Using Origami to Promote Geometric Communication

2003 ◽  
Vol 9 (4) ◽  
pp. 222-229
Author(s):  
Rebecca R. Robichaux ◽  
Paulette R. Rodrigue
Keyword(s):  
Geometric Modeling ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Middle School Mathematics ◽  
Mathematics Lesson ◽  
Mathematical Arguments ◽  
Spatial Sense ◽  
Teaching Geometry ◽  
Geometric Concepts

Rigami has been used frequently in teaching geometry to promote the development of spatial sense; to make multicultural connections with mathematical ideas; and to provide students with a visual representation of such geometric concepts as shape, properties of shapes, congruence, similarity, and symmetry. Such activities meet the Geometry Standard (NCTM 2000), which states that students should be engaged in activities that allow them to “analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships” and to “use visualization, spatial reasoning, and geometric modeling to solve problems” (p. 41). This article begins with an explanation of the importance of communication in the mathematics classroom and then describes a middle school mathematics lesson that uses origami to meet both the Geometry Standard as well as the Communication Standard.

Bringing Dynamic Geometry to Three Dimensions

2015 ◽  
pp. 68-99
Author(s):  
Nicholas H. Wasserman
Keyword(s):  
Teaching And Learning ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Dynamic Geometry ◽  
State Standards ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Common ◽  
K 12

Contemporary technologies have impacted the teaching and learning of mathematics in significant ways, particularly through the incorporation of dynamic software and applets. Interactive geometry software such as Geometers Sketchpad (GSP) and GeoGebra has transformed students' ability to interact with the geometry of plane figures, helping visualize and verify conjectures. Similar to what GSP and GeoGebra have done for two-dimensional geometry in mathematics education, SketchUp™ has the potential to do for aspects of three-dimensional geometry. This chapter provides example cases, aligned with the Common Core State Standards in mathematics, for how the dynamic and unique features of SketchUp™ can be integrated into the K-12 mathematics classroom to support and aid students' spatial reasoning and knowledge of three-dimensional figures.

Geometric Modeling and Robust Control of a Gyroscopic System

2015 ◽  
Author(s):  
Diego Colón ◽  
Bruno A. Angelico ◽  
Fabio Y. Toriumi ◽  
Paulo U. M. Liduário ◽  
José M. Balthazar
Keyword(s):  
Geometric Modeling ◽  
Three Dimensional ◽  
Control Technique ◽  
Loop Control ◽  
Control Moment Gyroscope ◽  
Differentiable Manifolds ◽  
Control Moment ◽  
Geometric Concepts ◽  
Multi Body ◽  
Gyroscopic Systems

Gyroscopic systems are multi-body systems which present coupled three dimensional motion. The configuration space and the state space are differentiable manifolds, and differential geometric concepts are frequently useful in the process of modeling. This paper deals with a Control Moment Gyroscope (CMG), which is not asymptotically stable, so it needs a stabilizing control law. We apply a new methodology of modeling kinematics and dynamics of rigid multi-body systems, based in the concept of Cartan’s connection and covariant derivative. The systems has two inputs (torques) and two outputs (angles) that will be controlled by a robust linear closed-loop control technique (LQG/LTR). Experimental results are presented in order to validate the proposal.

Advances in FEMN: The Code for Nuclear Noise Analysis Based on ICEM-CFD

2018 ◽  
Author(s):  
Baoxin Yuan ◽  
Herong Zeng ◽  
Wankui Yang ◽  
Songbao Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Geometric Modeling ◽  
Noise Analysis ◽  
Three Dimensional ◽  
Noise Spectrum ◽  
Benchmark Problem ◽  
Reactor Physics ◽  
Icem Cfd ◽  
Element Method

The finite element method based on unstructured mesh has good geometry adaptability, it has been used to solve reactor physics problems, manual description of geometric modeling and meshing makes the current finite element code very complicated, it greatly restricts the application of this method in the numerical calculation of reactor physics. Using the CAD pre-processing software ICEM-CFD, three dimensional geometry is divided into tetrahedral or hexahedral meshes, two dimensional geometry is divided into triangular or quadrilateral meshes, the main code of neutron calculation for nuclear noise analysis based on finite element method is developed. The steady state parameters are calculated and tested through benchmark problem, the test results show that the code has the corresponding computing capabilities. Finally, the neutron noise spectrum is calculated for the 3D PWR benchmark problem published by IAEA, and the noise distribution under given frequency is given.

Kinematics of Meshing Surfaces Using Geometric Algebra

2003 ◽  
Author(s):  
Scott M. Miller
Keyword(s):  
Geometric Algebra ◽  
Screw Theory ◽  
Three Dimensional ◽  
Normal Vector ◽  
The Past ◽  
Geometric Concepts ◽  
Vector Algebra ◽  
The Common ◽  
Two Bodies ◽  
Theoretical Developments

As is well known, analysis of two surfaces in mesh plays a fundamental role in gear theory. In the past, special coordinate systems, vector algebra, or screw theory was used to analyze the kinematics of meshing. The approach here instead relies on geometric algebra, an extension of conventional vector algebra. The elegance of geometric algebra for theoretical developments is demonstrated by examining the so-called “equation of meshing,” which requires that the relative velocity of two bodies at a point of contact be perpendicular to the common surface normal vector. With surprisingly little effort, several alternative forms of the equation of meshing are generated and, subsequently, interpreted geometrically. Via straightforward algebraic manipulations, the results of screw theory and vector algebra are unified. Due to the simplicity with which complex geometric concepts are expressed and manipulated, the effort required to grasp the general three-dimensional meshing of surfaces is minimized.

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