What is the definition of angle?

[Coder Hashtag]

TL;DR Summary

Till date, no Physics or Mathematics book in the world does contain the definition of our most favorite notation - theta. Though it is a dimension less quantity, why can't it be defined when temperature has a definition? Let's check out. And most importantly, it needs to be defined without using the word twice in the definition.

 

[fizzyfiz]

An angle is the area created between two lines crossing on the plane.

 

[Coder Hashtag]

But does it at all match with the dimensions of area?

 

[berkeman]

Summary: Till date, no Physics or Mathematics book in the world does contain the definition of our most favorite notation - theta. Though it is a dimension less quantity, why can't it be defined when temperature has a definition? Let's check out. And most importantly, it needs to be defined without using the word twice in the definition.

View attachment 249158

try -- https://www.mathopenref.com/angle.html

 

[anorlunda]

Here is a PF Insights article from someone who agrees with you. If you read the discussion on the article, you'll see that several others disagree.

https://www.physicsforums.com/insights/can-angles-assigned-dimension/

 

[Khashishi]

I would add to the above that an angle has a numerical scalar value, and when two angles are aligned such that the vertices intersect, and one ray of each angle intersects, then the value of the angle formed by the common vertex and the other two rays is the sum or difference of the values of the angles of the two original angles. Also, the value of an angle where the two rays intersect is either 0 or 2pi, depending on which way you go around. (If you have two rays in a plane intersecting at a vertex, you have both an inner and outer angle, since the rays split the plane into two sides. These are different angles, so it needs to be specified.)

There should be a more concise way of saying that.