Developing a dynamic geometry task platform for accessing students' perceptions of geometric properties through analysis of example spaces

2015 ◽  
Author(s):  
Man-sang, Arthur Lee
Keyword(s):  
Dynamic Geometry ◽  
Geometric Properties ◽  
Example Spaces

Dynamic Geometry

1947 ◽  
Vol 40 (4) ◽  
pp. 151-157
Author(s):  
John F. Schacht ◽  
John J. Kinsella
Keyword(s):  
Dynamic Geometry ◽  
Geometric Properties ◽  
Tenth Grade ◽  
Geometric Elements ◽  
Flexible Models

In 1938 Lloyd wrote: “Traditionally, geometry has been studied in the tenth grade as a system of rigid, non-flexible elements. The author advances the thesis that all geometric diagrams should be assumed as flexible linkages. …” The writer felt that the use of motion made the geometric materials more lifelike and, hence, more interesting, He also believed that many geometric properties were elucidated more clearly by the flexible models than by similar static ones. Finally, he pointed out that the variance and invariance of certain geometric elements were more easily demonstrated by jointed rather than fixed devices.

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

Effect of 12 months of creatine supplementation and whole-body resistance training on measures of bone, muscle and strength in older males

2020 ◽  
pp. 026010602097524
Author(s):  
Darren G Candow ◽  
Philip D Chilibeck ◽  
Julianne Gordon ◽  
Emelie Vogt ◽  
Tim Landeryou ◽  
...  
Keyword(s):  
Bone Mineral Density ◽  
Resistance Training ◽  
Bone Mineral ◽  
Creatine Supplementation ◽  
Whole Body ◽  
Mineral Density ◽  
Geometric Properties ◽  
Section Modulus ◽  
Body Resistance ◽  
Older Males

Background: The combination of creatine supplementation and resistance training (10–12 weeks) has been shown to increase bone mineral content and reduce a urinary indicator of bone resorption in older males compared with placebo. However, the longer-term effects (12 months) of creatine and resistance training on bone mineral density and bone geometric properties in older males is unknown. Aim: To assess the effects of 12 months of creatine supplementation and supervised, whole-body resistance training on bone mineral density, bone geometric properties, muscle accretion, and strength in older males. Methods: Participants were randomized to supplement with creatine ( n = 18, 49–69 years, 0.1 g·kg-1·d-1) or placebo ( n = 20, 49–67 years, 0.1 g·kg-1·d-1) during 12 months of supervised, whole-body resistance training. Results: After 12 months of training, both groups experienced similar changes in bone mineral density and geometry, bone speed of sound, lean tissue and fat mass, muscle thickness, and muscle strength. There was a trend ( p = 0.061) for creatine to increase the section modulus of the narrow part of the femoral neck, an indicator of bone bending strength, compared with placebo. Adverse events did not differ between creatine and placebo. Conclusions: Twelve months of creatine supplementation and supervised, whole-body resistance training had no greater effect on measures of bone, muscle, or strength in older males compared with placebo.

scholarly journals Remarkable Classes of Almost 3-Contact Metric Manifolds

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 8
Author(s):  
Giulia Dileo
Keyword(s):  
Geometric Properties ◽  
New Class ◽  
Contact Metric Manifolds ◽  
Cosymplectic Manifolds ◽  
Sasaki Manifolds

We introduce a new class of almost 3-contact metric manifolds, called 3-(0,δ)-Sasaki manifolds. We show fundamental geometric properties of these manifolds, analyzing analogies and differences with the known classes of 3-(α,δ)-Sasaki (α≠0) and 3-δ-cosymplectic manifolds.

scholarly journals On 3-syzygy and unexpected plane curves

2021 ◽  
Author(s):  
Grzegorz Malara ◽  
Piotr Pokora ◽  
Halszka Tutaj-Gasińska
Keyword(s):  
Projective Plane ◽  
Plane Curves ◽  
Complex Projective Plane ◽  
Geometric Properties ◽  
Complex Projective

AbstractIn this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study 3-syzygy curve arrangements and we present examples that admit unexpected curves.

scholarly journals Mathematics in the Digital Age: The Case of Simulation-Based Proofs

2021 ◽  
Author(s):  
Moritz Lucius Sümmermann ◽  
Daniel Sommerhoff ◽  
Benjamin Rott
Keyword(s):  
Dynamic Geometry ◽  
User Interaction ◽  
Alternative Form ◽  
Sociomathematical Norms ◽  
Mathematical Proofs ◽  
Mathematical Simulations ◽  
Simulation Based ◽  
Actual Use ◽  
Theory Yield ◽  
Functions Of Proof

AbstractDigital transformation has made possible the implementation of environments in which mathematics can be experienced in interplay with the computer. Examples are dynamic geometry environments or interactive computational environments, for example GeoGebra or Jupyter Notebook, respectively. We argue that a new possibility to construct and experience proofs arises alongside this development, as it enables the construction of environments capable of not only showing predefined animations, but actually allowing user interaction with mathematical objects and in this way supporting the construction of proofs. We precisely define such environments and call them “mathematical simulations.” Following a theoretical dissection of possible user interaction with these mathematical simulations, we categorize them in relation to other environments supporting the construction of mathematical proofs along the dimensions of “interactivity” and “formality.” Furthermore, we give an analysis of the functions of proofs that can be satisfied by simulation-based proofs. Finally, we provide examples of simulation-based proofs in Ariadne, a mathematical simulation for topology. The results of the analysis show that simulation-based proofs can in theory yield most functions of traditional symbolic proofs, showing promise for the consideration of simulation-based proofs as an alternative form of proof, as well as their use in this regard in education as well as in research. While a theoretical analysis can provide arguments for the possible functions of proof, they can fulfil their actual use and, in particular, their acceptance is of course subject to the sociomathematical norms of the respective communities and will be decided in the future.

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