Final answer:
Euclidean geometry does not implicitly assume an observer; it is based on a "flat" space with postulates that are accepted as universally applicable. However, relativity introduced by Einstein shows that observations of space and geometry can differ based on an observer's frame of reference, such as in high-speed or strong gravity conditions.
Step-by-step explanation:
The question asks if Euclidean geometry implicitly assumes an observer. To answer this, we must understand that Euclidean geometry is based on certain postulates that do not require the concept of an observer to validate its principles. It assumes a "flat" space, where the properties such as straight lines being the shortest distance between two points, the sum of angles in a triangle adding up to 180 degrees, and parallel lines never intersecting, are taken as universal truths, applicable in any frame of reference. These principles were undisputed until the advent of non-Euclidean geometry and Einstein's theory of relativity, which showed that the shape of space can be curved by gravity and that observations might differ based on the observer's frame of reference.
In contrast to Euclidean geometry, relativity introduces the idea that there is no absolute frame of reference. The laws of physics, including the geometry of space, may look different from various perspectives, especially when taking into account high velocities or strong gravitational fields as described by Einstein.