Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface “finishes,” such as color, shading, cross-hatching or real or apparent texture.

Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface “finishes,” such as color, shading, cross-hatching or real or apparent texture.

An information processing method includes displaying a graph on a display screen of a display, in response to a user operation of specifying at least part of the graph, displaying an icon corresponding to a numerical value which is associated with the at least part of the graph on the display screen, in response to a user operation of selecting the icon, as at least part of a mathematical expression to execute calculation using the numerical value which is associated with the icon selected, displaying the numerical value or a variable indicating the numerical value which is associated with the icon on the display screen.

A rotational device is provided that enables a user to tangibly experience movement of a three-dimensional object in a four dimensional space. The rotational device includes an inner cubic frame assembly rotatably supported within an outer frame. The outer frame is formed from a series of wires connected at hubs to enable the user to view the movement of the inner cubic frame. A rotation mechanism may be provided to allow a user to rotate the inner cubic frame within the outer frame. A fixed internal cubic frame is mounted within the outer frame to support the inner cubic frame assembly. The inner cubic frame assembly includes an inner cubic frame and a sphere supported within the inner cubic frame. Reference points or nodes are provided on the inner cubic frame to provided visually traceable reference points as the inner cubic frame rotates within the outer frame and fixed internal cubic frame.

A rotational device is provided that enables a user to tangibly experience movement of a three-dimensional object in a four dimensional space. The rotational device includes an inner cubic frame assembly rotatably supported within an outer frame. The outer frame is formed from a series of wires connected at hubs to enable the user to view the movement of the inner cubic frame. A rotation mechanism may be provided to allow a user to rotate the inner cubic frame within the outer frame. A fixed internal cubic frame is mounted within the outer frame to support the inner cubic frame assembly. The inner cubic frame assembly includes an inner cubic frame and a sphere supported within the inner cubic frame. Reference points or nodes are provided on the inner cubic frame to provided visually traceable reference points as the inner cubic frame rotates within the outer frame and fixed internal cubic frame.

A workflow deployment system comprising at least one computing device having a memory unit and a first communication unit, and a plurality of software agents, wherein each software agent is installable on an electronic apparatus of the plurality of electronic apparatuses, wherein each software agent exchanges data with the electronic apparatus, wherein the memory unit stores workflow data related to a workflow for performing a task, the workflow comprising at least a first workflow package for a first part of the task, wherein the computing device assigns the first workflow package to the first apparatus, and to provide workflow data related to the first workflow package to the software agent of the first apparatus, to receive a problem solution request from the software agent, to perform, upon reception of the request, a workflow modification process; and to provide the customized data to the software agent of the first apparatus.

A workflow deployment system comprising at least one computing device having a memory unit and a first communication unit, and a plurality of software agents, wherein each software agent is installable on an electronic apparatus of the plurality of electronic apparatuses, wherein each software agent exchanges data with the electronic apparatus, wherein the memory unit stores workflow data related to a workflow for performing a task, the workflow comprising at least a first workflow package for a first part of the task, wherein the computing device assigns the first workflow package to the first apparatus, and to provide workflow data related to the first workflow package to the software agent of the first apparatus, to receive a problem solution request from the software agent, to perform, upon reception of the request, a workflow modification process; and to provide the customized data to the software agent of the first apparatus.

A mobius zipper learning model is described. The learning model can include a device comprising two 3D printed, hard plastic, semi-circular halves connected by a plastic zipper, which could also be 3D printed, with top ends connected to the frame halves. The zipper can be twisted and then reconnected at the bottom of the frames using embedded fasteners (e.g., hook and eyelet, snaps, or hook and loop). The Mobius zipper permits topologists and others to explore and demonstrate Mobius properties without having to seek and size workable material (usually paper) and/or successfully slice the selected material. Further, use of the Mobius Zipper results in no waste of material.

A mobius zipper learning model is described. The learning model can include a device comprising two 3D printed, hard plastic, semi-circular halves connected by a plastic zipper, which could also be 3D printed, with top ends connected to the frame halves. The zipper can be twisted and then reconnected at the bottom of the frames using embedded fasteners (e.g., hook and eyelet, snaps, or hook and loop). The Mobius zipper permits topologists and others to explore and demonstrate Mobius properties without having to seek and size workable material (usually paper) and/or successfully slice the selected material. Further, use of the Mobius Zipper results in no waste of material.

A variety of tools for demonstrating the mathematical properties is disclosed. In one embodiment, a demonstrator uses the tools to illuminate geometric relationships between objects in two and three-dimensional space. The tools may be a stationary exhibit or collected into a portable kit. Whether portable or stationary, the tools provide an easy to use, multi-functional, and visually captivating vehicle for demonstration of geometric properties.