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Engineering Aid 3 - Beginning Structural engineering guide book | Next
TYPES OF NUMBERS |
CHAPTER 1
MATHEMATICS AND UNITS
OF MEASUREMENT
Mathematics is the Engineering Aid’s basic
tool. The use of mathematics is found in every
rating in the Navy, from the simple arithmetic
of counting for inventory purposes to the
complicated equations encountered in computer
and engineering designs. In the Occupational Field
13 ratings, the Engineering Aid is looked upon
as superior in knowledge when it comes to the
subject of mathematics, which generally is a
correct assumption; however, to be worthy of this
calling, you have the responsibility to learn more
about this subject. Mathematics is a broad science
that cannot be covered fully in formal service
school training, so it is up to you to devote
some of your own time to the study of this
subject.
The EA must have the ability to compute
easily, quickly, systematically, and accurately.
This requires a knowledge of the fundamental
properties of numbers and the ability to estimate
the accuracy of computations based on field
measurements or collected field data. To compute
rapidly, you need constant practice and should
be able to use any available device to speed
up and simplify computations. In solving a
mathematical problem, you should take a
different approach than you would if it were
simply a puzzle you were solving for fun.
Guesswork has no place in its consideration, and
the statement of the problem itself should be
devoid of anything that might obscure its true
meaning. Mathematics is not a course in memory
but one in reasoning. Mathematical problems
should be read and so carefully analyzed that all
conditions are well fixed in mind. Avoid all
unnecessary work and shorten the solution
wherever possible. Always apply some proof or
check to your work. Accuracy is of the greatest
importance; a wrong answer is valueless.
This chapter covers various principles of
mathematics. The instructions given will aid the
EA in making mathematical computations in the
field and the office. This chapter also covers units
of measurement and the conversion from one
system to the other; that is, from the English to
the metric system.
FUNDAMENTALS OF
MATHEMATICS
MATHEMATICS is, by broad definition, the
science that deals with the relationships between
quantities and operations and with methods by
which these relationships can be applied to
determine unknown quantities from given or
measured data. The fundamentals of mathematics
remain the same, no matter to what field they are
applied. Various authors have attempted to
classify mathematics according to its use. It has
been subdivided into a number of major branches.
Those with which you will be principally
concerned are arithmetic, algebra, geometry, and
trigonometry.
ARITHMETIC is the art of computation by
the use of positive real numbers. Starting with the
review of arithmetic, you will, by diligent effort,
build up to a study of algebra.
ALGEBRA is the branch of mathematics that
deals with the relations and properties of numbers
by means of letters, signs of operation, and other
symbols. Algebra includes solution of equations,
polynomials, verbal problems, graphs, and so on.
GEOMETRY is the branch of mathematics
that investigates the relations, properties, and
measurement of solids, surfaces, lines, and angles;
it also deals with the theory of space and of figures
in space.
TRIGONOMETRY is the branch of mathe-
matics that deals with certain constant relation-
ships that exist in triangles and with methods by
which they are applied to compute unknown
values from known values.
STUDY GUIDES
Mathematics is an
many books on the
exact science, and there are
subject. These numerous
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