Investigation of the spatial segment density distribution (SSDD) of a Gaussian coil, generated using an off-lattice Monte Carlo method, revealed detailed information about the instantaneous shape. This information is used to compare shape models based on the principal components of the radius of gyration with an analysis in terms of block copolymer shape employing characteristic separation parameters. To speed up an accurate analysis, an analytical procedure for calculating both eigenvalues and -vectors of the radius of gyration tensor is developed. The observed averaged shapes are essentially bimodal (dumbbell-like) and do not depend on chain length. The numerical results confirm that an ideal homopolymer is to a large extent segregated into two equal parts. The influences of the left and right parts of a chain on the total shape are presented. These results, together with the evaluation of the density of special segments and the distribution of the separation angle between the parts, reveal the approximation inherent to the biellipsoidal model (BEM) and explain why the SSDD results and the BEM are not compatible. Also, an average arrowhead-like shape (as predicted by the BEM) is not observed. A suggestion of the idea can be made visible, but only after artificial averaging.