Proportion, Proportion, Proportion! As Simple As "A is to B as B is to C"
"Location, location, and location" is the mantra of real estate professionals when describing the three most important elements of a property's worth. Proportion, proportion, and proportion are the three most important elements for decoding market movements. Time, the duration of the markets movements, and price, the measurable portion of perceived market value, always bear a definitive proportional relationship to previous market movements.
As simple as A is to B as B is to C is just another way of saying "as simple as a three term continuous proportion.," but we didn't want to intimidate anyone by using a "mathematical" expression. But, it is very simple:
"Three" refers to the quantity of terms/elements/items in the expression: A, B & C. If a 4th term is added, the expression would be "A is to B as B is to C as C is to D. Now the expression would be described as a four term continuous proportion.
Let's replace the letters A, B & C with numbers; 20 is to 10 as 10 is to 5. There are 3 terms, 20, 10 & 5.
When one number is divided by a second number the answer is called a ratio.
The ratio of 20 to 10, or 20 divided by 10, = 2.
The ratio of 10 to 5, or 10 divided by 5, = 2.
The important point to remember about the term ratio is that it is always used to compare quantities by division.
The words "ratio" and "proportion" have become almost interchangeable in everyday, conversational English, and nobody has a problem understanding what is meant when they are used. However, in mathematical terminology, these two words have precise definitions, and they are different.
Proportion refers to an equality of ratios. "An equality of ratios" is a fancy way of saying that the same ratio is generated in more than one place by different sets of numbers. Thus, in the previous example, since the ratio of 20 divided by 10 is equal to the ratio of 10 divided by 5, the three terms, 20, 10, 5, constitute a 3 TERM CONTINUOUS PROPORTION. "Continuous" refers to the fact that any pair of the 3 quantities, in ascending or descending order, generates two equal ratios.
A DISCONTINUOUS PROPORTION refers to a sequence of quantities that produce equal ratios, but the sequence is not "continuous". For example:
20 divided by 10 equals 2, and 8 divided by 4 equals 2. In descending order, 20-10-8-4 does not generate a "continuous" proportion because 10 divided by 8 is 1.25, not 2.
Therefore, the sequence would be described as a DISCONTINUOUS 4 TERM PROPORTION.
We apologize for this little exercise on definitions. You probably learned about ratio and proportion in grammar school. If you haven't thought about it lately, you probably forgot it. Our excuse for this simplistic lesson is that the words and phrases just defined will be used in the explanatory text for the examples that follow.