XSection vs Vectors and Planes

Learn how to construct cross sections of polyhedrons. Study different techniques, train yourself, and then solve geometric puzzles. > 105 tasks: from basics to challenges > 12 subjects to explore > Step-by-step instructions > 35 geometric terms in a glossary > Night mode > Easy to use > Develops your spatial imagination *** About *** XSection is an introduction to solid geometry. It teaches you how to perceive 2D representation of polyhedrons, lines, and planes from 3D Euclidean space. No calculations, a bit of theory, and a lot of practice. *** Is this game for you? *** XSection follows Euclidea/Pythagorea series of geometric games. With all these apps you can become a real Geometry Guru. *** All definitions at your fingertips *** If you forgot a definition, you can instantly find it in the app’s glossary. To find the definition of any term that is used in conditions of a problem, just tap on the Question (“?”) button in a problem statement. *** Main topics *** > Prisms, cubes, parallelepipeds, and cuboids > Pyramids and tetrahedrons > Diagonals of polyhedrons > Cross sections > Diagonal sections > Parallel and central projections > Method of traces > Method of inner projection *** Questions? Comments? *** Send in your inquiries and stay up-to-date on the latest XSection news at http://www.euclidea.xyz/

Vectors and Planes App helps visualize and understand 3D linear and quadric structures and their intersections. List of linear structures and combinations: 1. Two vector combination. 2. Plane. 3. Line and plane combination. 4. Two plane combination. 5. Three plane combination. Current list of quadric structures: 1. Two sphere combination. 2. Standard ellipsoid. 3. Ellipsoid in a form of positive-definite matrix. 4. Standard cone. 5. Cone in a form of indefinite matrix. 6. 1-sheet hyperboloid. 7. 1-sheet hyperboloid in a form of indefinite matrix. 8. 2-sheet hyperboloid. 9. 2-sheet hyperboloid in a form of indefinite matrix. 10. Standard cylinder. 11. Cylinder in a form of positive-semidefinite matrix. 12. Hyperbolic paraboloid. 13. Elliptic paraboloid. Current list of combinations of quadric and linear structures: 1. Matrix ellipsoid and line. 2. Standard ellipsoid and plane. 3. Matrix ellipsoid and plane. 4. Matrix cone and line. 5. Standard cone and plane. 6. 1-sheet hyperboloid in matrix form and line. 7. 2-sheet hyperboloid in matrix form and line. 8. Matrix cylinder and line. 9. Elliptic paraboloid and line. 10. Hyperbolic paraboloid and line. Interactive 3D graphs are provided for all of the above. Step by step calculation algorithms are provided for all intersection point sets. Many of the algorithms are based on Linear Algebra concepts. Those, in turn, are explained in our “Matrix Solver Step by Step” app. Version 10 was completely redesigned. Developers hope to get feedback from users at graphmath@aol.com.