The Collatz Conjecture
A mathematical conjecture is a statement or rule that is proposed, and likely true, but still unproven or disproven. A famous unsolved problem is mathematics is the Collatz Conjecture. It was first proposed by Lothar Collatz in 1937.
The conjecture is as follows:
For any positive integer, if it is even divide it by 2. If it is odd multiply it by 3 and add 1. Continue indefinitely. Eventually 1 will be reached. In fact, for every tested number an infinite cycle of 4, 2, 1 is reached.
The conjecture can be demonstrated in a program through a basic use of loops.
Basic Example
def collatz (num):
for iteration in range(1,100):
# If even, n / 2
if num % 2 == 0:
num /= 2
else:
# If odd, 3n + 1
num = (3 * num) + 1
print(num)
# Only accepts a positive integer
while (True):
num = int(input("Please enter a positive integer...\n"))
if num > 0:
break
collatz(num)
In addition to generating a sequence of Collatz numbers, it gets the number to begin the sequence from the user. Furthermore, a while loop is utilized to ensure the number is a positive integer. If you run this script, no matter the number you will always reach the 4,2,1 cycle. Keep in mind, the end of the range represents the number of iterations. Some numbers take more iterations to reach this cycle than others. so this range may need to be made larger depending on the number.
This project demonstrates that the ability to demonstrate some of the most unsolvable problems in math and science is now at your fingertips.
Further Reading and Watching
The Simplest Math Problem No One Can Solve - Collatz Conjecture