Hello To demonstrate that we can deduce from special relativity the existence of an observer who finds that his three-dimensional space is not euclidean (a conclusion that is false in my opinion), in subsection "Behaviour of Clocks and Measuring Rods on a Rotating Body of Reference" of his book "Relativity: The Special and the General Theory", Albert Einstein wrote: Thus, using the assumption that a body D is described by an inertial reference R as a rigid disc in uniform rotation about an axis perpendicular to the disc plane and passing through its center, it should be concluded : (i) There exists an observer of D who can state that "D is actually a rigid disk". (ii) The observer of D notices that the relationship which connects the circumference and diameter of D is not that of euclidean spaces in other words the ratio between these two quantities is not the number pi. We will show that (i) is questionable. Indeed, consider two material points which are fixed on D and such that one is on the center and the other on his circumference. Then: (a) By assumption, since D is a rigid body according to R, this inertial frame can assert that the spatial distance between these two points does not vary in time. (b) The Lorentz transformation allows to state that there is at least one inertial frame R' who can say that the spatial distance between these two points varies in time in other words D is a deformable body according to R'. Because R assert that D is an indeformable body and because R' asserts the opposite, knowing that all inertial frames are physically equivalent, it is impossible to express that there is an observer of D who notices that D is actually an indeformable body. Thus, (i) is questionable and the conclusion of Albert Einstein is wrong. To demonstrate (b) it is sufficient to choose R' as an inertial reference frame whose velocity vector v (with respect to R) is in the plane of D and is therefore orthogonal to the axis of rotation of D. Under these conditions, the transformation of Lorentz teaches that the contraction of the lengthes enters R and R' is maximal when the radius vector between both material points is colinear to v and this contraction of the lengthes enters R and R' is worthless when the radius vector between both material points is orthogonal to v. Finally, we know that the radius vector between the two material points travel alternately these two configurations because D is rotating. Cordially.