我们如何计算正多边形内最大圆的直径？

Question

我一直在接受以下编程练习的培训：Circles in Polygons。声明是：

You are the owner of a box making company.

Your company can produce any equal sided polygon box, but plenty of your customers want to transport circular objects in these boxes. Circles are a very common shape in the consumer industry. Tin cans, glasses, tyres and CD's are a few examples of these.

As a result you decide to add this information on your boxes: The largest (diameter) circular object that can fit into a given box.

我找到了以下公式：

取自：https://www.mathopenref.com/polygonincircle.html

所以要计算最大内切圆的直径，我们有：

sideLength / tan(180/numberOfSides)

我写了下面的代码：

public class Polygon {
    int sides;
    int sideLength;

    public Polygon(int sides, int sideLength) {
        this.sides = sides;
        this.sideLength = sideLength;
    }

    public double circleDiameter /**/(){
      double div = Math.toRadians(180/sides);
      System.out.println("div: "+div);
      double den = Math.tan(div);
      System.out.println("den: "+den);
      double diameter = sideLength / den;
      System.out.println("diameter: "+diameter);
      return diameter;
    }

}

但是我想知道为什么它没有通过一项测试并通过了其中两项。以下是从练习中提取的测试：

import static org.junit.Assert.assertEquals;
import org.junit.Test;

public class PolygonTest {

    @Test
    public void test1(){
        //Square with sides of 5 units
        Polygon poly=new Polygon(4, 5);
        assertEquals("5.000", String.format("%.3f", poly.circleDiameter()));
    }

    @Test
    public void test2() {
        //Octagon with sides of 9 units
        Polygon poly=new Polygon(8, 9);
        assertEquals("21.728", String.format("%.3f", poly.circleDiameter()));
    }

    @Test
    public void test3() {
        //Triangle with sides of 4 units
        Polygon poly=new Polygon(3, 4);
        assertEquals("2.309", String.format("%.3f", poly.circleDiameter()));
    }
}

并且我们的代码未通过八边形测试。痕迹是：

div: 0.3839724354387525
den: 0.4040262258351568
diameter: 22.275781680746665
expected:<2[1.728]> but was:<2[2.276]>

为什么代码会给出这个结果？我认为可能存在舍入误差。然而它太大了，我认为这是错误的公式。

我也看过：

Largest circle inside a non-convex polygon
Is there a simple algorithm for calculating the maximum inscribed circle into a convex polygon?

Answer 1

double div = Math.toRadians(180/sides);

当 sides 为 8 时，结果应为 22.5，但由于 180 和 sides 都是整数，因此使用整数数学进行计算，得出 22。

将一个或两个操作数更改为双精度数以确保没有意外舍入：

double div = Math.toRadians(180.0/sides);

我们如何计算正多边形内最大圆的直径？

How could we calculate the diameter of the largest circle inside a regular polygon?

java

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geometry

rounding