Relation between the number of hybridised orbitals and the number of sigma bonds
March's Advanced Organic Chemistry (8th Ed.), has in its first chapter several tantalizing statements of the following variety;
Boron has only three valence electrons available to form bonds, hence the valence of 3. Any hybridization model must take this into account.
If ethene is examined... each carbon has three σ bonds, one to each of the three atoms. Therefore, sp2 orbitals are used to form those three bonds.
When carbon is connected to another carbon atom by a triple bond, as in ethyne... each carbon is connected to only two other atoms by a σ bond and hence uses sp hybridization.
The key is to understand that an atom forms two σ bonds for sp hybridization and three σ bonds for sp2 hybridization.
From reading that section, I understood the author's technique of determining hybridisation as;
1) You call those bonds that form when there's maximum overlap between the bonding orbitals "sigma bonds" , and such initial bonds that form while using the author's method, are arranged so that they do so at max overlap(the atoms are arranged in space so as to have such a configuration). 2) You make a bond each between the central atom and the others this way, and the remaining orbitals, if any contain electrons left over, interact to form pi bonds(and they're not sigma bonds because in the simple molecules examined, these leftover electrons aren't in orbitals that overlap terribly well. 724
So you make a name for them-pi bonds- and say they interact in the way they do).
Now, all these statements seem to border on stating that the number of sigma bonds formed and the number of hybridised orbitals are the same, and that kind of makes sense to me. By the method of determining hybridisation (detailed above as I understood it), $\pi$-bonds seem to be defined to be those that're formed from unhybridised orbitals.
But the author never makes such a statement. And it's a chemistry textbook. Cue the alarm bells in my head. ​
On looking it up, there isn't any statement on the internet of that sort, either, except for this Quora thread where the general consensus seems to be that yeah, pi bonds can be formed from hybridised orbitals. But I don't get how.
Is there any such rule? If not, why? 793