What does sp³ hybridisation mean and why is methane shaped like that?

In its ground state, carbon has electrons as 2s2 2p2, which suggests only two unpaired electrons. But carbon forms four equal bonds in methane, so it must rearrange. One 2s electron is promoted to the empty 2p orbital, giving four unpaired electrons. Then the one 2s and three 2p orbitals mix to form four identical orbitals called sp3 hybrid orbitals, each with the same energy and shape. Four equal orbitals repel each other and spread out as far apart as possible in three dimensions, which gives a tetrahedral shape with bond angles of 109.5 degrees. Each sp3 orbital overlaps with a hydrogen 1s orbital to form a C-H bond. So hybridisation explains both why all four C-H bonds are identical and why methane is tetrahedral, not flat.