Arithmetic Quilts vs ER3D Euler Rotations in 3D

Arithmetic Quilts combines mathematics and art. Addition tables, multiplication tables, and tables based on more complex operations are displayed as colorful quilts by assigning a specific color to each positive whole number. This makes it much easier to discover and appreciate the beautiful patterns of mod arithmetic. Quilts defined by a recursive process can also be created.

Three-dimensional (3D) rotational kinematics are one of the most important, and yet also one of the most easily misunderstood topics of advanced mechanical engineering dynamics and trajectory simulation modeling. The ER3D mobile app aims to be a teaching aid for students and interested learners who want to understand these fundamental kinematics in an interactive and visually appealing setting, including in Augmented Reality (AR). Features of the app include: - Space Shuttle model for teaching a 3-2-1 rotation sequencee - Gyroscope model for teaching a 3-1-3 rotation sequence - Sliders to update 3-2-1 (yaw, pitch, and roll) or 3-1-3 (procession, nutation, and spin) angles - Globe Earth that may be rotated to visualize locations at different latitudes and longitudes - Context menus with text descriptions of the kinematic properties ER3D is free and open source, developed for iPhone, iPad, macOS, and VisionOS using SwiftUI and RealityKit.