The Collatz Conjecture Project
The Collatz conjecture is an unsolved math conjecture to find if all “seed numbers” end in the same repeated pattern. The conjecture is named after Lothar Collatz; a famous German mathematician. The pattern starts with a seed number of one and and continues to infinity however we only explored seed values up to twenty-five. Depending on whether the seed number is even or odd you determine the next number in the column. If the number if even, then you must divide it by by two and put the result in the next box. If the number is odd, then you must add three, subtract by one, and divide that number by two. Now you should see a repetition of ones and twos. One of the methods we used to look for patterns was to replace all of the even numbers on the spreadsheet with a 0 and all of the odd numbers with a 1. This will allow you to begin to see more patterns. To have a control for the conjecture you had the option of three different modifications. Instead of the original formula which 3n+1 you could choose 3n-1 or use negative integers. I used the 3n-1 extension and plotted the numbers on a new spreadsheet. When I colored in the patterns with a colored pencil, the patterns became a lot more clear.
A conjecture is an opinion or conclusion formed on the basis of incomplete information. Math research is similar to science research in the way that you have to test different patterns. In science they use the trial and error methods similar to what have to do in order to make our plot graphs. In this Collatz conjecture, we need to use different extensions and modifications to see if we can make this conjecture a theory. A theory is a supposition or a system of ideas intended to explain something based on general principles independent of the thing to be explained. Patterns are essential in math. An example of a pattern in the Collatz conjecture is color coding the spreadsheet. Another pattern is obviously the repeating string of numbers one and two and one and zero on the last data table. Patterns keep math problems organized and structured. For my plot graph I am plotting odd numbers and their repetition. They also allow me to get a better understanding of how I want my finished product to look. We recognize different growing patterns in conjectures like the Collatz conjecture that provide evidence to make a theory.
A conjecture is an opinion or conclusion formed on the basis of incomplete information. Math research is similar to science research in the way that you have to test different patterns. In science they use the trial and error methods similar to what have to do in order to make our plot graphs. In this Collatz conjecture, we need to use different extensions and modifications to see if we can make this conjecture a theory. A theory is a supposition or a system of ideas intended to explain something based on general principles independent of the thing to be explained. Patterns are essential in math. An example of a pattern in the Collatz conjecture is color coding the spreadsheet. Another pattern is obviously the repeating string of numbers one and two and one and zero on the last data table. Patterns keep math problems organized and structured. For my plot graph I am plotting odd numbers and their repetition. They also allow me to get a better understanding of how I want my finished product to look. We recognize different growing patterns in conjectures like the Collatz conjecture that provide evidence to make a theory.