Pieri's formula describes the intersection product of a Schubert cycle
by a special Schubert cycle on a Grassmannian. We present a new geome
tric proof, exhibiting an explicit chain of rational equivalences from
a suitable sum of distinct Schubert cycles to the intersection of a S
chubert cycle with a special Schubert cycle. The geometry of these rat
ional equivalences indicates a link to a combinatorial proof of Pieri'
s formula using Schensted insertion.