# 「圖形板」的圖形軌跡之探討及其延伸

2007年

## 摘要或動機

Starting from the problem in AMC competition of Australia, we try to find out the
locus and its length when a point in a regular polygon rolls in a circle. The result
is that the locus has a wonderful and regular cycle.Next, we discuss the regularity
of the cycle when a regular polygon（n sides） rolls in another regular polygon. Furthermore,we
discuss the the equation of the locus by changing the radius and the angle of rolling.
we find out the argument function of the locus of a point inside when a a regular
polygon（n sides）rolls in another regular polygon （m sides）：
Aj is the summits of the
regular polygon（m sides）, Bjcorresponds Aj when a point inside the regular polygon (n sides) rolls,
) And then, we do some moving
simulation with some computer math software, such as Cabri Geometry、Mupad, etc.
We discuss the regularity of the locus and its equation of a point inside when some
special cycloids, like asteroids, cardioids, etc, roll in a certain condition. Moreover,
with the result of research 2, we create the “plate＂ and apply for a patent on it.
We hope to study math by playing games.

Aj 為 正m 邊形之各頂點、Bj 為正n 邊形中內部一點旋轉時對應 Aj 之點，

「為配合國家發展委員會「推動ODF-CNS15251為政府為文件標準格式實施計畫」，以及 提供使用者有文書軟體選擇的權利，本館檔案下載部分文件將公布ODF開放文件格式， 免費開源軟體可至LibreOffice 下載安裝使用，或依貴慣用的軟體開啟文件。」

「圖形板」的圖形軌跡之探討及其延伸 2 MB