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Plane and Frieze Symmetry Group Determination for Educational Purposes.

ABSTRACT: Three-dimensional symmetry plays a crucial role in crystallography education. The educational process can be facilitated by introducing the analysis of friezes and plane patterns such as parquets before presenting more sophisticated crystal structures. Analysis of the symmetry of parquets can serve as an opportunity to follow the full routine of finding symmetry group symbols through incorporation of a two-step procedure involving the determination of Bravais lattice type. The aim of this paper is to provide a simple description of the analysis of Bravais lattices and pattern symmetry that can be used by students as well as crystallography educators. The procedure is also summarized in the form of comprehensive tree charts. This form is easy to use and popular with students. It may also aid in the retention of certain facts concerning crystallographic methodology. Examples of patterns in frieze and parquet forms were taken from the interiors of Kórnik Castle (Poland), which exhibit Moorish-style ornamentation including dichroic patterns and constitute an important locus of cultural heritage capable of strengthening students' motivation.

SUBMITTER: Duda M

PROVIDER: S-EPMC7588026 | biostudies-literature | 2020 Aug

REPOSITORIES: biostudies-literature

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Plane and Frieze Symmetry Group Determination for Educational Purposes.

Duda Michał M Rafalska-Łasocha Alicja A Łasocha Wiesław W

Journal of chemical education 20200626 8

Three-dimensional symmetry plays a crucial role in crystallography education. The educational process can be facilitated by introducing the analysis of friezes and plane patterns such as parquets before presenting more sophisticated crystal structures. Analysis of the symmetry of parquets can serve as an opportunity to follow the full routine of finding symmetry group symbols through incorporation of a two-step procedure involving the determination of Bravais lattice type. The aim of this paper ...[more]

PMID: 33122864

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Project description:BackgroundBiomechanical knee asymmetry is commonly present after anterior cruciate ligament (ACL) reconstruction. Factors that could assist in identification of asymmetrical biomechanics after ACL reconstruction could help clinicians in making return-to-play decisions. The purpose of this study is to determine factors that may contribute to knee biomechanical asymmetry present after ACL reconstruction.HypothesisWe hypothesized that quadriceps strength and activation and patient-reported function would allow for identification of patients with symmetrical knee biomechanics.Study designCross-sectional study.Level of evidenceLevel 3.MethodsThirty-one subjects (18 women; time since ACL reconstruction = 284.4 ± 53.6 days) who underwent ACL reconstruction and were to return to activity were recruited. Participants completed bilateral assessments of isokinetic quadriceps strength, quadriceps activation using the superimposed burst technique, and biomechanical function testing during a single-leg forward hop. The International Knee Documentation Committee (IKDC) subjective knee form was also completed. Symmetry values were calculated for each variable. Decision trees were utilized to determine which input factors (quadriceps strength symmetry, quadriceps activation symmetry, IKDC score, age, sex, height, mass, graft type) were able to identify participants who had symmetrical knee flexion angles (KFAs) and extension moments. Angles and moments were considered symmetrical if symmetry values were ≥90%.ResultsQuadriceps strength and activation symmetry were able to predict whether a patient landed with symmetrical or asymmetrical KFAs, with thresholds of 77.2% strength symmetry and 91.3% activation symmetry being established. Patient-reported function and quadriceps strength were factors that allowed for classification of participants with symmetrical/asymmetrical knee extension moments, with thresholds of 89.1 for the IKDC and 80.0% for quadriceps strength symmetry.ConclusionsQuadriceps strength contributed to both models and appears to be a critical factor for achieving symmetrical knee biomechanics. High patient-reported function and quadriceps activation are also important for restoring knee biomechanical symmetry after ACL reconstruction.Clinical relevanceQuadriceps strength and activation and patient-reported function may be able to assist clinicians in identifying ACL patients with symmetrical/asymmetrical knee biomechanics.

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Plane and Frieze Symmetry Group Determination for Educational Purposes.

Publications

Plane and Frieze Symmetry Group Determination for Educational Purposes.

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