Figure Plate Set for Geometric Thinking via Triangular Segmentation
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Solution Overview
Problem
Existing figure plate sets do not adequately facilitate deep understanding of geometric thinking related to triangles, particularly the relationships between side lengths, angles, and trigonometric functions, as they primarily focus on shape recognition rather than positional and relational understanding.
Innovation Solution
A figure plate set comprising a first triangular plate with 45°, 45°, and 90° angles and a second triangular plate with 30°, 60°, and 90° angles, allowing users to form acute-angled and obtuse-angled triangles, which helps experientially understand angle sums and side length ratios, and includes features like color coding and indicators for circumscribed and inscribed circles to enhance geometric thinking.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional figure plates with basic shapes are used, then shape recognition is improved, but deep geometric thinking understanding deteriorates
Solution Approach 1:
The figure plate is divided into multiple triangular regions with different angle measurements (30°, 45°, 60°, 90°) and side length ratios. This segmentation allows users to separately study and combine different geometric properties, enabling both basic shape recognition and deep geometric thinking about angle relationships and trigonometric functions.
Solution Approach 2:
Different regions of the figure plate are designed with specific local geometric qualities - some triangles have equal sides, others have specific angle measurements. This local quality differentiation allows users to understand how specific local properties (angle ratios, side length relationships) contribute to overall geometric understanding, rather than treating all shapes uniformly.
2Device complexity
If only basic triangle shapes are provided, then simplicity is improved, but understanding of angle relationships and trigonometric functions deteriorates
Solution Approach 1:
The figure plate is designed as a universal learning tool that serves multiple functions: basic shape recognition, angle measurement, side length ratio understanding, and trigonometric function visualization. By integrating these multiple functions into a single plate with carefully designed triangular regions, the device maintains simplicity while providing comprehensive geometric learning opportunities.
3Ease of operation
If figure plates focus on shape recognition only, then ease of use is improved, but operational understanding of geometric relationships deteriorates
Solution Approach 1:
The figure plate design enables dynamic exploration of geometric relationships by allowing users to mentally or physically combine different triangular regions to form new triangles with various angle combinations (e.g., 30°+45°=75°, 60°+45°=105°). This dynamic aspect transforms static shape recognition into an operational learning process where users actively construct and analyze geometric relationships.
Data Source
AI summary
The present invention provides a figure plate set for learning that comprises a first triangular plate (1) having an angle of 45°, an angle of 45°, and an angle of 90° and a second triangular plate (2) having an angle of 30°, an angle of 60°, and an angle of 90°. A length of one of two orthogonal sides (7, 8) of the first triangular plate (1) is same as a length of one of two orthogonal sides (14, 16) of the second triangular plate. A new triangular shape can be formed by combining the first triangular plate (1) and the second triangular plate (2).