探討凸多邊形，由邊的等分點出發，其路徑平行邊之回到原出發點的研究

The Study of Exploring Convex Polygons About Its Paths from Parallel Edges (starting from the equal-division point of edges) to The Original Departure Point

何雅琪(Ya-Chi Ho)

指導教授 ： 吳裕振

中原大學/理學院/應用數學研究所/碩士(2021年)

https://doi.org/10.6840/cycu202100202

摘要

研究者主要研究凸多邊形由邊的等分點出發，走的路徑必須都要等分點對等分點，且要平行某一邊，回到原出發點的最短步數。
本論文主要內容有三：透過圖形探討凸正多邊形、國中部分提到的特殊四邊形(包含平行四邊形、長方形、菱形、箏形、梯形)、與一般凸多邊形的情況，並推論出正多邊形有其規律性且可推出一般式。若能將此推論方法融入國中八年級的幾何圖形課程內，相信可以訓練學生的邏輯性思考，引導出更多學習數學的樂趣!

關鍵字

凸多邊形 ； 平行 ； 最短步數 ； 等分點

並列摘要

The thesis is mainly based on analyzing convex polygons about its shortest path from the equal-division point of edges to the original departure point. The path must be point to point (equal division) and parallel with one another.
There are three contents of the research. First, exploring convex regular polygons through graphics. Second, discussing on the special quadrilaterals which are taught in junior high school, such as parallelogram, rectangle, rhombus, koto shape and trapezoid. Last, analyzing the circumstances of general convex polygons, and infer a conclusion that general polygons have their regularity. According to its regularity, we can come up with a formula. If this inference method can be integrated into the geometry curriculum of the eighth grade of junior high school, it’ll be feasible to train students to think logically and lead to more fun for them in learning mathematics.

並列關鍵字

Convex Polygon ； Parallel ； Shortest route ； Equal-division point

參考文獻

1.國中數學課本第二冊第三章，康軒出版社(2019)。

2.國中數學課本第二冊第三章，翰林出版社(2019)。

3. 國中數學課本第二冊第三章，南一出版社(2019)。

4.國中數學課本第四冊第四章，康軒出版社(2020)。

5.國中數學課本第四冊第四章，翰林出版社(2020)。