摘要或動機

畢氏定理(a²+b²=c²)歷經25世紀，發現了數百種的幾何論證法；而畢氏定理演繹出的正三角形 ( (/4)
a²+(/4) b²=(/4)
c² )幾何分割研究，卻一直沒有人研究。因此，承襲著之前處理幾何問題的經驗，決定挑戰畢氏定理演譯的正三角形分割研究。本文研究兩正三角形，經切割後拼成另一大正三角形；期間以GSP及AutoCAD繪製分析幾何圖形，並建立了4種分割模式，得到了3段式「最佳分割模式」及準「通用分割模式」，提供這方面問題一個可應用於所有條件之完善解決方案。本研究成果豐碩，補足了相關領域的空檔，且可製成益智又富挑戰性之拼圖系列，不管用做教具或遊戲，對建立意至己和相關資料有莫大貢獻！

Twenty five centuries after its discovery, hundreds of proofs have been given for
the Pythagorean Theorem (a²+b²=c²). But, research about regular triangle dissection
extending from Pythagorean Theorem has always been lacking. So, based on previous
experience with geometric dissection problems, I have decided to do a research on
regular triangle dissection extending from Pythagorean theorem. This research dissects
two regular triangles and assembles them into a large regular triangle. Using GSP
and AutoCAD to draw and analyze geometric shapes, four dissection models and nine
dissection methods are constructed. The extreme values under all conditions are
also discussed, as are the best and generic dissection models. There is a Three-section
type “best dissection model” and a semi “generic dissection model.” offering a perfect
solution to this kind of problem that can be used under all conditions. This study
yields numerous results as well as filling in blanks in similar fields. It can also
be made into challenging jigsaw puzzles for educational or entertainment purposes.