Automated Generation of Geometric Theorems from Images of Diagrams

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial Intelligence (special issue on Geometric Reasoning

PCB Origami: A Material-Based Design Approach to Computer-Aided Foldable Electronic Devices

Origami is traditionally implemented in paper, which is a passive material. This research explores the use of material with embedded electronics such as printed circuit boards (PCB) as the medium for origami folding to create an interactive folding experience and to generate foldable objects with added functionalities. PCBs are produced as 2D shapes. By folding PCB arrays, it is possible to create 3D objects that contain electronic functions. Conductivity, output devices (such as light emitting diodes) and microcontroller computation can create an interactive folding experience, for user guidance and verification of the folding. We call this approach and methodology PCB origami. The work presented in this paper describes two unique interaction and fabrication techniques for creating and folding electronic materials. We demonstrate prototypes and present verification/evaluation strategies for guiding the user through the folding process

Origami Simulator: folding beyond paper

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Anna Puig Puig[en] This project aims to create a multi-platform application that allows the user to emulate the folding of a paper into an origami figure in a virtual environment. This application would start to solve the very time-consuming task in the origami world of diagramming, creating instructions for a specific model. In this proposal, a list of possible simple folds has been selected and each has been mathematically described with its constraints and requirements. A data structure that adapts to the complex origami folding process has been designed and a Unity application has been coded to allow the user to visualize and intuitively interact with it in a simple and clean graphic interface

Manufacture of Arbitrary Cross-Section Composite Honeycomb Cores Based on Origami Techniques

In recent years, the use of composite materials has drastically increased in the construction of aerospace components. In the case of sandwich panels, they have been extensively used as face sheets with aluminum honeycomb cores. Currently, space structures are increasing in size and require greater degrees of accuracy; hence, the use of composites as a core material is a natural progression. However, these composite core materials are not regularly used in sandwich construction. Compared to standard aluminum honeycombs, their manufacturing costs are very high and they have limited applications. Another problem is difficulty of machining. In the manufacture of complex-shaped parts, the cores must have some degree of curvature. For aluminum honeycombs, this can be done using a contour cutter, a 3-D tracer, and numerically controlled machines. However, burrs and buckling of cell walls present a difficult problem for surface accuracy. It is clear that the machining of composite cores requires more expensive and sophisticated systems. This study illustrates a new strategy to fabricate arbitrary cross-section honeycomb cores with applications of advanced composite materials. These types of honeycombs are usually manufactured from normal flat honeycombs by curving or carving, but the proposed method enables us to construct objective shaped honeycombs directly. The basic idea originates from the fold-made paper honeycombs proposed by authors, in which they attempted to apply origami and kirigami techniques to the creation of sandwich structures. Origami is the traditional Japanese art of paper folding. Kirigami is a variation of origami. We first introduce the concept of the origami honeycomb, which is made from single flat sheets with periodical slits resembling origami. In previous studies, honeycombs having various shapes were made using this method, and were realized by only changing folding line diagrams (FLDs). In this study, these 3D origami honeycombs are generalized by numerical parameters and fabricated using a newly proposed FLD design method, which enables us to draw the FLD of arbitrary cross-section honeycombs. Next, we describe a method of applying this technique to advanced composite materials. For partially soft composites, folding lines are materialized by silicon rubber hinges on carbon fiber reinforced plastic. Complex FLD patterns are then printed using masks on carbon fabrics. Finally, these foldable composites that are cured in corrugated shapes in autoclaves are folded into honeycomb shapes, and some typical samples are shown with their FLDs

A health-oriented emotion-centred origami-based PSS concept. A product-service system concept aimed to help users manage and reduce their stress more tangibly to improve their health and well-being.

Emotions have a fundamental role in the experience, perception, cognition, and development of people (Barrett et al., 2016; Plutchik, 2001). Negative emotions such as stress, if not managed appropriately, may be a risk factor in developing diseases such as dementia, cardiovascular problems, and depression, amongst others (Dum et al., 2016; Sandi et al., 2001). This interdisciplinary research presents OrigamEase, a health-oriented emotion-centred origami-based PSS concept to help adults manage their stress more tangibly, in response to its main research question: How can engineering design research contribute to improving people’s emotional health and wellbeing? OrigamEase was designed throughout this research, and its design and testing served to develop a health & well-being oriented, emotion-centred engineering design methodology (HWOEED). Therefore, the design of this methodology is the result of the structuring and ordering of the developmental process of exploring, conducting and streamlining the research, design and testing of OrigamEase. The design of OrigamEase (both the product and the service part) is based on the cognitive research stream of emotions and stress. Therefore, this research also aims to broaden the knowledge about the implications and management of the emotional experience of stress from an engineering and design point of view, complementing the available solutions for stress management through a structured, measurable, and tangible tool. The HWOEED methodology is influenced by Kansei Engineering and Design Thinking methodologies and integrates various engineering design research methods. However, this methodology proposes a different application of the integration of emotional considerations into engineering design processes., it seeks to improve the emotional experience of users to preserve and promote their health and well-being through specifically designed products, services or PSS. Therefore, these designs become the means and not the end of the engineering design efforts. Also, this methodology can be transferrable to other engineering design solutions. OrigamEase was tested with 114 adults between 18 and 70 years old through three pilot tests (n=43) and six trial tests (n=71) using a concurrent triangulation mixed methods design. Then the results from these tests were contrasted with two control tests (n=22). The results show that using OrigamEase reduced the measured stress levels of participants (self-reported, heart rate and electrodermal activity) significantly, supporting the experiment hypothesis. Stress levels were recorded before and after using OrigamEase; then, a repeated-measures t-test was applied to find if these differences were significant or not. After using OrigamEase, 73.2% of participants reported feeling less stressed (mean reduction=13.94%), 85.5% experienced a reduction in their heart rate (mean reduction=9.8 bpm), and 78.9% had a lower electrodermal activity (mean reduction= 10.8 points). The testing of OrigamEase served as an initial application validation of the HWOEED methodology. This research demonstrates that engineering and design fields not only can but need to contribute to research on emotions through interdisciplinary research. Emotions are a fundamental part of all human experiences, impacting a person’s health and well-being profoundly

The Formal Language and Design Principles of Autonomous DNA Walker Circuits.

Simple computation can be performed using the interactions between single-stranded molecules of DNA. These interactions are typically toehold-mediated strand displacement reactions in a well-mixed solution. We demonstrate that a DNA circuit with tethered reactants is a distributed system and show how it can be described as a stochastic Petri net. The system can be verified by mapping the Petri net onto a continuous-time Markov chain, which can also be used to find an optimal design for the circuit. This theoretical machinery can be applied to create software that automatically designs a DNA circuit, linking an abstract propositional formula to a physical DNA computation system that is capable of evaluating it. We conclude by introducing example mechanisms that can implement such circuits experimentally and discuss their individual strengths and weaknesses

A Sangaku Revived

In this paper we give an account on our mathematical and visual explorations inspired by a sangaku. First we introduce sangakus – traditional Japanese mathematical tablets. Then we give four examples of our static contemporary variants. Finally, we discuss in detail how a fifth sangaku led us to simulate the growth of water lilies, as a means of visualizing the problem. This approach lead to the mathematical field of circle packing, and made it possible to experience the visually intriguing process with different settings of the algorithm

Effectiveness and User Experience of Augmented and Mixed Reality for Procedural Task Training

Use of augmented reality (AR) and mixed reality (MR) technologies for training is increasing, due in part to opportunities for increased immersion, safer training, and reduced costs. However, AR/MR training effectiveness and user experience, particularly for head-mounted displays (HMDs), is not well understood. The purpose of this study is to investigate user perceptions and retention of AR/MR training delivered through a HMD for a procedural task. This two-part study utilized a within-subjects experimental design with 30 participants to determine how instruction method (paper vs. AR vs. MR) and time of procedure recall (immediate vs. post-test vs. retention) influenced completion time, perceived task difficulty, perceived confidence in successfully completing the task, workload, user experience, and trainee reactions. Results indicate differences between instruction methods for user experience and preference, with significantly higher user experience ratings for MR and lower preference rankings for AR. Findings also show decreased performance, increased perceived task difficulty, and decreased confidence as time since training increased, with no significant differences in these measures between instruction methods. Completion times and workload were also found to be comparable between instruction methods. This work provides insight into objective and subjective differences between paper-, AR-, and MR-based training experiences, which can be used to determine which type of training is best suited for a particular use case. Recommendations for appropriately matching training modalities and scenarios, as well as for how to successfully design AR/MR training experiences, are discussed