Collatz conjecture 101 (Explanation, examples, simulation)

Collatz conjecture 101 (Explanation, examples, simulation)

📄S𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗼𝗻 𝗳𝗶𝗹𝗲:
https://drive.google.com/file/d/1URb9lpQ7r7I62EA_wHA1ChbivS_fhNp1/view?usp=sharing

📫𝐎𝐮𝐫 𝐅𝐁 𝐏𝐚𝐠𝐞:
https://www.facebook.com/ScienceWorld-106933907791981

🎬𝐈𝐦𝐚𝐠𝐞𝐬, 𝐚𝐧𝐢𝐦𝐚𝐭𝐢𝐨𝐧𝐬 𝐚𝐧𝐝 𝐯𝐢𝐝𝐞𝐨𝐬 𝐜𝐫𝐞𝐝𝐢𝐭𝐬:
- Pixabay
- Pexel

📚𝐃𝐚𝐯𝐢𝐝'𝐬 𝐁𝐨𝐨𝐤𝐬
📕 𝗪𝗲𝗶𝗿𝗱 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝗜𝗻𝗳𝗶𝗻𝗶𝘁𝘆 𝗮𝗻𝗱 𝗕𝗲𝘆𝗼𝗻𝗱
(https://www.amazon.com/Weird-Maths-Agnijo-Banerjee-Darling/dp/1786072645)
📙 𝗪𝗲𝗶𝗿𝗱𝗲𝗿 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝘁𝗵𝗲 𝗣𝗼𝘀𝘀𝗶𝗯𝗹𝗲
(https://www.amazon.com/Weirder-Maths-At-Edge-Possible/dp/1786075083/)
📗 𝗪𝗲𝗶𝗿𝗱𝗲𝘀𝘁 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗙𝗿𝗼𝗻𝘁𝗶𝗲𝗿𝘀 𝗼𝗳 𝗥𝗲𝗮𝘀𝗼𝗻
(https://www.amazon.com/Weirdest-Maths-David-Darling/dp/1786078058/)
** The kindle versions are available
*** For more details : http://weirdmaths.com/

📄𝗧𝗿𝗮𝗻𝘀𝗰𝗿𝗶𝗽𝘁𝗶𝗼𝗻:
The so-called Collatz conjecture is easy to explain. Choose any positive integer. If it’s even, divide it by 2; if it’s odd multiply by 3 and add 1. Repeat this process with the result, and just keep on going.

For example, say we pick the number 5. It’s odd, therefore we multiply by 3 and add 1, which gives us 16. 16 is even so we divide it by 2 to get 8. Dividing by 2 again gives 4, dividing by 2 again gives 2, and finally dividing this by 2 we end up with 1. 1 is odd, so now we multiply by 3 and add 1 which gives 4. So we find ourselves in an infinite loop just repeating 4, 2, 1, 4, 2, 1, 4, 2, 1…

Nobody has found a starting number that doesn’t lead to the 4, 2, 1 loop. The Collatz conjecture is that every number, without exception, will lead to the repeating sequence 4, 2, 1. No one has been able to prove that the conjecture is true. Mathematicians have checked all the integers between 1 and 268 and found that they all lead to the 4, 2, 1 loop. But that doesn’t amount to a proof because there might be a number bigger than 268 which doesn’t obey the rule.

If we want to do our own checking, we don’t have to run through the calculations for every number. For example, if the starting number is 16, this was included in the calculations when we picked 5. If we choose 27 as a starting point, it turns out we’ve checked these numbers as well.

The main problem is we can’t develop a formula for the Collatz conjecture. This is because the calculations don’t have any pattern: they seem random. At least we haven’t found any regular pattern yet. So no one’s come up with a formula that includes all integers.

Let’s run a simulation using some different starting numbers and check if they obey the Collatz conjecture.

#collatz #conjecture #simulation

Видео Collatz conjecture 101 (Explanation, examples, simulation) канала ScienceWorld