Marking using “Method of Two” and “Method of Three”

Both methods are irreplaceable when you have to divide a certain linear space into a number of smaller equal spaces. This operation doesn’t pose any threat or difficulty if a value of each space is a whole number. Say, you need to line up 20 marks with a distance of 10 mm between them. No problem. You will just lay down a ruler and place a mark every 10 mm, preferably without moving the ruler.

When you have to deal with non-round numbers, such technique will not be effective. Any attempt to lay down the ruler and draw marks with a distance between them described by a number with 2-3 digits after the comma will lead you to a mistake in overall distance. A smallest mistake in representing a complex value of the smaller space along with significant number of divisions will create a phenomena known as a Combined Mistake, which was discussed in a separate article.

Division using “method of two” and “method of three” will eliminate the very possibility of a combined mistake, help you to mark your material or component with maximum accuracy and preserve the value of the main overall distance. Both methods require you to reverse the technique of linear marking and to start from greater distance dividing it equally, piece by piece. Using these methods you don’t have to be concerned anymore about accurate representation of complex values of each particular smaller space – all you have to represent is a quantity of spaces. As a result of accurate equal division values of the smaller spaces will be kept automatically.

Let’s start with simplest example. Say, you have to mark 4 spaces with certain overall distance between the first and the last mark. You start with marking the overall distance first. Than you put a mark right in the middle. Last step, divide each half in the middle as well. This is a “method of two”.

Another example. You have to divide a certain linear space into 9 smaller equal spaces. You are starting again by marking the first and the last mark. Than you dividing it in three equal spaces. The last step is to divide each of three spaces in three again. This is a “method of three”. As you can see, no matter how complex the values of the greater and smaller spaces, as long as you perform equal divisions of each smaller space the division will be maximal close to accurate. Naturally, you are not guaranteed from making small single mistakes. However, step by step division of initially accurately represented greater space creates a grid of some sort which automatically compensate for single mistakes and prevents them from building up into a combined mistake. Also, a single mistake made marking a larger spaces is less significant as it applies on a value greater than a smallest resulting spaces.

The next example is for a combined use of both methods. We will be dividing a linear space into 6 equal spaces. After marking the overall space between the first and last mark, divide it in half. Than divide each half in 3. Or you can divide an overall space in 3 and than divide each third in half. In each case you will receive an accurate division in 6 equal spaces.

No doubt that a division in half is much easier to calculate and preform than a division in three parts. Also there is more margin for making a single mistake, no matter how small it is. This last example will show you how to “force” and turn a division in 3 into a more convenient division in 2. Let’s go back to the second example where we had to divide a linear space in 9 parts. After marking the overall space between the first and last mark, calculate the value of the smallest required space and mark it as accurate as you can after the first mark or before the last one. The first (or last) mark and the new mark will render a new space which than can be finally divided using only a “method of two”.

Although these methods might look like exercise for third grader, do not make a mistake by underestimating them. I saw quite a few inexperienced model makers, marking a complex value linear spaces, one after another, sweating and panicking when a resulting overall distance ran far away from a required value. You wouldn’t believe what a discovery and a relief was for them an introduction of these two simple and elegant methods.