Every birthday, you get a new number. However old you might have been the day before, on your birthday, the number changes and you are a year older.
Here’s a little game you can play with yourself on your birthday. It gives you a chance to fool around with the new number. You also get to think about your life a bit, which is always good thing to do on your birthday.
Imagine that you are writing a book called Life Story So Far. This book is divided into chapters, and each chapter covers the same number of years.
On your birthday, take a minute and ask yourself how many chapters the story of your life will have this year, and how many years will be in each chapter. It turns out you will have some choices.
For instance, imagine a person who is turning 6. One way to tell their life story would be in two chapters. Each of those chapters would have three years in it. The first would tell the story up until their third birthday. The second chapter would run from their third birthday to the present.
On the other hand, as a six-year-old, a person’s life story could be a book that’s three chapters long. Then each of the three chapters would cover two years.
A six-year-old person could even decide to tell their story in six chapters, each of them being one year long. Or they could turn that idea on its head and decide to put their life story into one big chapter that had six years in it.
At age six, a person couldn’t begin their life story with a chapter that covered four years. Because they haven’t lived long enough yet to write a second chapter that is four years long.
A person who was five years old, would have different choices. For example, dividing the story into two chapters isn’t going to work, because there’s no way to make both chapters have the same number of years in them.
Five-year-olds don’t have many choices about how they can divide up their book. Neither do seven-year-olds. But if a person is 12…
Old people can play, too! How can a person divide up the book called Life Story So Far when they turn 40, 41, and 42? What are the options of dividing the book into chapters upon turning 72, 73 and 74?
If you think about this on your birthday—what your number is and how you can divide your life into even-sized chapters—you’ll be amused by what the chapters are and how things divvy up differently from year to year. If you get serious about it, you can name the chapters.
If you get math-y about it, you could say that you were thinking about factorization. When you do that, you are tromping about in the field called Number Theory.
