The discrepancy you observe between the calculated length using the Pythagorean theorem and the predictions of special relativity (SR) theory is due to the fact that the Pythagorean theorem is a Euclidean geometry concept that applies to objects moving at low speeds relative to the observer. Special relativity, on the other hand, introduces a new framework for describing the behavior of objects moving at high speeds, close to the speed of light.
In special relativity, lengths and distances are not simply measured using the Euclidean geometry of everyday life. Instead, there is a phenomenon called length contraction, where objects that are moving relative to an observer appear shorter in the direction of their motion. This effect becomes more pronounced as the object's velocity approaches the speed of light.
The discrepancy arises because the Pythagorean theorem assumes a constant, non-relativistic relationship between space and time, which is not valid at high speeds. Special relativity introduces the concept of spacetime, where space and time are combined into a four-dimensional framework. The relationships between length, time, and velocity are described by the Lorentz transformations, which take into account the effects of time dilation and length contraction.
To accurately calculate the length of a fast-moving object using special relativity, you need to employ the appropriate formulas and incorporate the principles of SR, rather than relying solely on the Pythagorean theorem. The length contraction predicted by special relativity has been experimentally confirmed in numerous studies, and it is a fundamental aspect of our current understanding of relativistic physics.