LiveMath vs Surface Explorer

A symbolic algebra and graphing platform for the rest of us - visual exploration and intuitive interaction without writing code. Looks like math. Feels like math. No programming headaches. Do algebra by picking up expressions and dragging or applying commands to them - you feel the tactile operations. Drag expressions onto graph windows to add them to the graph. Plot and compute: • Parametric and implicit curves and surfaces, including tubes • Differential equation solutions as numerical Flow plots • Inequalities plots for linear programming • Polygons and polyhedra with the Shapes plot • Embedded videos in notebooks • Full Unicode, including emoji, in math computations • Significantly improved integration and differentiation engines • Laplace Transform computations • Statistics and linear algebra built in, including SVD and Eigenfactor • Drag-and-drop matrix row operations for classroom presentation Free to read and interact with any premade notebook. LiveMath Pro unlocks adding new expressions and computations, saving and exporting. iPhone, iPad, Mac and Windows. Fifteen languages. LiveMath Pro is an auto-renewable yearly subscription. Payment is charged to your Apple Account at confirmation of purchase; the subscription renews automatically unless canceled at least 24 hours before the end of the current period. Manage or cancel in Settings. Terms of Use: https://www.apple.com/legal/internet-services/itunes/dev/stdeula/ Privacy Policy: https://www.livemath.com/privacy

Surface Explorer is a high-performance visualizer for intricate mathematical surfaces — 2D manifolds embedded in three- or four-dimensional space, and 3D slices of four-dimensional hypersurfaces — bringing abstract geometry to life with real-time GPU rendering. KEY FEATURES • Cross Section — slice four-dimensional hypersurfaces and watch their 3D sections change shape as you rotate them in 4D or slide the cutting plane along the fourth axis, even along a 4D camera path. • Ray Marching Engine — real-time rendering of implicit surfaces and signed-distance fields, with procedural displacement, transparency, adjustable shells, and a precise mode for high-degree equations. • Multi-Mesh Surfaces — build figures from several independent grids, each with its own color, transparency, texture and domain. • Geodesic Flow — explore intrinsic geometry on curved manifolds (S³, H²×R, SL(2,R) and more), integrating geodesics from initial conditions. • 4D Spatial Exploration — dedicated controls for hyperspatial rotation (Omega, Phi, Psi), projection, and 3D and 4D camera paths. • 4D Lighting Models — Directional, Observer, and Slice lighting designed for hyperspace. • Dynamic GLSL Scripting — write custom shaders for procedural textures and surface logic in the built-in editor. • Backgrounds — images and procedural effects, fixed on screen or wrapped around the scene as a sphere, cylinder or cube. • Audio-Visual Synthesis — synchronize geometric parameters with a mathematical sound synthesizer. • Video Recording — capture your explorations directly in the app and save them to your device. A library of ready-made presets ships with the app, from classic parametric surfaces to black-hole ergospheres, curved-space tori and slices of the 3-torus, together with a searchable built-in manual. Built with Qt and Metal for smooth, native performance on iPhone and iPad.