The website "Explorable Flexagons" offers an interactive introduction to creating and manipulating flexagons, a type of folded paper polygon that reveals hidden faces when "flexed." It provides clear instructions and diagrams for building common flexagons like the trihexaflexagon and hexahexaflexagon, along with tools to virtually fold and explore these fascinating mathematical objects. The site also delves into the underlying mathematical principles, including notations for tracking face transitions and exploring different flexing patterns. It encourages experimentation and discovery, allowing users to design their own flexagon templates and discover new flexing possibilities.
Designer and maker Nick DeMarco created a simple yet effective laptop stand using just a single sheet of recycled paper. By cleverly folding the paper using a series of creases, he formed a sturdy structure capable of supporting a laptop. The design is lightweight, portable, easily replicated, and demonstrates a resourceful approach to utilizing readily available materials. The stand is specifically designed for smaller, lighter laptops and aims to improve ergonomics by raising the screen to a more comfortable viewing height.
Hacker News commenters generally expressed skepticism about the practicality and durability of the single-sheet paper laptop stand. Several questioned its ability to support the weight of a laptop, especially over extended periods, and predicted it would quickly collapse or tear. Some suggested that while it might work for lighter devices like tablets, it wouldn't be suitable for heavier laptops. Others pointed out the potential for instability and wobbling. There was some discussion of alternative DIY laptop stand solutions, including using cardboard or other more robust materials. A few commenters appreciated the minimalist and eco-friendly concept, but overall the sentiment was that the design was more of a novelty than a practical solution.
Summary of Comments ( 7 )
https://news.ycombinator.com/item?id=42961795
HN users generally praise the interactive flexagon explorer for its clear explanations and engaging visualizations. Several commenters share nostalgic memories of making flexagons as children, spurred by articles in Scientific American or books like Martin Gardner's "Mathematical Puzzles and Diversions." Some discuss the mathematical underpinnings of flexagons, mentioning group theory and combinatorial geometry. A few users express interest in physical construction techniques and different types of flexagons beyond the basic trihexaflexagon. The top comment highlights the value of interactive explanations, noting how it transforms a potentially dry topic into an enjoyable learning experience.
The Hacker News post "Explorable Flexagons: Learn to create and flex flexagons (2020)" has generated a moderate amount of discussion, with a handful of comments exploring different facets of flexagons.
One commenter reminisces about encountering flexagons as a child through a Scientific American article and expresses delight in the interactive nature of the linked resource. They highlight the value of the tool in providing a tangible experience, making the concept of flexagons much easier to grasp compared to static diagrams or written explanations. This commenter appreciates the ability to "play" with the flexagon virtually.
Another commenter focuses on the practical element, mentioning their use of flexagons as a teaching aid for children, demonstrating basic topological principles. They appreciate the hands-on nature of physical flexagons and view the digital exploration tool as a valuable complement.
A separate comment thread discusses the mathematical underpinnings of flexagons, touching upon group theory and its relevance to understanding the transformations and symmetries within the flexagon structures. This thread delves into the deeper mathematical concepts connected to these seemingly simple paper constructions.
Another commenter points out the connection between flexagons and magic tricks, suggesting that the surprising nature of their transformations lends itself well to illusionism.
Finally, one commenter briefly mentions other geometric paper constructions, expanding the conversation beyond flexagons and suggesting further avenues for exploration within the realm of paper folding and geometric manipulation. Specifically, they mention "kaleidocycles," suggesting they are also interesting.
While the comments aren't extensive, they offer diverse perspectives – from nostalgic recollections to mathematical analysis and practical applications – reflecting the multifaceted nature of flexagons and their appeal to a wide range of interests.