When performing a mathematical calculation by hand, what symbol do you use to signify division? Do you use a slash (/), a horizontal line with the numerator and divisor above and below, or the divide (÷) symbol? Personally, I use one of the first two, depending on the context. And, I can’t remember the last time I used ÷. However, a good estimate would be back in grade school.
Chris Spooner, over at line25.com wrote an interesting article titled “10 HTML Entity Crimes You Really Shouldn’t Commit” (found via Twitter thanks to Lester Chan). I however, don’t agree with crime #8, which deals with the multiply (cross product) and division symbols. The divide symbol is hardly used outside of elementary math, and the cross product multiply symbol is used incorrectly in scalar math. Here’s an hint: the multiplication of two scalars is a form of the dot product.
Why shouldn’t I use × for scalar multiplication?
The short answer is vector math. Back in middle school, our teacher used · rather than ×, and claimed that the switch was to reduce confusion with using x as a variable in algebra. There was also a quick mention of the fact that it was technically more correct to use ·. It wasn’t until high school that I saw vectors and the dot product and the change made much more sense.
In vector math, there are two vector multiplication operations; the cross product (×), and the dot product (·). These are two distinct operations that take two vectors and produce vastly different results. The cross product takes two vectors and returns a vector. The dot product takes two vectors and returns a scalar. The dot product on two single element vectors is the same as multiplication of two scalars. Hence it is slightly more correct, and definitely less confusing to use · for multiplication rather than ×.
As with ÷, I haven’t used × for scalar multiplication since middle school. And, I don’t see myself changing from this style any time soon. When pencil hits paper, which multiplication symbol do you use? And, does anyone still use ÷?
[end of transmission, stay tuned]