The origin of degree scale in angles

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Discussion Overview

The discussion revolves around the origin of the degree scale in angles, specifically in relation to regular polygons and their internal angles. Participants explore the connection between the number of sides in a polygon and the measurement of angles in degrees, as well as the implications of integer internal angles.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes that the origin of the degree scale in angles is linked to the regular polygon with the greatest number of sides (360), which has an internal angle of 179 degrees.
  • Another participant challenges this view, suggesting that the argument is circular since it relies on the premise of integer internal angles in degrees without considering other systems, such as grads.
  • A later reply acknowledges a mistake in reasoning and reflects on the learning process involved.
  • Some participants correct the initial claim about the number of polygons, stating that only 22 polygons satisfy the condition of having integer internal angles, excluding polygons with 1 or 2 sides.
  • There is mention of external resources, including Wikipedia articles on Babylonian numerals and the concept of degrees, which may provide additional context or theories.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of the original thesis about the degree scale's origin. There is no consensus on the correctness of the initial claim, and multiple viewpoints regarding the number of polygons and the reasoning behind the degree scale are presented.

Contextual Notes

Some assumptions regarding the definitions of polygons and angle measurements are not fully explored, and the discussion includes unresolved mathematical considerations about the conditions for integer internal angles.

Aikon
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A student showed me a problem, this week, it was: What is the number of regular polygons whose intern angle is an integer number?

I used the equation i=180 (n-2)/n, where i is the internal angle of the polygon and n is the number of the sides of the polygon.

After some trials, i got to the answer. The regular polygon with greater number of sides has n=360 sides and internal angle i = 179 degrees. The answer of the question is that there are 24 polygons with the needed conditions (you need to factorize 360 = 2³ 3² 5 and make the permutations of the exponents, that are 4 (0,1,2,3), and 3 and 2, then you have the total number of divisors of 360).

The interesting thing, I thought today, is that there are 360 sides, this means that when this polygon is limited by a circumference you find that 2 consecutive vertices connected to the center had a 1 degree angle between the lines that connect them. So it appears to me that this is the origin of the degree scale in angles, the polygon with greatest number of sides that have an integer internal angle.

Someone confirms my thesis??
 
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Thank you,
There are some theories in:
http://en.wikipedia.org/wiki/Degree_(angle )

Maybe my theory is a new one??! : )
 
Last edited by a moderator:
Someone confirms my thesis??

I can confirm that yours is a circular argument.
 
A circular argument because you started looking for polygons where the internal angle is an integer number of degrees and determined the largest such had 360 sides and angles of 1 degree.

Had you looked for polygons where the internal angle is an integer number of grads (there are 100 grads in a right angle so 400 grads in a circle), you would have determined that the largest such had 400 sides and angles of 1 grad.
 
Yeah i got it...it is a mistake of the type "think a litle more about this...and you will not do".
Well...Living and learning.
 
Actually, there are only 22 polygons that satisfy this question...you cannot have a polygon with 1 side or 2 sides.
 
Makin Bacon said:
Actually, there are only 22 polygons that satisfy this question...you cannot have a polygon with 1 side or 2 sides.

Great remark...You are right...Thanks a lot!

Just one thing...I said that i got to the answer...It was a year ago and was a multiple choice question that had answers in the book. Maybe the book was with the wrong answer!
 

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