Applications of Euclidean Geometry: The Elastic Line Concept

In classical Euclidean geometry, a straight line is regarded as a rigid, immutable, and infinitely extendable entity. However, in phys- ical, informational, and phenomenological contexts, the notion of a line often deviates from this rigid abstraction: light refracts, beams bend, and paths within networks fluctuate. This paper introduces the concept of an elastic line, defined as a straight line endowed with a pa- rameter of elasticity. We explore its mathematical structure, physical implications, and philosophical significance, reinterpreting Euclidean geometry in light of elastic deformation and contextual relativity.