reviewed by knowledge people creators
on
February 02, 2020
Rating: