Python Numbers and Mathematical Operations

Practical Examples

Temperature Converter

def celsius_to_fahrenheit(celsius):
    """Convert temperature from Celsius to Fahrenheit."""
    return (celsius * 9/5) + 32

def fahrenheit_to_celsius(fahrenheit):
    """Convert temperature from Fahrenheit to Celsius."""
    return (fahrenheit - 32) * 5/9

# Example conversions
temp_c = 25
temp_f = celsius_to_fahrenheit(temp_c)
print(f"{temp_c}°C = {temp_f:.1f}°F")  # 25°C = 77.0°F

temp_f = 98.6
temp_c = fahrenheit_to_celsius(temp_f)
print(f"{temp_f}°F = {temp_c:.1f}°C")  # 98.6°F = 37.0°C

Simple Calculator

def calculator():
    """A simple command-line calculator."""
    print("Simple Calculator")
    print("Operations: +, -, *, /, ^ (power), % (modulo)")
    print("Enter 'q' to quit")
    
    while True:
        # Get user input
        expression = input("\nEnter expression (e.g., 2 + 3): ")
        
        if expression.lower() == 'q':
            print("Calculator closed.")
            break
        
        # Parse the expression
        try:
            # Split the expression into parts
            parts = expression.split()
            if len(parts) != 3:
                print("Invalid format. Please use 'number operator number'")
                continue
                
            num1 = float(parts[0])
            operator = parts[1]
            num2 = float(parts[2])
            
            # Perform the calculation
            if operator == '+':
                result = num1 + num2
            elif operator == '-':
                result = num1 - num2
            elif operator == '*':
                result = num1 * num2
            elif operator == '/':
                if num2 == 0:
                    print("Error: Division by zero")
                    continue
                result = num1 / num2
            elif operator == '^':
                result = num1 ** num2
            elif operator == '%':
                result = num1 % num2
            else:
                print(f"Unknown operator: {operator}")
                continue
                
            print(f"Result: {result}")
            
        except ValueError:
            print("Invalid numbers. Please enter valid numbers.")
        except Exception as e:
            print(f"An error occurred: {e}")

# Uncomment to run the calculator
# calculator()

Monte Carlo Pi Approximation

A classic example of using random numbers to approximate Pi:

import random
import math

def estimate_pi(num_points):
    """
    Estimate Pi using Monte Carlo method.
    
    Args:
        num_points: Number of random points to generate
    
    Returns:
        An approximation of Pi
    """
    points_in_circle = 0
    
    for _ in range(num_points):
        # Generate random point in the square [-1,1] x [-1,1]
        x = random.uniform(-1, 1)
        y = random.uniform(-1, 1)
        
        # Check if the point is in the unit circle
        if x**2 + y**2 <= 1:
            points_in_circle += 1
    
    # Area of circle / Area of square = pi/4
    return 4 * points_in_circle / num_points

# Estimate Pi with different numbers of points
for points in [1000, 10000, 100000, 1000000]:
    pi_estimate = estimate_pi(points)
    error = abs(pi_estimate - math.pi)
    print(f"Pi estimate with {points} points: {pi_estimate:.6f} (error: {error:.6f})")

Fibonacci Sequence Generator

def fibonacci_sequence(n):
    """
    Generate the first n Fibonacci numbers.
    
    Args:
        n: Number of Fibonacci numbers to generate
    
    Returns:
        A list of the first n Fibonacci numbers
    """
    sequence = []
    a, b = 0, 1
    
    for _ in range(n):
        sequence.append(a)
        a, b = b, a + b
        
    return sequence

# Generate and print the first 15 Fibonacci numbers
fib_numbers = fibonacci_sequence(15)
print(fib_numbers)  # [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]

# Print with their golden ratio approximations
print("\nFibonacci numbers and their ratios:")
for i in range(1, len(fib_numbers)):
    if fib_numbers[i-1] > 0:  # Avoid division by zero
        ratio = fib_numbers[i] / fib_numbers[i-1]
        print(f"F({i+1})/F({i}) = {fib_numbers[i]}/{fib_numbers[i-1]} = {ratio:.8f}")