C语言中如何判断多边形边数为整数及实现内切圆多边形面积计算

Let's break down how to address both of your requirements step by step, with practical code examples:

1. Validating num_pol is an Integer (Not a Decimal) #

The key here is to avoid reading the side count directly as an integer—since decimal inputs (like 5.5) would get truncated to 5 and slip past your checks. Instead:

• Read the input as a double first
• Verify it has no fractional part
• Ensure the integer value is at least 3 (since a polygon needs 3+ sides)

Update your validation condition to include this check:

double num_pol_double;
int num_pol;

// Read side count as a floating-point value
printf("Enter number of sides: ");
scanf("%lf", &num_pol_double);

// Combined validation check (including decimal detection)
if (side_a < 0 || radius < 0 || diameter < side_a || 
    num_pol_double < 3 || num_pol_double != (int)num_pol_double) {
    printf("Invalid input! Number of sides must be an integer ≥3, and all values must be positive with diameter ≥ side length.\n");
    return 1; // Exit with error code
}

// Convert to integer now that we've confirmed it's valid
num_pol = (int)num_pol_double;

For strict floating-point precision (to handle tiny rounding errors), you can replace the equality check with:

fmod(num_pol_double, 1.0) > 1e-9

This checks if there's a remainder when divided by 1, which indicates a decimal value.

2. Calculating the Area of the Polygon with an Inscribed Circle #

Your formula is correct, but remember: C's tan() function uses radians, not degrees. Convert 180/num_pol degrees to radians by substituting π / num_pol (since 180° = π radians).

Implementation Steps: #

1. Define _USE_MATH_DEFINES before including math.h to access the M_PI macro
2. Use either pow(radius, 2) or the more efficient radius * radius for the squared radius
3. Compute the area with the adjusted formula

Here's the code snippet:

#define _USE_MATH_DEFINES
#include <math.h>

// ... after validating num_pol is an integer ...
double area = radius * radius * num_pol * tan(M_PI / num_pol);
printf("Area of the polygon with inscribed circle: %.2lf\n", area);

Complete Working Example #

Putting it all together into a full program:

#define _USE_MATH_DEFINES
#include <stdio.h>
#include <math.h>

int main() {
    double side_a, radius, diameter, num_pol_double;
    int num_pol;

    // Collect user inputs
    printf("Enter side length: ");
    scanf("%lf", &side_a);
    printf("Enter inscribed circle radius: ");
    scanf("%lf", &radius);
    printf("Enter diameter: ");
    scanf("%lf", &diameter);
    printf("Enter number of sides: ");
    scanf("%lf", &num_pol_double);

    // Validate all inputs
    if (side_a < 0 || radius < 0 || diameter < side_a || 
        num_pol_double < 3 || fmod(num_pol_double, 1.0) > 1e-9) {
        printf("Error: Invalid input!\n");
        printf("- Side length and radius must be positive.\n");
        printf("- Diameter must be greater than or equal to side length.\n");
        printf("- Number of sides must be an integer ≥3.\n");
        return 1;
    }

    num_pol = (int)num_pol_double;

    // Calculate and display area
    double area = radius * radius * num_pol * tan(M_PI / num_pol);
    printf("Calculated polygon area: %.2lf\n", area);

    return 0;
}

Compilation Note: #

When compiling with GCC, link the math library using the -lm flag:

gcc polygon_area.c -o polygon_area -lm

内容的提问来源于stack exchange，提问作者Amir J.