内接在等边三角形内接的正方形内的最大三角形
原文:https://www . geesforgeks . org/maximum-reuleaux-triangle-内接正方形-内接等边三角形/
这里给定的是一个边长为的等边三角形，它刻出一个正方形，正方形又刻出一个三角形。任务是找到这个 reuleaux 三角的最大可能面积。 举例:
Input : a = 5
Output : 3.79335
Input : a = 9
Output : 12.2905
逼近:我们知道内接在边长
等边三角形内的正方形的边是，x = 0.464 * aT5(请参考此处)。
同样，在 reuleaux 三角形中， h = x 。
所以，勒乌三角的面积 :
A = 0.70477*h2
= 0.70477*(0.464*a)2
以下是上述方法的实现:
C++
// C++ Program to find the biggest Reuleaux triangle
// inscribed within in a square which in turn
// is inscribed within an equilateral triangle
#include <bits/stdc++.h>
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 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 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
Python 3
# 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
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
// 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
$x = 0.464 * $a;
// area of the reuleaux triangle
$A = 0.70477 * pow($x, 2);
return $A;
}
// Driver code
$a = 5;
echo Area($a) . "\n";
// This code is contributed
// by Akanksha Rai
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 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
</script>
Output:
3.79335
版权属于：月萌API www.moonapi.com，转载请注明出处
