Java Reference
In-Depth Information
2
2
2
abc
c
+=
=
2
2
c
=
2
Therefore, the length of the hypotenuse in a right triangle with unit
sides is a number that, when multiplied by itself, gives 2. This number
(approximately 1.414213562) cannot be expressed as the exact ratio of
two integers. Other irrational numbers are
,
, as well as the mathe-
3
5
matical constants
p
and e.
Real and complex numbers
Thesetofnumbersthatincludesthenaturalnumbers,thewholenumbers,
and the rational and irrational numbers is called the
real numbers
. Most
commonmathematicalproblemsaresolvedusingrealnumbers.However,
during the investigation of squares and roots we notice the following:
+2*+2=4
-2*-2=4
Since the square of a positive number is positive and the square of a
negative number is also positive, there can be no real number whose
square is negative. Therefore, the value of does not exist in the real
number system. But mathematicians of the 18th century extended the
number system to include operations with roots of negative numbers.
They defined the
imaginary unit
as
−
2
i
2
=−
1
i
=−
1
Numbers that consist of a real part and an imaginary part are called
complex numbers
. Some of the uses of complex numbers are in finding
the solution of a quadratic equation, in vector analysis, graphics, and in
solving many engineering, scientific, and mathematical problems.
Storage of Numerical Data
ThevonNeumanndefinitionrequiresthatthecomputingmachinebecapa-
ble of storing and retrieving numerical data. In practice, numerical data
itemsarestoredinstandardformats,designedtominimizespaceandopti-
mizeprocessingefficiency.Historically,numericdatawasstoredinstruc-
tures devised according to the architecture of a specific machine, or the
preferencesofthedesigners.Itwasnotuntil1985thattheInstituteofElec-
