Cycloids, Billiards, Lissajou: Using the Computer to Visualize Irrational Numbers, and What Can This Be Good For

Barabash, Marita

doi:10.1023/b:ijco.0000021933.32305.f2

Cited by 5 publications

(2 citation statements)

References 1 publication

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“…A curve is called a hypocycloid [7][8] if it is described by a point of the perimeter of a circle, while this circle rolls along the inside of another fixed circle without sliding, as shown in Fig. 1.…”

Section: A Hypocycloid Characteristicmentioning

confidence: 99%

Notice of Retraction: Finite element modeling and analysis for key parts of a new type internal combustion engine

Nie

2010

2010 International Conference on Computer Application and System Modeling (ICCASM 2010)

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Based on hypocycloid characteristic and transmission principle, a new kind of hypocycloid energy transformation mechanism was proposed.This new mechanism could realize the transformation between rectilinear movement of piston and rotating movement of crank and eliminate the piston sideforce. And the prototype and FEM model for the new mechanism was built by Solidworks and ANSYS software. Then the analysis and optimization for their intension and stiffness were carried out. The stress distribution and strain distribution of the key parts were obtained under the maximum exerted force. Further more, the safety factor was obtained and the strength evaluation was performed. The result shows, the intension and stiffness of the new mechanism is adequate. And the simulation results established the important theoretical foundation for further study of the new type hypocycloid energy transformation mechanism.

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Section: A Hypocycloid Characteristicmentioning

confidence: 99%

Notice of Retraction: Finite element modeling and analysis for key parts of a new type internal combustion engine

Nie

2010

2010 International Conference on Computer Application and System Modeling (ICCASM 2010)

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“…If the pitch circle (reference circle) of the planetary gear is regard as the rolling circle and the pitch circle (reference circle) of the ring gear is regard as the fixed one, a trajectory of a point fixed in the pitch circle of the planetary gear is a hypocycloid [7]. Consequently, a new type hypocycloid mechanism for power transmission can be designed according to above hypocycloid characteristic, as shown in Fig.1 …”

Section: A Mechanism Principlementioning

confidence: 99%

Virtual prototyping of the new type hypocycloid energy transformation mechanism

Xue

Huang

et al. 2009

2009 International Conference on Information and Automation

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This paper aimed at proposing a new hypocycloid mechanism to actually realize energy transformation between rectilinear motion and rotary motion. The 3D virtual prototype mechanism is presented and it's simplified to reduce the complexity of analysis. The kinematics and dynamics characteristics of this mechanism were studied. For obtaining motion characteristic of the parts in new mechanism, the motion parameters relationship between input and output was setup by the kinematics model. Based on Lagrange equation, the driving force of every joint for the new mechanism was calculated. It is conformed that calculation results were correct through dynamics simulation. All the above analytical models can provide intelligent control strategies for the application of the new mechanism to achieve the motion transformation between the rectilinear movement and rotary movement.

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Teachers’ professional development for inclusion of experimental mathematics and interactive resources in the classroom

Naftaliev,

Barabash

2024

ZDM Mathematics Education

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Information technology enhances the nature of mathematics as an empirical discipline, leading to an approach called “experimental mathematics” (EM). It fosters the use of technology-based interactive resources (IRs) in mathematics education, giving mathematics an experimental dimension and reflecting a tension between the empirical-inductive nature of IRs and formal mathematics (FM). Our qualitative research focused on professional development (PD) for IR-based teaching of EM intertwined with FM based on a threefold theoretical framework that combines the mathematical knowledge required by EM, the pedagogical functionality of IRs, and instrumental orchestration. The research analyzed 14 high school teachers’ documents generated in the course of a PD program, revealing the evolution of their orientation. We argue that teachers’ evolving orientation toward IR-based EM inclusion in school mathematics is the result of meticulous dynamic PD design implementing three key aspects framed by the threefold theoretical framework: teachers playing various roles during the PD, teacher-researcher collaboration, and theoretical support. The beginning of the evolution of the teachers’ orientation toward IR-based EM inclusion in school mathematics was made possible by a design grounded in the above theoretical framework and observed through its lens.

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Cycloids, Billiards, Lissajou: Using the Computer to Visualize Irrational Numbers, and What Can This Be Good For

Cited by 5 publications

References 1 publication

Notice of Retraction: Finite element modeling and analysis for key parts of a new type internal combustion engine

Notice of Retraction: Finite element modeling and analysis for key parts of a new type internal combustion engine

Virtual prototyping of the new type hypocycloid energy transformation mechanism

Teachers’ professional development for inclusion of experimental mathematics and interactive resources in the classroom

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