EMpolarization vs Drawing with Math

EMpolarization is an app to aid teaching and learning of electromagnetics (EM) using mobile devices on the topic of wave polarization. The app is designed to provide interactive visualization to help students better understand wave polarization concepts. Through the use of the app, various polarizations could be explained better with the aid of 2D and 3D animations. Users are allowed to input various wave parameters to see the change in real time in the polarization ellipse and/or handedness. More advanced topics such as polarization ellipse parameters, Poincare sphere and Stokes parameters are also presented. For more graphical interaction with fun, the polarization state is further presented as a point located on Poincare sphere that coincides with the earth globe. For more information, please refer to the article "Teaching and Learning Electromagnetic Polarization using Mobile Devices," IEEE Antennas and Propagation Magazine, vol. 60, no. 4, pp. 112-121, 2018. User interface: - 3D view may be zoomed or rotated - double tap to revert to default view - touch on any underlined field to input/change value - use long slider to change the last field touched - use short slider to change animation speed - press 'Linear/Circular/Elliptical' for preset examples - press 'More' to switch views

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.