Torus Games vs Drawing with Math

Nine familiar games introduce children ages 10 and up to the mind-stretching possibility of a “multiconnected universe”. Games include: tic-tac-toe, mazes, crossword puzzles, word search puzzles, jigsaw puzzles, chess, pool and gomoku. While playing the games, kids develop an intuitive visual understanding of a model universe that is finite yet has no boundary. Players who master the games in 2D may enjoy the extra challenge of solving 3D mazes and playing 3D tic-tac-toe in multiconnected 3D spaces. Even though the games were designed with kids in mind, adults interested in topology, geometry and cosmology have also found them enjoyable and enlightening.

Our “Drawing with Math (Vector and Pixel Art)” app combines two main components: * uniquely versatile image editors, * various methods of linear transformations of both user-entered and system images. Image editors are available in vector and pixelated forms. The editors offer such options as: * free drawing, * entry of all standard shapes, * entry of regular Cartesian, polar, or parametric function into image editor. List of several visually appealing functions is provided. The App stores 10 most recent user entries for each type. Vector images can be linearly transformed in a variety of user-defined ways: * 2x2 matrix, * eigenvalues and eigenvectors, * rotation by degree, * reflection across a given vector. Pixelated images can be compressed by segments to user-selected rank. Mathematical context for the above is provided, whenever possible. Explanation of image compression algorithms requires significant understanding of Linear Algebra, and is available in our “Matrix Solver Step by Step” app. Several bonus images with animations and editable greeting cards are also available. Suggestions and any other feedback are welcome! Write to us at graphmath@aol.com.