Every day, I challenge our students to think about the many ways in which mathematics impact our lives. Today, I challenge you in the same way! Can you answer this simple question — how many times do you have to fold a piece of paper until you reach the moon?
At first, you might think this number is astronomical. The moon is about 384,400 km away from Earth. A standard piece of paper is about 0.1 mm thick. This means you must stack about 3,844,000,000,000 pieces of paper to reach the moon. It seems like it would take a ridiculous amount of folds to make that happen. However, when you think about the math, you might be surprised by the answer! It all boils down to exponential growth.
Have you ever heard of the scenario about whether you would choose a million dollars or start with a penny and double the result each day for a month? Well, the more profitable scenario is starting with a penny and doubling the result each day. On day one, you have $0.01. On day two, you have $0.02. On day three, you have $0.04. On day four, you have $0.08. This pattern continues for 30 total days. When you arrive at day 30, you will have $5,368,709.12.
Using this logic, we can try to answer the original question about the piece of paper. When you fold a piece of paper in half, it is like two sheets stacked on top of each other. When you fold it a second time, there are four sheets stacked on top of each other. After a third fold, you now have eight sheets stacked on top of each other. This exponential growth quickly reaches huge numbers. In fact, when you fold a piece of paper 27 times, you have essentially stacked 134,217,728 pieces of paper on top of each other. At this point, you have surpassed Mount Everest!
To answer the original question, you need to fold a piece of paper 42 times in order to reach the moon. After 42 folds, it is as if 4,398,046,511,000 pieces of paper are stacked on top of each other. This amounts to approximately 439,805 km, which is beyond the moon! Taking this concept one step further, after 100 folds, you have reached a distance beyond the visible universe!
Of course, this cannot be physically tested, since it is impossible to fold a standard piece of paper more than about eight times, however, it is really neat to think about how this works! Questions and conversations like this are at the core of my students’ classroom learning; I hope they, like you, will continue to be lifelong learners and questioners in this area and many more!
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