一个正方形内可内切的最大六边形
给定一个正方形的边 a ，任务是找到可以在给定正方形内内接的最大六边形的边。 例:
输入: a = 6 输出: 3.1056 输入: a = 8 输出: 4.1408
逼近::假设，六边形的边为 x ，假设正方形的边为 a 分成更小的长度bT14】更大的长度 c 即 a = b + c 现在从图中我们看到，
b2+b2= x2这就给出了 b = x / √2 现在再来一次， d / (2 * x) = cos(30) = √3 / 2 即 d = x√3 ， c 2 + c 2 所以，a = x/√2+x√3/√2 =((1+√3)/√2) x = 1.932 * xT31】所以，六边形的边，x = 0.5176 * aT34】*
以下是上述方法的实现:
C++
// C++ Program to find the biggest hexagon which
// can be inscribed within the given square
#include <bits/stdc++.h>
using namespace std;
// Function to return the side
// of the hexagon
float hexagonside(float a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Side of the hexagon
float x = 0.5176 * a;
return x;
}
// Driver code
int main()
{
float a = 6;
cout << hexagonside(a) << endl;
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java Program to find the biggest hexagon which
// can be inscribed within the given square
import java.io.*;
class GFG {
// Function to return the side
// of the hexagon
static double hexagonside(double a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Side of the hexagon
double x = (0.5176 * a);
return x;
}
// Driver code
public static void main (String[] args) {
double a = 6;
System.out.println (hexagonside(a));
}
//This code is contributed by ajit.
}
Python 3
# Python 3 Program to find the biggest
# hexagon which can be inscribed within
# the given square
# Function to return the side
# of the hexagon
def hexagonside(a):
# Side cannot be negative
if (a < 0):
return -1;
# Side of the hexagon
x = 0.5176 * a;
return x;
# Driver code
a = 6;
print(hexagonside(a));
# This code is contributed
# by Akanksha Rai
C
// C# Program to find the biggest hexagon which
// can be inscribed within the given square
using System;
class GFG
{
// Function to return the side
// of the hexagon
static double hexagonside(double a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Side of the hexagon
double x = (0.5176 * a);
return x;
}
// Driver code
public static void Main ()
{
double a = 6;
Console.WriteLine(hexagonside(a));
}
}
// This code is contributed by Ryuga.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the biggest hexagon which
// can be inscribed within the given square
// Function to return the side of the hexagon
function hexagonside($a)
{
// Side cannot be negative
if ($a < 0)
return -1;
// Side of the hexagon
$x = 0.5176 * $a;
return $x;
}
// Driver code
$a = 6;
echo hexagonside($a);
// This code is contributed by akt_mit
?>
java 描述语言
<script>
// Javascript Program to find the biggest hexagon which
// can be inscribed within the given square
// Function to return the side
// of the hexagon
function hexagonside(a)
{
// Side cannot be negative
if (a < 0)
return -1;
// Side of the hexagon
let x = 0.5176 * a;
return x;
}
// Driver code
let a = 6;
document.write(hexagonside(a) + "<br>");
// This code is contributed by Manoj
</script>
Output:
3.1056
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