paradox”. This paradox consists in that, if we make a microscopical analysis of a sys- tem which treated as a rigid body has a finite number of degree of freedom, it turns out that it has an infinite number of degrees of free- dom and therefore, infinite heat capacities, which is absurd [10]. This contradiction was attributed to a flaw in classical mechanics. Our work suggests that rather, it is a result of not knowing how to count the number of degrees of freedom particle by particle. the difference between the state of lowest en- ergy (the ground state) and the state that fol- lows is such, that the leap from the ground state to the next may only be achieved at temperatures of approximately 3500 K. Thus, at room temperatures, the vibrational energy will remain in the ground state and its con- tributions to the total internal energy of the molecule is negligible. Something very dif- ferent occurs with polyatomic gases, where the molecules have several independent vi- bration modes. For some of this modes, the spacing between energy states is considerably smaller than for diatomic molecules. Hence, the vibrational energy will make an impor- tant contribution to the total internal energy of a polyatomic molecule at room tempera- ture, or even less. Once the vibrational en- ergy is considered, the predicted heat capac- ities have a very good correspondence with experimental values [8],[9]. This work may also imply that statements like the following are not correct. According to Herbert Goldstein, ”a rigid body with N particles can at most have 3 N degrees of free- dom”, as can be read in his Classical Mechan- ics textbook [3], in the chapter dealing with the kinematics of rigid body motion. How- ever, our analysis shows that the maximum number of degrees of freedom for any rigid body in three dimensional space is six. Anyhow, the aditional consideration of this quanticized vibrational energy does not modify the fact that the rotational and traslational energies of a gas molecule are cal- culated by treating this molecule as a rigid body. Treating molecules as rigid bodies is correct, but it had never been formally justi- fied. This work gives a formal justification to this procedure. In conclusion, we obtained expression which yield the number of degrees of free- dom of a rigid body constituted by n par- ticles in a three-dimensional space and we extended our results to an arbitrary number D of spatial dimentions. The results for the three-dimensional case disagree with those obtained by Albert Einstein and which ap- pear in [5]. We believe that with our analy- sis of the three-dimentional case we can jus- tify, formally, that a rigid non-linear poly- Furthermore, we believe that this pa- per clarifies the so-called ”degree of freedom 7