Mathematical definition of direction?

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SUMMARY

The mathematical definition of direction is established as a ray, which is defined as the part of a line segment on one side of a given point. Direction is not inherently linked to movement or transfer; rather, it is determined by selecting one endpoint of a directed line segment as the base for the ray. The concept of direction is clarified through the understanding that a point divides a segment into two parts, allowing for the selection of either part to define the direction.

PREREQUISITES
  • Understanding of basic geometric concepts, specifically line segments and rays.
  • Familiarity with the definitions of directed line segments in geometry.
  • Knowledge of points and their role in dividing segments.
  • Basic comprehension of mathematical terminology related to direction.
NEXT STEPS
  • Study the properties of rays and their applications in geometry.
  • Explore the concept of directed line segments in greater detail.
  • Learn about geometric definitions and their implications in mathematical proofs.
  • Investigate the relationship between direction and vector representation in mathematics.
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Students of mathematics, educators teaching geometry, and anyone interested in the foundational concepts of direction in mathematical contexts.

sadhu
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what is the mathematical definition of direction ?

is it always associated with movement or transfer ?

if not then what is the meaning of initial and final point in the definition of directed line segment?
 
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Since neither movement nor transfer is a "mathematical term", no, direction is not mathematically defined in terms of them. "Direction" is defined as a ray- that part of a line segment on one side of a given point. Of course, "on one side of" is just defined as "a point divides a segment into two parts: choose either of them."

I apparently don't understand your last question. I don't see what it has to do with "if not". A "directed" line segment starts with a line segment. Then you choose one of the end points as the 'base' for the ray that determines the direction. Neither movement nor transfer required there.
 

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