正多边形的圆内切、外接时,其几何尺寸

n—多边形的边数

C—多边形的边长

R—外接圆半径

r—内切圆半径

A—多边形的面积

n

C

R

r

A

3

1.732R

3.464r

0.577C

2.000r

0.289C

0.500R

0.433C²

1.299R²

5.196r²

4

1.414R

2.000r

0.707C

1.414r

0.500C

0.707R

1.000C²

2.000R²

4.000r²

5

1.176R

1.453r

0.851C

1.236r

0.688C

0.809R

1.721C²

2.378R²

3.633r²

6

1.000R

1.155r

1.000C

1.155r

0.866C

0.866R

2.598C²

2.598R²

3.464r²

7

0.868R

0.963r

1.152C

1.110r

1.038C

0.901R

3.635C²

2.736R²

3.371r²

8

0.765R

0.828r

1.307C

1.082r

1.207C

0.924R

4.828C²

2.828R²

3.314r²

9

0.684R

0.728r

1.462C

1.064r

1.374C

0.940R

6.182C²

2.893R²

3.276r²

10

0.618R

0.650r

1.618C

1.052r

1.539C

0.951R

7.694C²

2.939R²

3.249r²

11

0.564R

0.587r

1.775C

1.042r

1.703C

0.960R

9.364C²

2.974R²

3.230r²

12

0.518R

0.536r

1.932C

1.035r

1.866C

0.966R

11.196C²

3.000R²

3.215r²

16

0.390R

0.398r

2.563C

1.020r

2.514C

0.981R

20.109C²

3.062R²

3.183r²

20

0.313R

0.317r

3.196C

1.013r

3.157C

0.988R

31.569C²

3.090R²

3.168r²

24

0.261R

0.263r

3.831C

1.009r

3.798C

0.991R

45.575C²

3.106R²

3.160r²

32

0.196R

0.197r

5.101C

1.005r

5.077C

0.995R

81.225C²

3.121R²

3.152r²

48

0.131R

0.131r

7.645C

1.002r

7.629C

0.998R

183.08C²

3.133R²

3.146r²

64

0.098R

0.098r

10.190C

1.001r

10.178C

0.999R

325.69C²

3.137R²

3.144r²