Jeffrey's Tutoring Blog

When using C++ for object-oriented programming, there are some basic concepts and best practices that should be followed for good software engineering. First is the use of public and private in class definitions. Most programmers moving from C to C++ are accustomed to using structs, where all fields are "public" for others to access; in C++, all fields in a class are "private" by default instead. There is a good reason for this: everything in a class should be private unless otherwise necessary. If there is some data that you wish to "expose", you are best off using getter/setter methods...

A struct is a datatype from the C programming language that encapsulates a number of different datatypes into a single object. This can be used to easily handle a set of values as a single "package", while also being able to access the individual members of the structure. One example of this may be a ContactInfo structure that contains a person's first name, last name, e-mail address, phone number, birthday, etc.

It's easy to see how this would later be extended into the notion of a "class", where the object could have methods defined to access the data or otherwise manipulate its contents,...

Here's an interesting math fact: the sum of any sequence of odd numbers from 1 to n is always a perfect square.

1 = 1
1+3 = 4
1+3+5 = 9
1+3+5+7 = 16
1+3+5+7+9 = 25
1+3+5+7+9+11 = 36
etc.

The sum is actually the square of (n+1)/2.

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What this also means is that every odd number can be expressed as a difference of consecutive squares:

1-0 = 1
4-1 = 3
9-4 = 5
16-9 = 7
25-16 = 9
36-25 = 11
etc.

In this case, each odd number n can be expressed as the square of (n+1)/2 minus the square of (n-1)/2.

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You can now use this knowledge to derive an infinite number of Pythagorean...

Think of a number. Any number at all... between 10 and one billion.

Now, since that number has at least two digits, add up all of the digits, and subtract that sum from your original number.

Next, add up all of the digits of the number you just got after that subtraction, to get another new number. And then do it again with THAT number (if you have only a one-digit number, you would just get that same number again).

Finally, subtract 1 from that last number, and find the letter of the alphabet that corresponds to the result (1=A, 2=B, 3=C, etc.) Now think of one of the 50 United States...

I'm about to share a secret with you that can instantly reduce the amount of time spent on math tests and homework where you need to find the greatest common factor (GCF) of two whole numbers, such as when reducing fractions to simplest form. This is a methodology/short-cut that I came up with long ago, but never saw described in any textbook, much to my surprise. The basic idea is actually quite simple:

Given two whole numbers A and B where A > B, the GCF of A and B must also be a factor of their difference: A-B.

Here's an example. You need to reduce the fraction 84/105 to simplest form...