Circle simulation

🎯 Circle simulation – When Geometry comes alive
TUTBook™ – xBook: Intuitive, interactive, and explore Geometry through virtual reality experience

The book “Circle simulation” offers learners a completely new approach to the concepts of circle, chord, tangent, and the relationship between circles.
No longer dry formulas, all knowledge is dynamically simulated, dragged – dropped – and directly observed right on the screen.

🔹 Visualize every geometric concept
Learners are free to drag the center, change the radius, and adjust the position of two circles to see when they intersect, are externally tangent, or internally tangent.
Every change comes with automatic explanation and data display, helping to understand the nature of geometry instead of memorizing.

🔹 Explore the relationship between circular elements

• Observe how the chord changes when dragging point P.

• Visually compare the diameter and the largest chord.

• Practice determining the relative position between two circles (intersecting – tangent – non-intersecting).

🔹 Control Panel – real-time interaction
Learners can directly input the center coordinates, radius, or adjust using sliders to create new scenarios.
The system displays the status:

🟢 Two intersecting circles
🟣 Externally tangent
🟠 Internally tangent
🔴 Non-intersecting

🔹 Application in Teaching and Self-Study
The book supports both teachers in projecting dynamic lectures, and students in visual practice.
Each section has an automatic simulation mode, helping to illustrate definitions, formulas, and geometric rules more easily than ever.

📘 Highlights of the “Circle simulation”:

• Interactive 3D interface – direct drag and drop.

• Vivid explanation of the relationship between two circles.

• The data control panel helps students self-discover (or self-explore).

• Combine theory and simulation to understand deeply and remember longer.

📗 Subject: Mathematics – Geometry (Mathematics / Geometry)
🏷️ Published by: TUTBook™ on the xBook platform – Learn visually, understand by discovery.