This week we had watched 5 videos about varying subjects. They were different things that made a good mathematician. Each video took us through the habits of a mathematician. The habits that I took from the most were be willing to make mistakes, no one is a math person, speed is not the answer. These habits opened up our minds and also helped with our confidence in our math skills. Although we might have not known it these habits are inside all of our brains. The significance of Speed is not the answer and be willing to make mistakes our. Taking time in your work to acknowledge all possible answers and to revise your work will lead you to successful work where you can find the answer. Being able to take risks even if the outcome is the wrong answer is also amazing because it builds pathways in your brain that help you remember what you did wrong so you don’t do it again.
In this week of inspirational math we had done four separate problems in class that we did. The problem I will be continuing on with is Hailstone Sequences. I chose this problem because, I found it especially interesting that the original equation for this problem has been put into a computer program to test every single number and each and every number that has been used in the program has ended with the same pattern. I plan on furthering the problem and seeing if I can find any interesting patterns myself. Hailstone Sequences are two equations plus one starting number that causes a sequence that ends in 4,2,1. I am going to change the equations and see what happens to the sequences.
The original equations are, if your number is even divide by 2. If it is a negative number multiply by 2 and add 1
I am going to change the equations to if the number is even multiply by 2 subtract 1 and if you have a negative divide by 2 add .5
Original:
18: 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
40: 20, 10, 5, 16, 8, 4, 2, 1
9: 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
New Equations:
18: 71, 36, 71, 36, 71........
This set keeps on repeating itself and doesn’t show progression that ends with the same pattern. I will have to make a new equation and test to see if it works
My 2nd equation is going to be divide by 2 if it as an even number and multiply by 2 and add 3 if it is odd
18: 9, 15, 42, 21, 60, 30, 15, 42, 21, 60, 30, 15.....
40: 20, 10, 5, 12, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3....
9: 24, 12, 6, 3, 6, 3, 6, 3....
The patterns that I have seen here our the hailstone sequence with 18 will continue on to loop forever with 42 21 60 30 15. The other set of sequences loop with 6 and 3. I find this really intriguing that there are two different loops. It is even more astounding when every single number that has ever been used with the original equation ends in 4 2 1. A challenge that I had came across in this was getting an equation that just made the numbers loop in the same pattern no matter the starting number. This would occur within the first 3 numbers. I got past this by trying to make what I change more subtle to get my results. This ended up working for me. A habit that I had used while furthering this problem was speed is not key. I made sure to cut up the work for this assignment throughout the week and try not to overwork myself. This ended up with a finished product with minimal errors.
Reflection
This week of inspirational math has set a foundation for me as a student. It has given me different ways to cope with stress in math, and ways to approach problems. I feel like this week will help me with the rest of the year especially during the psat. It has shown me how much I can actually grow as a learner in math.
In this week of inspirational math we had done four separate problems in class that we did. The problem I will be continuing on with is Hailstone Sequences. I chose this problem because, I found it especially interesting that the original equation for this problem has been put into a computer program to test every single number and each and every number that has been used in the program has ended with the same pattern. I plan on furthering the problem and seeing if I can find any interesting patterns myself. Hailstone Sequences are two equations plus one starting number that causes a sequence that ends in 4,2,1. I am going to change the equations and see what happens to the sequences.
The original equations are, if your number is even divide by 2. If it is a negative number multiply by 2 and add 1
I am going to change the equations to if the number is even multiply by 2 subtract 1 and if you have a negative divide by 2 add .5
Original:
18: 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
40: 20, 10, 5, 16, 8, 4, 2, 1
9: 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
New Equations:
18: 71, 36, 71, 36, 71........
This set keeps on repeating itself and doesn’t show progression that ends with the same pattern. I will have to make a new equation and test to see if it works
My 2nd equation is going to be divide by 2 if it as an even number and multiply by 2 and add 3 if it is odd
18: 9, 15, 42, 21, 60, 30, 15, 42, 21, 60, 30, 15.....
40: 20, 10, 5, 12, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3....
9: 24, 12, 6, 3, 6, 3, 6, 3....
The patterns that I have seen here our the hailstone sequence with 18 will continue on to loop forever with 42 21 60 30 15. The other set of sequences loop with 6 and 3. I find this really intriguing that there are two different loops. It is even more astounding when every single number that has ever been used with the original equation ends in 4 2 1. A challenge that I had came across in this was getting an equation that just made the numbers loop in the same pattern no matter the starting number. This would occur within the first 3 numbers. I got past this by trying to make what I change more subtle to get my results. This ended up working for me. A habit that I had used while furthering this problem was speed is not key. I made sure to cut up the work for this assignment throughout the week and try not to overwork myself. This ended up with a finished product with minimal errors.
Reflection
This week of inspirational math has set a foundation for me as a student. It has given me different ways to cope with stress in math, and ways to approach problems. I feel like this week will help me with the rest of the year especially during the psat. It has shown me how much I can actually grow as a learner in math.