The Expanded Mathematics book is a set of learning materials for students who want to deeply understand the core essence of Mathematics, instead of just memorizing formulas. The unique feature of this book is its directly integrated interactive simulation system: students can drag – drop – change parameters – observe the results to discover principles and theorems for themselves. This makes Mathematics easy to understand – engaging – logical.

Highlights

• Geometry & Algebra Simulations: tangents, similarity, line ratios, loci, and more are clearly illustrated through visual models.
• Step-by-Step Interaction: learn following a sequence (Step 1 → Step 2 → Step 3…) to develop systematic problem-solving thinking.
• Self-Discovery – No Rote Learning: formulas are the obvious result of what students observe themselves.
• Practical Applications: connections to measurements, maps, motion, architecture… to see the real value of Mathematics.
• Suitable for Self-Study & Classroom Teaching: teachers can project simulations directly for illustration.

Who should use it?

Typical Simulation Examples

Tangent of a Circle: Drag point C to change its position → D and E adjust accordingly → students observe the length relationships themselves → verify the theorem visually and directly.

Similar Triangles: Change a side → the ratio remains constant → students recognize the pattern → deep understanding, not rote memorization.

Benefits Gained

• Understand the core concepts instead of memorizing.
• Enhance thinking and reasoning skills.
• Be quick with new types of problems.
• Develop more daily interest in Mathematics.

Conclusion

Expanded Math Book opens the way to smart – visual – active learning in Mathematics. When students see the patterns themselves, Mathematics becomes easier to understand and more enjoyable.