We present gclc/Wingclc— a tool for visualizing geometrical (and not only geometrical) objects and notions, for teaching/studying mathematics, and for producing mathematical illustrations of high quality. gclc uses a language gc for declarative representation of figures and for storing mathematical contents of visual nature in textual form. In gclc, there is a build-in geometrical theorem prove...

The buckling torque may be much less than the yield torque in very thin rectangular tubes under torsion. In this paper, simple closed-form formulae are presented for buckling analysis of long hollow rectangular tubes under torsion. By the presented formulae, one can obtain the critical torque or the critical angle of twist of the tube in terms of its geometrical parameters and material constant...

The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The using of skew-symmetric differential forms enables one to reveal a mechanism...

The action for the D = 10 type II Dirichlet super–p–branes, which has been obtained recently, is reconstructed in a more geometrical form involving Lorentz harmonic variables. This new (Lorentz harmonic) formulation possesses κ–symmetry in an irreducible form and is used as a basis for applying a generalized action principle that provides the superfield equations of motion and clarifies the geo...

Geometrical specification is the bridge to link function, design, manufacture and verification together for a product. The next-generation GPS utilizes duality principle to combine specification and verification of a geometrical product tightly, and to ensure its desired intention (functional requirements). This makes the geometrical specification of a product complete and unambiguous, to reduc...