# 正N 邊形光圈之路徑追蹤

2004年

## 摘要或動機

1.根據[光的反射原理]，探討光圈之存在性，發現除定點P 在正2m 邊形或正三角形的頂點外，其餘皆有光圈。

2.將可形成光圈的路徑圖展開成[直線路徑圖]來探討。

3.由[直線路徑圖]，觀察到形成光圈的光線行進路徑，可能存在下列情況： (1)不通過正n 邊形的頂點，且產生路徑循環與不循環問題。 (2)通過正n 邊形的頂點。

4.發現正2m 邊形光圈皆為[完美光圈]。

5.發現正2m+1 邊形光圈之路徑與有理數、無理數之特質有關。即當s 值為有理數時，路徑會循環；當s 值為無理數時，路徑不循環。

The research is about [on Point P (including the angles) on the side of regular
polygons A1、A2…An , imagine the light goes from Point P to the closest side,
then bumps each side sequentially counterclockwise. After going a circle, it’s back
to Point P. The track is called “the circle of light.” I try to trace the light
track of the circle of light and other correlative questions.]

In this research, we suppose,and
we discuss the circle of light according counterclockwise direction:1.According
to the light reflective principles, we discuss whether the circle of light exists
or not. And then we discover that the circle of light really exists except when
Point P is on the angles of regular triangle or regular 2m polygons. 2.Spread out
the circle of light’s track to [rectilinear track.] 3.By [the picture of rectilinear
track], observing there are two kinds of the circle of light’s track: (1)If the
light doesn’t go through the angles of regular polygons, it can be a circulative
track or a non-circulative track. (2)When the light goes through the angles, it
stops. 4.We discover that all the circles of light in regular 2m polygons are [the
perfect circles of light.] 5.We discover the circle of light’s track is correlative
with rational numbers and irrantional numbers. When s is a rational number, the
track is circulative, if s is a irrantional number, the track is not circulative.

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