there a local mapping that we use to approximate some in this case function so we have a blue function we want to approximate here and we approximate it we're gonna be interested in piecewise a fine or piecewise linear splines by just in this case four piecewise of fine mappings okay makes sense to everybody but really this yin-yang relationship between the partition and the mapping that that works the magic in splines there's two big classes of splines there's the really powerful splines for example free not splines this is where