刻在等边三角形内的正方形内的最大Reuleaux三角形

这里给出的是边长为a的等边三角形，其内接一个正方形，该内接点又接一个reuleaux三角形。任务是找到该reuleaux三角形的最大可能面积。
例子：

Input : a = 5 
Output : 3.79335

Input : a = 9
Output : 12.2905

方法：我们知道正方形的边内切成边长的等边三角形$a$是， x = 0.464 * a (请参阅此处)。
同样，在鲁洛三角形中， h = x 。
因此，Reuleaux三角形区域：

A = 0.70477*h2 
  = 0.70477*(0.464*a)2

下面是上述方法的实现：

C++

// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an equilateral triangle
#include 
using namespace std;
 
// Function to find the biggest reuleaux triangle
float Area(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    float x = 0.464 * a;
 
    // area of the reuleaux triangle
    float A = 0.70477 * pow(x, 2);
 
    return A;
}
 
// Driver code
int main()
{
    float a = 5;
    cout << Area(a) << endl;
 
    return 0;
}

Java

// Java Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an equilateral triangle
 
class GFG
{
     
// Function to find the biggest reuleaux triangle
static float Area(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    float x = 0.464f * a;
 
    // area of the reuleaux triangle
    float A = 0.70477f * (float)Math.pow(x, 2);
 
    return A;
}
 
// Driver code
public static void main (String[] args)
{
    float a = 5;
    System.out.println(String.format("%.5f", Area(a)));
}
}
 
// This code is contributed by chandan_jnu

Python3

# Python3 Program to find the biggest
# Reuleaux triangle inscribed within
# in a square which in turn is inscribed
# within an equilateral triangle
import math as mt
 
# Function to find the biggest
# reuleaux triangle
def Area(a):
 
    # side cannot be negative
    if (a < 0):
        return -1
 
    # height of the reuleaux triangle
    x = 0.464 * a
 
    # area of the reuleaux triangle
    A = 0.70477 * pow(x, 2)
 
    return A
 
# Driver code
a = 5
print(Area(a))
 
# This code is contributed by
# Mohit Kumar 29

C#

// C# Program to find the biggest Reuleaux
// triangle inscribed within in a square
// which in turn is inscribed within an
// equilateral triangle
using System;
 
class GFG
{
     
// Function to find the biggest
// reuleaux triangle
static float Area(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    float x = 0.464f * a;
 
    // area of the reuleaux triangle
    float A = 0.70477f * (float)Math.Pow(x, 2);
 
    return A;
}
 
// Driver code
public static void Main ()
{
    float a = 5;
    Console.WriteLine(String.Format("{0,0:#.00000}",
                                          Area(a)));
}
}
 
// This code is contributed by Akanksha Rai

---

Javascript

 
// Javascript Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an equilateral triangle
 
// Function to find the biggest reuleaux triangle
function Area( a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // height of the reuleaux triangle
    let x = 0.464 * a;
 
    // area of the reuleaux triangle
    let A = 0.70477 * Math.pow(x, 2);
 
    return A;
}
 
// Driver code
 
    let a = 5;
    document.write( Area(a).toFixed(5));
 
// This code contributed by Rajput-Ji
 

输出：

3.79335