Two routes, the same endpoints

Invented flat-coordinate example. Units are kilometers. This is not eel tracking data and does not model Earth curvature, currents or vertical travel.

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JourneyRecorded or assumed pointsTime
A(0,0) → (300,400), straight route assumed100 days
B(0,0) → (0,400) → (300,400)100 days
  1. Calculate straight-line endpoint separation using the Pythagorean theorem.
  2. Calculate the length of B's two segments.
  3. Divide both quantities by 100 days.
  4. Erase B's middle point. Which journey facts remain known?
Check the arithmetic

Endpoint separation: √(300² + 400²) = 500 km. Journey B path length: 400 + 300 = 700 km. The displacement-based rate is 5 km/day. B's path-length rate is 7 km/day. With only endpoints, 500 km remains the shortest possible planar route; 700 km no longer follows from the available observations.

In a real study, distinguish recorded positions, reconstructed positions, straight-line segments, tag drift and assumptions. A map can combine more than one kind of evidence.

Incoprea