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📜  刻在等边三角形内的正方形内的最大Reuleaux三角形

📅  最后修改于: 2021-05-31 22:35:34             🧑  作者: Mango

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


PHP


Javascript


输出:
3.79335