What Is the Term for Increasing Angle Sides?

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    Angle Increasing Term
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Discussion Overview

The discussion revolves around the geometric relationship between the sides of an angle and the distance from the vertex of the angle. Participants explore whether there is a specific term or definition that describes the phenomenon where the distance between the sides of an angle increases as the distance from the angle's origin increases. The scope includes conceptual understanding and mathematical relationships in geometry.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant questions if there is a term for the observation that the distance between the sides of an angle increases with distance from the angle's vertex.
  • Another participant describes a triangle with points a, b, and c, proposing a mathematical relationship where the lengths of the sides are proportional to each other based on a constant angle.
  • A third participant introduces the definition of an angle in terms of arc length and radius, suggesting that if the angle remains constant, the arc length must increase proportionally with the radius to maintain the ratio.
  • A later reply suggests the term "diverge" to describe the behavior of the lines extending from the angle's vertex.

Areas of Agreement / Disagreement

Participants express varying perspectives on the terminology and mathematical relationships involved, with no consensus reached on a specific term for the phenomenon described.

Contextual Notes

Participants reference different geometric concepts and relationships, but the discussion does not resolve the definitions or terms being sought, leaving some assumptions and conditions unaddressed.

Devin Alexander
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This is my first post on this forum so sry if this is in the wrong place, but also it’s a weird question so I don’t know where it falls exactly.

Anyways my question is: when you have an angle, the further the distance is from the point where the angle forms, the distance between the two inner sides of the angel increases. My question is is there a term or something for making that statement, the statement being the distance between the sides of the angle increase as the distance to the angles origin increase. Is there a term for that?

Like I said, it’s kind of a weird question but it’s sometjing I’ve always wondered for some reason.
 
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Consider a triangle with endpoints a, b, and c. We'll put you angle at point a. The length of sides ab and ac will be equal and that length will represent the distance "from the point where the angle forms" to the place where you are measuring it. The length of the remaining side, bc, will be "the distance between the two inner sides".
Let's call the angle at a, ##\alpha##; the distance between the sides (the length of line segment bc), ##J##; and the distance from the angle (length ab or ac), ##K##.
Then we can say that given a constant ##\alpha##, lengths ##J## and ##K## will be proportional to each other.

More specifically, ##J = 2sin(\alpha/2)K##
 
The term or somethng is the definition of the angle, ##\theta = S/R##, where ##S## is the arc that subtends the angle (what you call the distance between the sides of the angle) and ##R## is the radius of the arc (what you call the distance to the angle origin). If the angle is kept constant and ##S## is increased, ##R## must increase proportionally to keep the ratio constant.
 
Devin Alexander said:
the statement being the distance between the sides of the angle increase as the distance to the angles origin increase. Is there a term for that?
It is said that the lines Diverge: "to move, lie, or extend in different directions from a common point; branch off."

Above from: http://www.dictionary.com/browse/diverge
 

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