Galton Board vs Binomial Toolkit

Originally conceived in 1894 by Galton, the board consists of countless balls traversing down through a maze of pins. At every pin, they have a single choice: go left or right. Although the possibilities seem limitless, a pattern soon emerges. But how does this really work? This app is a simulation of the famous Galton board and is intended for educational purposes. You can adjust the board size, and send over a thousand balls bouncing down the board. On iPad you can even run multiple simulations simultaneously with multiple windows. The results are visualized by a bar chart. The Galton Board is closely related to Pascal's Triangle, Newton's binomium and probability theory in general. For experiment fidelity and performance, the balls do not collide with each other. I hope this app helps people grasp chance at least a little bit better. Love the app, or have improvements/suggestions? Let me know!

Binomial Toolkit helps students learn, solve, and practice binomial expansion with clarity. Whether you are preparing for exams or reviewing algebra fundamentals, the app combines fast solving tools with guided learning features so you can understand every step, not just the final answer. Key Features • Quick Expand: Enter expressions like (x+2)^5 and get instant full expansion. • Step-by-Step Solutions: Learn how each term is formed using the binomial theorem. • Pascal's Triangle Explorer: Interactively inspect rows and coefficients. • Practice Mode: Train with beginner, intermediate, and advanced challenges. • History: Revisit recent calculations anytime. • Favorites (Premium): Save important expressions for fast access. • Clean Interface: Built for focused learning with smooth, student-friendly workflows. Free vs Premium • Free version includes core solving and learning tools with daily limits for selected features. • Premium is a one-time purchase that removes ads and unlocks full access. Who is this for? • High school and college students • Teachers and tutors • Anyone practicing algebra and binomial theorem Make binomial expansion simpler, faster, and easier to understand with Binomial Toolkit.