What is the distance in terms of millimetre between each degree on a circle?
I'm totally a beginner in Trigonometry so my question may seem so trivial for many of you. If my understanding is correct, based on the trigonometry a degree is defined by dividing the circumference of a circle into 360 equals parts so that each of those parts is called a degree. Now imagine that you open a circle and roll it on the table to form a simple straight segment (as if you actually drew a segment on a piece of paper using a ruler). You would then have a straight segment divided by 360 equal parts. What would be the distance between each degree ( = each division) in terms of millimetre on that segment? The reason that I ask this question is that I was looking to a protractor as you can see in the picture below:
The bottom of this protractor is an ordinary ruler and above of that we can see the measures of the degrees from 0 to 180. When I compare visually the measures on the ruler on the bottom with the degrees measures on the top of the protractor, it seems that they are the same and each degree has a distance of 1 millimetre from the next or previous degree. Is this true? Sorry if the question seems somewhat trivial for many of you but I'm completely a beginner in the field and I just try to understand how these units were actually defined.
The circumference of a circle is pi * the diameter, where pi is about 3.14159.
The diameter of your protractor looks to be about 120mm, so the circumference would be about 377 mm. Dividing by 360, each degree would be 1.05 mm -- pretty close.
That's so close that I wouldn't be surprised at all if the diameter of your protractor was actually designed to be 114.6mm, just to space the degree marks out by exactly 1mm.
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