I make paper art and design paper models for a living, and I also like origami. It is quite often that I need to divide a piece of paper into equal parts. The most common and easiest of them all is dividing in half. You can do it without a ruler or any other tool. Others like quarters and eighths are basically multiplications of two, so it’s only a few more times of folding. However, if you want to divide a length into thirds, fifths, sixths, sevenths, ninths or tenths, it would be anything but intuitive. On a computer it can be easy to do, but on paper, you usually have to measure with a ruler, calculate the length of each equal part, then mark the paper with a pen and a ruler. It is a lot of work.
There is a way to measure various equal parts using engineering drawing, but it still requires tools such as a ruler, a set square and a compass. How it works is shown in the picture below:
Construct a line(AB) of 5 equal segments
- Use a ruler to find the right angle for line segment AC
- Find the right radius with a compass, starting from point A, continuously mark the D, E, F, G, H points for the 5 equal parts on line segment AC.
- Align the hypotenuse of the set square to line HB, and align the ruler to the perpendicular long edge under the set square.
- Move the set square to the left along the fixed ruler, once the hypotenuse of the set square meets point G, mark it as point I on line segment AB.
- Keep moving the set square to the left along the fixed ruler, once the hypotenuse of the set square meets point F, mark it as point J on line segment AB.
- Keep moving the set square to the left along the fixed ruler, once the hypotenuse of the set square meets point E, mark it as point K on line segment AB.
- Keep moving the set square to the left along the fixed ruler, once the hypotenuse of the set square meets point D, mark it as point L on line segment AB. Now all 5 line segments AL, LK, KJ, JI and IB should have equally divided line segment AB.
I am hoping to replace this complicated construction with a simple cardboard that serves as an equal dividing tool, and you can quickly mark a certain number(N) of equal segments on any A4 paper(N＝2～10). I also hope to add extra helping lines for both square and A4 ratios, so you can use it on papers with square or A4 ratios of various sizes.
Below is the prototype for this equal segment divider I made on a computer:
以印表機及 A4 紙列印輸出後，實際尺寸長寬為 28 × 19.8 公分。因為設定可等分數為 10，因此將垂直短邊預先劃成 10 等份，並加上等分數刻度 2～10，另外預先劃出正方及 A4 比例的對角線。
Once you have printed it out on an A4 paper, it will measure 28 × 19.8 cm. The max number of equal segments is set to 10, so the perpendicular short edge is drawn into 10 segments, and marked with scales from 2 to 10. The diagonals for the square and A4 ratios are drawn in advance as well.
How to use the A4 equal divider:
Example 1: Into thirds
Example 2: Into fifths
Example 3: Scaling on a square paper
Example 4: Scaling on an A4 paper