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INTERNATIONAL PROJECTIONIST
VOLUME VI
NUMBER 2
NOVEMBER 1933
MATHEMATICS FOR THE PROJECTIONIST
Gordon S. Mitchell and Harlan R. Asquith
III. Algebra
IN this lesson we will consider the subject of algebra. Although algebra may seem to be of little use in projection practice, there are many common problems which cannot be solved by arithmetical means but must be attacked through the methods of algebra.
In arithmetic we deal entirely with numbers, including whole numbers, fractions and decimal numbers. In algebra, numbers are often represented by letters of the alphabet, and the various operations are performed on these letters rather than upon the numbers for which they stand.
For example, if a certain coil of wire has a resistance of 6 ohms, instead of using the 6, we might say that it has a resistance of "b" ohms. That is, we let b=6, and then use the "b" in making our calculations.
One of the most important things to
remember is the fact that the same operations which you have performed with numbers can also be performed with letters. These operations include addition, subtraction, multiplication, division, raising to powers, and extracting roots. In the example above, if we have three coils in series — one with a resistance of "a" ohms, one with a resistance of "b" ohms, and the third with a resistance of "c" ohms — we would find the total resistance, which we might indicate as "R" ohms, by adding the three numbers and indicating the sum thus:
R=a+b+c
In actual practice, however, we cannot add "a" and "b" together any more than we can add one screen and one projector to get any more simple expression than one screen and one projector. However, we can add "a" and "a" to get the sum "2a", — just as we may add one
screen to one screen, to get the expression ''2 screens".
To find the difference between the resistance of a and b we indicate the subtraction thus: a — b.
Multiplication in algebra is indicated in any one of several ways: "a x b", "a • b", or simply by "ab". If instead of the coils discussed above, we have three coils in series, each with a resistance of "b" ohms, the total resistance would be three times b, or 3b.
In the expression 3b the number 3 is called the coefficient of b, because it means that b is taken three times. Similarly, if we have "n" coils in series the total resistance is "n times b", or "nb". In this case "n" is the coefficient of "b". A coefficient may be one or more letters (nrb) ; a whole number (35b) ; a common fraction (V^b) '•> or a decimal fraction (2.37b).
If no coefficient is expressed — that is, the term "b" (or any other term), appears alone — a coefficient of one is un
This is the third of a series of articles on mathematics written especially for the projectionist. Appended is
a group of questions bearing on the information given immediately preceding, a procedure which will be a
regular feature of this series. Also appended hereto are the answers to the questions in Article II, together
with the names of those who submitted correct answers thereto. — Editor.
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