GRAPHICAL ALGEBRA INVOLVING FUNCTIONS 
F THE nt? DEGREE. 
Francois EK. NreHer.* 
In the study of algebra, there is a strong tendency 
among the young learners to follow rules, without giving 
Serious attention to the fundamentals upon which rules 
are based. There are many graduates in algebra who 
could at once answer the question, What is the area of 
the square, whose sides are x — a. A diagram showing the 
original square, with the lengths a cut off from its sides 
would show that when the two strips 27a have been sub- 
tracted from the area 22, the area a? has been subtracted 
twice. Therefore the final term a? is properly added. 
It often happens that a diagram suggests something 
which its symbolic representation does not suggest. 
When they are both presented, the suggestion is still 
more likely to come. : 
_ As is well known, the difference between the squares 
of two numbers y and z is 
y — a? = (y—2) (ya) 
=y(y—a2)+ta(y—2) (1) 
¢ 5 Fig. 1. 
The two terms of the second member represent the 
areas of two rectangles marked a and b in Fig. 1. They 
have equal width y—z. Their lengths are y and 2. 
tie resented before The Academy of Science of St. Louis, March 18, 
| (193) 
ca 
