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A Suggestive Interface for Untangling Mathematical Knots.

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    This study introduces a user-friendly interface for untangling complex mathematical knots using suggested Reidemeister moves. It simplifies knot deformation analysis by guiding users through mathematically legal steps.

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    Area of Science:

    • Mathematics
    • Computational Topology
    • Computer-Aided Design

    Background:

    • Mathematical knots are complex structures often visualized as 3D ropes.
    • Untangling knots typically requires understanding and applying specific mathematical transformations.

    Purpose of the Study:

    • To present a user-friendly, sketching-based interface for simplifying the process of untangling mathematical knots.
    • To guide users through mathematically legal moves for knot deformation and analysis.

    Main Methods:

    • Developed a suggestive interface that proposes Reidemeister moves.
    • Implemented a Reidemeister move analyzer using Gauss code to predict necessary moves.
    • Constrained user input to ensure only legal moves are applied.

    Main Results:

    • The interface allows users to visualize, analyze, and deform mathematical knot diagrams.
    • It guides users to untangle knots to the fewest possible crossings.
    • Visual analysis of deformation sequences is enhanced by highlighting key moments.

    Conclusions:

    • The developed interface provides a novel way to study mathematical knots and their dynamics.
    • It significantly simplifies the exploration and understanding of knot deformation.
    • This tool offers a cleaner approach to analyzing complex knot structures.