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