Triangular Coordinate System for Complex Problem Visualization
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Solution Overview
Problem
Conventional rectangular coordinates fail to adequately represent complex problems with inherent non-linear relationships, lacking the necessary geometry to isolate and juxtapose cognitive units effectively, limiting the analysis and solution of complex issues across diverse domains.
Innovation Solution
A method employing a triangular frame of reference to visualize and analyze complex problems by iteratively adding sets of three parameters, allowing for a synoptic view of undisclosed dimensions and enabling the treatment of diverse domains like administrative, engineering, and manufacturing, using an equilateral triangle to decompose domains into corners, edges, and midpoints, thereby providing a qualitative and quantitative representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If rectangular coordinates are used to analyze complex problems, then quantitative manipulation is made easier, but the inherent geometry and non-linear relationships of the problem cannot be adequately represented
Solution Approach 1:
The patent transitions from two-dimensional rectangular coordinates to three-dimensional triangular coordinates, adding a new dimension of analysis. The triangular coordinate system introduces a third dimension that enables representation of non-linear relationships and contextual interdependencies while maintaining quantitative manipulation capability through defined geometric relationships between planes and points.
2Adaptability or versatility
If conventional rectangular coordinates are used, then a uniform matrix of causal factors can be created, but no inherent geometry or articulation exists to isolate cognitive units
Solution Approach 1:
The triangular coordinate system segments the analysis space into distinct geometric regions including corners, edges, and internal points, each representing different cognitive units or factors. This segmentation provides inherent geometric articulation that isolates and juxtaposes individual elements while maintaining their relationships within the overall triangular framework.
Solution Approach 2:
The triangular coordinate system introduces asymmetric geometric relationships that reflect the non-linear nature of complex problems. The unequal angles and side lengths of the triangle create inherent articulation points that allow selective isolation of cognitive units based on their specific contextual relationships, rather than treating all factors uniformly.
3Productivity
If the contextual world is represented using linearly independent coordinates, then mathematical analysis is simplified, but the non-linear nature of real-world contexts cannot be captured
Solution Approach 1:
The patent changes the fundamental parameters of the coordinate system from linearly independent rectangular coordinates to triangular coordinates with inherent geometric relationships. This parameter change enables the system to represent non-linear relationships through the geometric properties of the triangle (angles, side lengths, and spatial relationships) while maintaining mathematical tractability through defined geometric rules.
Data Source
AI summary
A computer-assisted method for analyzing a complex problem and creating an alpha-triadic representation with five degrees of articulation illustrating the relationships among its various parameters.