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Graphics and Visualization

Understanding the Mathematical Foundations Behind Challenging Puzzle Design

image of a disentanglement puzzle. A blue square with a three by three grid with a red donut looped around one of the grid lines of the square. View from top and view from bottom.

02/01/2024 - Researchers from The University of Texas at Austin and McGill University delve into the mathematical intricacies of wire puzzle design. Focusing on geometrical aspects, they establish criteria for puzzle characteristics, emphasizing the importance of a challenging experience. The team introduces quantitative metrics to assess tunnel-bubble structures, demonstrating their effectiveness in distinguishing puzzles from non-puzzles. Their findings provide a foundation for an optimization model, shaping the future of wire puzzle design.

These Mathematical Techniques Could Help Design Shape-shifting Materials

A snapdragon flower petal grown from a cylinder. In each state, the colors show the growth factors of the top (left) and bottom (right) layer, and the thin black lines indicate the direction of growth. The top layer is viewed from the front, and the bottom layer is viewed from the back, to highlight the complexity of the geometries. (Credit Harvard SEAS)

05/08/2018 - UT College of Natural Sciences News | October 16, 2017 Nature has a way of making complex shapes from a set of simple growth rules. The curve of a petal, the swoop of a branch, even the contours of our face are shaped by these processes. What if we could unlock those rules and reverse engineer nature's ability to grow an infinitely diverse array of shapes?

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