内接在正方形内的最大三角形，该正方形内接在椭圆内
原文:https://www . geesforgeks . org/maximum-reuleaux-三角形-内接正方形-内接椭圆/
给定一个椭圆，其长轴和短轴分别为 2a & 2b ，该椭圆画出一个正方形，该正方形又画出一个三角形。任务是找到这个 reuleaux 三角形的最大可能面积。 例:
Input: a = 5, b = 4
Output: 0.0722389
Input: a = 7, b = 11
Output: 0.0202076
逼近 : As，椭圆内接正方形的边为， x = √(a^2 + b^2)/ab.请参考椭圆内接最大正方形的面积。 同样，在 reuleaux 三角中， h = x = √(a^2 + b^2)/ab 。 所以，地区的 reuleaux 三角，a = 0.70477h^2 = 0.70477((a^2+b^2)/a^2b^2)。 以下是上述方法的实施:
C++
// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an ellipse
#include <bits/stdc++.h>
using namespace std;
// Function to find the biggest reuleaux triangle
float Area(float a, float b)
{
// length of the axes cannot be negative
if (a < 0 && b < 0)
return -1;
// height of the reuleaux triangle
float h = sqrt(((pow(a, 2) + pow(b, 2))
/ (pow(a, 2) * pow(b, 2))));
// area of the reuleaux triangle
float A = 0.70477 * pow(h, 2);
return A;
}
// Driver code
int main()
{
float a = 5, b = 4;
cout << Area(a, b) << 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 Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an ellipse
import java.io.*;
class GFG
{
// Function to find the biggest reuleaux triangle
static float Area(float a, float b)
{
// length of the axes cannot be negative
if (a < 0 && b < 0)
return -1;
// height of the reuleaux triangle
float h = (float)Math.sqrt(((Math.pow(a, 2) + Math.pow(b, 2))
/ (Math.pow(a, 2) * Math.pow(b, 2))));
// area of the reuleaux triangle
float A = (float)(0.70477 * Math.pow(h, 2));
return A;
}
// Driver code
public static void main (String[] args)
{
float a = 5, b = 4;
System.out.println(Area(a, b));
}
}
// This code is contributed by anuj_67..
Python 3
# Python3 Program to find the biggest Reuleaux
# triangle inscribed within in a square
# which in turn is inscribed within an ellipse
import math;
# Function to find the biggest
# reuleaux triangle
def Area(a, b):
# length of the axes cannot
# be negative
if (a < 0 and b < 0):
return -1;
# height of the reuleaux triangle
h = math.sqrt(((pow(a, 2) + pow(b, 2)) /
(pow(a, 2) * pow(b, 2))));
# area of the reuleaux triangle
A = 0.70477 * pow(h, 2);
return A;
# Driver code
a = 5;
b = 4;
print(round(Area(a, b), 7));
# This code is contributed by chandan_jnu
C
// C# Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an ellipse
using System;
class GFG
{
// Function to find the biggest reuleaux triangle
static double Area(double a, double b)
{
// length of the axes cannot be negative
if (a < 0 && b < 0)
return -1;
// height of the reuleaux triangle
double h = (double)Math.Sqrt(((Math.Pow(a, 2) +
Math.Pow(b, 2)) /
(Math.Pow(a, 2) *
Math.Pow(b, 2))));
// area of the reuleaux triangle
double A = (double)(0.70477 * Math.Pow(h, 2));
return A;
}
// Driver code
static void Main()
{
double a = 5, b = 4;
Console.WriteLine(Math.Round(Area(a, b),7));
}
}
// This code is contributed by chandan_jnu
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP Program to find the biggest Reuleaux
// triangle inscribed within in a square
// which in turn is inscribed within an ellipse
// Function to find the biggest
// reuleaux triangle
function Area($a, $b)
{
// length of the axes cannot
// be negative
if ($a < 0 && $b < 0)
return -1;
// height of the reuleaux triangle
$h = sqrt(((pow($a, 2) + pow($b, 2)) /
(pow($a, 2) * pow($b, 2))));
// area of the reuleaux triangle
$A = 0.70477 * pow($h, 2);
return $A;
}
// Driver code
$a = 5;
$b = 4;
echo round(Area($a, $b), 7);
// This code is contributed by Ryuga
?>
java 描述语言
<script>
// Javascript Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an ellipse
// Function to find the biggest reuleaux triangle
function Area(a, b)
{
// length of the axes cannot be negative
if (a < 0 && b < 0)
return -1;
// height of the reuleaux triangle
let h = Math.sqrt(((Math.pow(a, 2) + Math.pow(b, 2))
/ (Math.pow(a, 2) * Math.pow(b, 2))));
// area of the reuleaux triangle
let A = 0.70477 * Math.pow(h, 2);
return A;
}
// Driver code
let a = 5, b = 4;
document.write(Area(a, b) + "<br>");
// This code is contributed by Mayank Tyagi
</script>
Output:
0.0722389
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