Encapsulate

Information hiding is a simple, proven concept that results in software that is easier to test and easier still to maintain. Most software modules should hide some information from all other software. This information could be the structure of data; the contents of data; an algorithm; a design decision; or an interface to hardware, to a user, or to another piece of software. Information hiding aids in isolating faults because, when the hidden information becomes unacceptable in some manner (such as when it fails or it must be changed to accommodate a new requirement), only the piece of software hiding that information need be examined or altered. Encapsulation refers to a uniform set of rules about which types of information should be hidden. For example, encapsulation in object-oriented design usually refers to the hiding of attributes (data) and methods (algorithms) inside each object. No other objects may affect the values of the attributes except via requests to the methods.


Reference:
Parnas, D., "On the Criteria to Be Used in Decomposing Systems into Modules," Communications of the ACM, December 1972.

Don't Reinvent the Wheel

When electrical engineers design new printed circuit boards, they go to a catalog of available integrated circuits to select the most appropriate components. When architects design homes, they go to catalogs of prefabricated doors, windows, moldings, and other components. All this is called "engineering." Software engineers usually reinvent components over and over again; they rarely salvage existing software components. It is interesting that the software industry calls this rare practice "reuse" rather than "engineering."

Magic Square Corollary

The following definition for a Magic Square series is from the EDU-BLOG:

In recreational mathematics, a magic square of order ‘n’ is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.  A normal magic square contains the integers from 1 to n2. The term “magic square” is also sometimes used to refer to any of various types of word square.

The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the value 

Thus the magic square series is like this: 1, 5, 15, 34, 65, 111, 175, 260…

Often when I want to practice programing I'll write some code to calculate some interesting mathematical number or series. Recently I picked the magic square series. When I finished I noticed that for each order of magnitude beyond n = 20 there was a pattern.

Magic Square Corollary

for y = 0 to ∞

n	M(n)
20	4,010
200	4,000,100
2,000	4,000,001,000
20,000	4,000,000,010,000
...	...

This was done solely for the enjoyment of playing around with some numbers. I used Roger's Online Equation Editor to make the above equation image. Very handy tool.

Next I noticed that any value of n = 10, 20, 30, ..., 90 can have the above equation applied to it. For example, n = 10:

M(10) = 505

Split 505 at the two least significant digits. Maintain the order of the left half to get 500 and 5. Then apply those values on the left and right of the plus sign, as so:

M(n) = M(10 * 10^y) = 500*10^(3y)+5*10^y

M(100) = 500,050

M(1,000) = 500,000,500

...

M(90) = 364,545

M(n) = M(90 * 10^y) = 3,645*10^(3y)+45*10^y

M(900) = 364,500,450

M(9,000) = 364,500,004,500

...

Avoid Numerous Special Cases

There are often exceptional situations to an algorithm's design. Exceptional situations cause special cases to be added to the algorithm. Every special case makes it more difficult to debug, modify, maintain, and enhance an algorithm.

If you find too many special cases, you probably have an inappropriate algorithm. Rethink and redesign the algorithm.