The first and foremost important task of making any physically relevant mensuration tool is to generate all possible numbers(measurements of some quantity) through those instruments.
1. To measure distance first a unit distance has to be defined(fixed), this requires a Ruler.
1.1 To generate fractional numbers you need to cut a line with some precise angle.
2. To draw intersecting lines of some angle we need a measurement of angle.
3. total angle is 2pi , which can be produced by a Compass.
4. Later you have to cut that 2pi to get other fractions of angles.
So if you can construct any number using Compass-Ruler then that will be the least complex method to generate that fractional number.
1. To measure distance first a unit distance has to be defined(fixed), this requires a Ruler.
1.1 To generate fractional numbers you need to cut a line with some precise angle.
2. To draw intersecting lines of some angle we need a measurement of angle.
3. total angle is 2pi , which can be produced by a Compass.
4. Later you have to cut that 2pi to get other fractions of angles.
So if you can construct any number using Compass-Ruler then that will be the least complex method to generate that fractional number.
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