Cartesian Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 2

• Section 1.4 concludes the chapter by quickly reviewing assorted pre-

requisites.

1.1 1D Mathematics

You're reading this topic because you want to know about 3D mathematics,
so you're probably wondering why we're bothering to talk about 1D math.
Well, there are a couple of issues about number systems and counting that
we would like to clear up before we get to 3D.

The natural numbers, often called the counting numbers, were invented
millennia ago, probably to keep track of dead sheep. The concept of “one
sheep” came easily (see Figure 1.1), then “two sheep,” “three sheep,” but
people very quickly became convinced that this was too much work, and
gave up counting at some point that they invariably called “many sheep.”
Different cultures gave up at different points, depending on their threshold
of boredom. Eventually, civilization expanded to the point where we could
afford to have people sitting around thinking about numbers instead of
doing more survival-oriented tasks such as killing sheep and eating them.
These savvy thinkers immortalized the concept of zero (no sheep), and
although they didn't get around to naming all of the natural numbers,
they figured out various systems whereby they could name them if they
really wanted to using digits such as 1, 2, etc. (or if you were Roman, M,
X, I, etc.). Thus, mathematics was born.
The habit of lining sheep up in a row so that they can be easily counted
leads to the concept of a number line, that is, a line with the numbers
marked off at regular intervals, as in Figure 1.2. This line can in principle
go on for as long as we wish, but to avoid boredom we have stopped at five
sheep and used an arrowhead to let you know that the line can continue.
Clearer thinkers can visualize it going off to infinity, but historical purveyors
of dead sheep probably gave this concept little thought outside of their
dreams and fevered imaginings.

Figure 1.1
One dead sheep

Figure 1.2. A number line for the natural numbers