Related papers: Routh's Theorem for Tetrahedra

It is shown in our earlier paper that, using only tools of elementary geometry, the classical Routh's theorem for triangles can be fully extended to tetrahedra. In this article we first give another proof of Routh's theorem for tetrahedra…

We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.

We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

In this note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.

We give a geometric approach to the proof of the $\lambda$-lemma. In particular, we point out the role pseudoconvexity plays in the proof.

We show that the theorem of the three perpendiculars holds in any n-dimensional space form.

A tropical version of the Schauder fixed point theorem for compact subsets of tropical linear spaces is proved.

We prove a uniformization theorem in complex algebraic geometry.

We prove De Giorgi-Nash-Moser Theory using a geometric approach.

This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.

This paper proposes a totally constructive approach for the proof of Hilbert's theorem on ternary quartic forms. The main contribution is the ladder technique, with which the Hilbert's theorem is proved vividly.

We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

Using toric geometry we prove a B\'ezout type theorem for weighted projective spaces.

In Euclidean geometry, the Pythagorean theorem is presented as an equation involving three squares. This paper explores how analogous expressions may be identified in spherical and hyperbolic geometries.

This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.

We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.

We generalize Rado's extension theorem to complex spaces.

Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.