Conjugate Compositions in Even-Dimensional Affinely Connected Spaces without a Torsion

Let in even-dimensional a±nely connected space without a torsion A2m be given a composition Xm£Xm by the affinor a¯ ®. The affinor b¯ ®, determined with the help of the eigen-vectors of the matrix (a¯ ®), de¯nes the second composition Ym £ Y m. Conjugate compositions are introduced by the condition: the a±nors of any of both compositions transform the vectors from the one position of the composition, generated by the other a±nor, in the vectors from the another its position. It is proved that the compositions de¯ne by a±nors a¯ ® and b¯ ® are conjugate. It is proved also that if the composition Xm£Xm is Cartesian and composition Ym£Y m is Cartesian or chebyshevian, or geodesic than the space A2m is affine

One Application of the Informatics in the Descriptive Geometry

This work acquaints with a program for interactive computer training to students on the subject "Mutual intersecting of pyramids in axonometry ”. Our software is a set of three modules, which we call "student", "teacher" and "autopilot". It gives the final solution of the problem, the traceability of various significant moments in its solution and 3D-image of the finished composition of the two intersecting polyhedra, stripped of the working lines and subjected to rotation and translation

Intersection of Polyhedrons and a Plane with GeoGebra

Using GeoGebra, we present an innovative method for teaching of the intersection of polyhedrons with a plane using infinite points and the swap of finite and infinite points. The method presented is efficient and powerful, allowing one to generate solutions of a whole set of problems by solving one instance and using a pre-made applet at any stage of the solution process