@roundsquare I agree. Simply memorizing the formula does not mean that you understand the math. You have to learn why the formula works. If a person knows why the math works, then he is able to create new formulas and to better use them.
Here’s one example:
Area of regular polygon = ½ * apothem * perimeter
Regardless of number of sides.
That is one simple formula that is very useful in a geometry class, but I don’t know if anyone realizes how this equation works. It is derived by dissecting the regular polygon with N sides into N congruent triangles, each with its base as a side of the polygon. The formula for each triangle is (Apothem * Side Length / 2). The total area is then (N * (Apothem * Side Length / 2)). From this, the (N * Side Length) = Perimenter, so the formula then simplifies to the above.
Not understanding shortcuts is another reason why some people find math harder than it should be. I have witnessed people pull out a calculator to divide by 1000. If a person understood the trick (move the decimal point to the left three spaces, which is the number of zeros in the number), then they could do the problem without any real effort.
Very few people understand how the quadratic formula works. The fact that there is a quadratic formula “song” shows how we are concerned with memorization. In 8th grade, I managed to (re-)derive the quadratic formula from scratch.
@NostalgicChills Sorry for getting off topic.