Hailstone sequence
Investigation and Video watching / overview of activities and videos
The reason for this week's inspirational math was to get us in a creative mind where we can visualize the problems. We watched these Inspirational Mind Setting videos where they talked about failure not being a bad thing. It can be helpful because your brain is making a better connection to the synapses, which makes your brain grow and become better at the problem at hand. We worked on several kinds of problems: tiling an 11x13 rectangle, Squares to Stairs, Hailstone Sequences, and Painted Cube. These were done as table groups to show how each of us has our own ways of seeing visual work.
Messages that stuck with me
This week, we had watched inspirational videos. The video about making mistakes being a good thing is one of the biggest things that stuck in my head; when you grow up, you try to strive for perfection and in reality, making an error is helping you get to the perfection stage. Learning that people aren't born as math people was something that stuck with me because we typically see people that are really good with numbers. Sometimes I have struggling moments and hearing that makes me feel good knowing that I can get better at math. Ways that I can do so is to give myself harder topics to really make my brain grow and make better connections.
Problem that was chosen to be extended
For this week of inspirational math, I chose the Hailstone Sequence. It starts with a number you choose followed by a certain sequence. Divide by 2 if your number is even; multiply by 3 and add 1 if your number is odd. I really found the Hailstone Sequence really fascinating because it is one of those problems that still has not been answered. It is fascinating to see the numbers from the starting number to another and to see of their ordering has some kind of pattern throughout them. These patterns are really amazing to see because I started with the number 30 and it had a long line of numbers to reach 1, but I started a new row with 35 and it was much shorter. This has to be one of the things that really intrigue me because we have these numbers that are changing even though we had a smaller number and it was longer than the number that was larger than itself. Once I took the problem and tried to change the sequence, I started to change the amount it gets multiplied, divided, and added by. I started out with the origin sequence A. Then I tried to divide by 6, multiply by 5, and add 1 sequence B. Then I decided what would happen if all we affected was the adding side so the sequence looked like divide by 2, multiply by 3, add sequence C. With this sequence, I found a few fascinating things. If you look at the data below, you can see how sequence B uses decimals instead of whole numbers. If you look at sequence C, you will be noticed that it will never actually reach 1 because it will start to repeat 12, 6, 3.
A.) 30, 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1
Divide by 2 if even/ Multiply by 3 adds 1 if odd
B.) 30, 5, 26, 4.333, 0.7222
Divide by 6/ Multiply by 5 add 1 if odd
C.) 30, 15, 48, 24, 12, 6, 3, 12, 6, 3
Divide by 2/ Multiply by 3 add 3 if odd
One challenge that I had while working on the Hailstone Sequence would be trying to figure out how the sequence worked and how to make it change in a drastic way. The ways I was able to work around this was by changing certain parts of the sequence like in sequence B. I changed everything whereas in sequence C, I only changed the amount we add by. When working on this, we used so many habits of a mathematician. I really found myself starting small and working up to a larger piece of work. I noticed this the most because we have this sequence that has to be completed and starting with the root number and building your way up, the order that's created is the best way to make sure this is fully finished.