An inquiry-based learning environment was created for students to engage in argumentation. The instruction was enriched by use of a dynamic geometry software, namely GeoGebra, to assist students in visualizing and reasoning about 3D shapes. Rasmussen and Stephan's three-phase method (2008) was ...
VR may be especially beneficial for presenting 3D objects in a manner that supports collaborative embodied interactions, as learners can interact with 3D objects in a 3D world. New forms of VR enable multiple learners to manipulate the same mathematical shapes presented as dynamic objects projected i...
For most SE shapes, bλ can be generated from λ−1 successive dilations—that is, bλ=δb⌣(λ−1)(b). This is obviously not true with disk-shaped SE, where •λ={p:d(p,o)≤λ} with o the origin or center of the disk, and d the exact or approximated Euclidean ...
Mathematically, the section lines for each type of 3D shapes are continuous and they can be accurately defined. However, knitted fabrics are made of stitches of certain dimensions that must be taken into consideration when defining the mathematical models of the straight or curved fashioning line ...
For any incremental sheet forming, the fabrication of 3D shapes is done by making the tool move over the sheet and providing increments to the tool so that it can perform fabrication in different passes. For fabricating a conical wall, the increments are provided in vertical and horizontal direc...