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The construction of regular polygons with a compass and straightedge is a well-known task and this problem has interested mathematicians for a long time. In particular, for a long time they could not answer the question of whether is it possible to construct a regular 17-gon with a compass and straightedge. C. F. Gauss solved this problem in 1796.
openaire +2 more sources
Cyclic pursuit without coordinates: Convergence to regular polygon formations [PDF]
, 2014 -We study a multi-agent cyclic pursuit model where each of the identical agents moves like a Dubins car and maintains a fixed heading angle with respect to the next agent. We establish that stationary shapes for this system are regular polygons.
Maxim Arnold +2 more
core
Explaining the Origin of Negative Poisson's Ratio in Amorphous Networks With Machine Learning
Advanced Intelligent Discovery, EarlyView.This review summarizes how machine learning (ML) breaks the “vicious cycle” in designing auxetic amorphous networks. By transitioning from traditional “black‐box” optimization to an interpretable “AI‐Physics” closed‐loop paradigm, ML is shown to not only discover highly optimized structures—such as all‐convex polygon networks—but also unveil hidden ...
Shengyu Lu, Xiangying Shen
wiley +1 more source
Advanced Intelligent Discovery, EarlyView.AI‐based tools enable rapid characterization of bacterial ultrastructure in low‐dose cryogenic transmission electron microscopy. The envelope thickness tool quantifies membrane thickness and anisotropy. The flagella module analyzes filament morphology and detects cell‐flagella contacts.
Sita Sirisha Madugula +10 more
wiley +1 more source
Products of diagonal lengths in the regular polygon
, 2011 A regular polygon is scaled up in size so that its side length equals the length of some diagonal from the smaller polygon (the magnification diagonal). The diagonal lengths in the large polygon are seen to be sums of those in the smaller.
Hurley, Susan
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Proof without words: The vertex angle sum of a regular star polygon
, 2015 We visually prove the formula for the vertex angle sum of a regular star ...
Viglione, Raymond, Jakubowski, Matthew
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Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.Quantitative phase maps of single cells recorded in flow cytometry modality feed a hierarchical architecture of machine learning models for the label‐free identification of subtypes of ovarian cancer. The employment of a priori clinical information improves the classification performance, thus emulating the clinical application of liquid biopsy during ...
Daniele Pirone +11 more
wiley +1 more source
Products of diagonal lengths in the regular polygon
, 2016 A regular polygon is scaled up in size so that its side length equals the length of some diagonal from the smaller polygon (the magnification diagonal). The diagonal lengths in the large polygon are seen to be sums of those in the smaller.
Hurley, Susan
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Advanced Intelligent Systems, EarlyView.Origami turns a single silicone chamber into three different soft fluidic actuators. Crease angles alone decide whether it elongates, bends, or twists, and the fully folded chambers are cast monolithically in one day. Below 15 kPa, they reach 268% axial stretch, 72° bending, and 55° twist—no strain‐limiting layers, no rigid reinforcements, no vacuum ...
Alexia Le Gall +4 more
wiley +1 more source
Advanced Intelligent Systems, EarlyView.TwinX shows how a single interbody wire connecting two robots can support both integrated morphological reconfiguration and distributed wire‐mediated cooperation. When the robots dock, they reconfigure into different forms for locomotion and manipulation.
Shintaro Inoue +5 more
wiley +1 more source