Through the using of combinatorial method that contains Sperner Lemma and the using of topology fundamental properties that contain continuity and Compactness,and the relationship between continuous transformation and the corresponding vector field,we provide a new method about the Brouwer fixed point theorem in three dimensions,which is different from the past algebraic topology proofs.

By using valuation theorem and Sperner lemma in topology,a result having a close relation with Stein s conjecture is obtained,that is, for any special polygon P , there are a family of special polygons { P n|n ∈N} such that lim n→∞P n=P , lim h→∞A(P n)=A(P) ,and P n can not be cut into an odd number of triangles of equal areas.