PiBase: Topology 與 Drawing with Math 使用情況與統計

π-Base Topology is a community database of topological counterexamples. The database has: - Topological Spaces - Topological Theorems. - Topological Properties. - References (Books, Articles, Forums). Information inside the app: - Space, Theorem and Property descriptions. - Properties that are (and aren´t) satisfied by a given space. - Converses of theorems for which a given space is a counterexample. - Given a property, which spaces satisfy and don´t satisfy it. - Counterexamples for the converse of a given theorem. If the converse is True, a proof or reference is given. - Spaces that satisfy a given logical formula formed with properties (search by formula). - References.
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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. A number of future upgrades for the “Drawing with Math” are planned! Suggestions and any other feedback are welcome! Write to us at graphmath@aol.com.
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PiBase: Topology VS.
Drawing with Math

12月 17, 2024