Python Programming Essentials

import math

radius = float(input("Enter the radius of the circle: "))
area = math.pi * radius**2
print(f"The area of the circle is: {area:.2f}")

import math

leg1 = float(input("Enter the length of the first leg: "))
leg2 = float(input("Enter the length of the second leg: "))
hypotenuse = math.sqrt(leg1**2 + leg2**2)
print(f"The length of the hypotenuse is: {hypotenuse:.2f}")

import math

degrees = float(input("Enter an angle in degrees: "))
radians = math.radians(degrees)
print(f"The angle in radians is: {radians:.2f}")

import math

a = float(input("Enter the coefficient of x^2: "))
b = float(input("Enter the coefficient of x: "))
c = float(input("Enter the constant term: "))

discriminant = b**2 - 4*a*c

if discriminant < 0:
    print("The equation has no real roots.")
elif discriminant == 0:
    root = -b / (2*a)
    print(f"The equation has one real root: {root:.2f}")
else:
    root1 = (-b + math.sqrt(discriminant)) / (2*a)
    root2 = (-b - math.sqrt(discriminant)) / (2*a)
    print(f"The equation has two real roots: {root1:.2f} and {root2:.2f}")

n = int(input("Enter the number of terms: "))

a, b = 0, 1
for i in range(n):
    print(a, end=" ")
    a, b = b, a + b

n = int(input("Enter a non-negative integer: "))

factorial = 1
for i in range(1, n+1):
    factorial *= i

print(f"The factorial of {n} is: {factorial}")

a = int(input("Enter the first positive integer: "))
b = int(input("Enter the second positive integer: "))

while b != 0:
    a, b = b, a % b

print(f"The GCD of {a} and {b} is: {a}")

a = int(input("Enter the first positive integer: "))
b = int(input("Enter the second positive integer: "))

lcm = a*b
while a != b:
    if a < b:
        a += a
    else:
        b += b
    if a*b < lcm:
        lcm = a*b

print(f"The LCM of {a} and {b} is: {lcm}")

n = int(input("Enter the number of prime numbers to generate: "))

primes = []
num = 2
while len(primes) < n:
    is_prime = True
    for i in range(2, int(num**0.5) + 1):
        if num % i == 0:
            is_prime = False
            break
    if is_prime:
        primes.append(num)
    num += 1

print(f"The first {n} prime numbers are: {primes}")

b1 = float(input("Enter the length of the first base: "))
b2 = float(input("Enter the length of the second base: "))
h = float(input("Enter the height: "))

area = (b1 + b2) * h / 2
print(f"The area of the trapezoid is: {area:.2f}")

import math

radius = float(input("Enter the radius of the sphere: "))
volume = 4/3 * math.pi * radius**3
print(f"The volume of the sphere is: {volume:.2f}")

import math

x1 = float(input("Enter the x-coordinate of the first point: "))
y1 = float(input("Enter the y-coordinate of the first point: "))
z1 = float(input("Enter the z-coordinate of the first point: "))

x2 = float(input("Enter the x-coordinate of the second point: "))
y2 = float(input("Enter the y-coordinate of the second point: "))
z2 = float(input("Enter the z-coordinate of the second point: "))

distance = math.sqrt((x2-x1)**2 + (y2-y1)**2 + (z2-z1)**2)
print(f"The distance between the two points is: {distance:.2f}")

a = float(input("Enter the coefficient of x in the first equation: "))
b = float(input("Enter the coefficient of y in the first equation: "))
c = float(input("Enter the constant term in the first equation: "))

d = float(input("Enter the coefficient of x in the second equation: "))
e = float(input("Enter the coefficient of y in the second equation: "))
f = float(input("Enter the constant term in the second equation: "))

determinant = a*e - b*d

if determinant == 0:
    print("The system has no unique solution.")
else:
    x = (c*e - b*f) / determinant
    y = (a*f - c*d) / determinant
    print(f"The solution is: x={x:.2f}, y={y:.2f}")

# This program uses recursion to generate the first n terms of the Fibonacci sequence.

def fibonacci(n):
    if n <= 1:
        return n
    else:
        return fibonacci(n-1) + fibonacci(n-2)

n = int(input("Enter the number of terms: "))

for i in range(n):
    print(fibonacci(i), end=" ")