Designing the Equal Angle Divider

Since the last time I released the easy equal length divider, I have decided to continue this topic, this time on dividing angles, instead of length.

For dividing equal angles, when it’s the powers of 2, it can be done easily with a compass-and-straightedge construction or just fold the paper in half, a few times, but when you want to divide angles equally into odd numbers or prime numbers like 3, 5 or 7, it is going to be much more difficult. You will need a protractor with some calculation or even computer-aided drafting, it’s just too much trouble. This is why I want to design a passive device that can equally divide angles into 2 to 7 parts, or even more when expanded.

The initial plan is based on the folding principle of the framework of things like an umbrella or a handheld fan. Because I personally love origami, I have decided to do a little test run on a piece of paper.

等分角輔具圖紙

Print the above picture on an A4 paper and fold it according to its folding lines. There are 16 folds here, and can be added as many as the paper size allows.

等分角輔具打樣示意

Insert a toothpick through the middle as its axis, and wrap it with rubber band.

The finished sample will look like a paper fan. Move the toothpick axis to the center of the test angle, expand the fan until both sides reach the test angles. The areas between the mountain and valley folds will spread equally and automatically. You can then easily divide the angles at each point marked by the mountain and valley folds

Below is the demonstration of this divider on 3 different angles:

75度-5等分-15度 示範

75 degrees into 5 equal parts, 15 degrees each

90度-5等分-18度 示範

90 degrees into 5 equal parts, 18 degrees each

108度-3等分-36度 示範

108 degrees into 3 equal parts, 36 degrees each

Advantage:

  • Easy to make with just paper, intuitive to use, easy to keep, material is easy to come by.

Disadvantages:

  • Paper gets wet or damaged easily, not sturdy enough.
  • Paper is opaque, so it’s difficult to aim at your angles with the center axis and both its sides.
  • You have to hold it with your left hand, so it’s difficult to open or close, and keep it in place.
  • Thickness will accumulate at the center over time, causing slight errors in measuring angles.

Improvements:

  • I will try to replace paper with transparency film to improve sturdiness, so it’s easier to aim the angles.
  • Handles similar to a pair of scissors’ will be added down the sides of this divider, so it’s easier to control with your left hand.
  • The way the center opens and closes will be improved, to get closer to the ideal center and angles, for higher accuracy.

For more paper models and in-depth tutorials please visit Fun Paper.

 

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