Isosceles Triangular Plates for Pentagon and Decagon Geometry
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Solution Overview
Problem
Existing figure plate sets are inadequate for deepening the understanding of geometric thinking related to regular pentagons and decagons, as they do not effectively utilize similarity relations and angle relationships to enhance user comprehension.
Innovation Solution
A figure plate set comprising isosceles triangular plates with specific apex angles (108° and 36°) that can be combined to form various isosceles triangles and polygons, including regular pentagons and decagons, allowing users to experientially understand geometric relationships and similarity transformations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If traditional figure plates with basic shapes are used, then users can understand basic geometric shapes, but users cannot deepen their understanding of geometric thinking related to regular pentagons and decagons
Solution Approach 1:
The regular pentagon and decagon are segmented into multiple isosceles triangular parts with specific angles (36°, 72°, 108°). Users assemble these triangular segments to form the complete polygons, enabling them to understand the internal geometric structure and angle relationships of regular pentagons and decagons that cannot be grasped by studying the complete shape alone.
Solution Approach 2:
The figure plates are designed with specific local geometric properties - isosceles triangles with precise angle measurements (36°, 72°, 108°) that correspond to the internal angles of regular pentagons and decagons. These localized angular characteristics enable users to understand the specific geometric thinking required for these polygons.
2Shape
If five triangular plates made by equally dividing the regular pentagon are used, then the outer shape can be formed, but the understanding of similarity relations and angle relationships cannot be deepened
Solution Approach 1:
Instead of using five identical equilateral-like triangles, the invention employs isosceles triangles with specific local angle qualities (36°, 72°, 108°) that reflect the actual angular relationships in regular pentagons and decagons. This localized angular precision enables users to understand similarity relations and angle relationships while forming the outer shape.
Solution Approach 2:
The triangular plates are designed with specific angular parameters (36°, 72°, 108°) that are mathematically related to the geometry of regular pentagons and decagons. By changing the angular parameters from equal division to these specific values, users can understand the true geometric relationships including similarity transformations between different polygon configurations.
3Adaptability or versatility
If a plurality of figure plates with arbitrary arrangements are provided, then various outer shapes can be formed, but the geometric thinking related to regular pentagons and decagons cannot be deepened
Solution Approach 1:
The figure plates maintain versatility for forming various shapes while incorporating specific local angular qualities (36°, 72°, 108°) in the isosceles triangular designs. This enables users to explore diverse geometric configurations while consistently engaging with the angular relationships characteristic of regular pentagons and decagons, deepening geometric thinking without limiting shape variety.
Solution Approach 2:
The isosceles triangular plates with specific angles serve multiple functions: they can form regular pentagons, decagons, and various other geometric shapes. This multi-functionality allows users to deepen their understanding of regular pentagon and decagon geometry while maintaining the versatility to explore other geometric configurations, addressing both specificity and adaptability requirements.
Data Source
AI summary
The present invention provides a figure plate set (10) for learning that comprises a first triangular plate (1) that has an isosceles triangular shape having an apex angle of 108° and base angles of 36°; and a second triangular plate (2) that has an isosceles triangular shape having an apex angle of 36° and base angles of 72°, wherein a length of isosceles sides (7, 8) of the first triangular plate (1) is same as a length of isosceles sides (14, 15) or a bottom side (16) of the second triangular plate (2), and a new triangular shape can be formed by combining the first triangular plate (1) and the second triangular plate (2).