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A double or triple bond can only be formed if orbitals from the two bonding atoms overlap side by side, otherwise there'd be no space for electron bonding. This side by side alignment is a pi bond -- that's why in a non-single bond, the first bond is sigma and the rest are necessarily pi.
There must be a side by side overlap between orbitals in order for them to form double or triple bonds, this specific arrangement, wherein orbitals are bonded side by side as opposed to end to end, is referred to as pi bonding.
when you have double and triple bonds, the orbitals are overlapping side by side and this side by side overlap is called pi bonds. Everything overlapping is called pi bonds so the ones that are no overlapping, which only happens once is called sigma bonds.
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