Do You Know What Will Happen If You Fold a Paper 42 Times?

You will reach the moon.

The claim that folding a piece of paper 42 times would reach the moon is a fascinating example of how quickly exponential growth can escalate. This idea is based on the concept of exponential increase in the thickness of the paper with each fold.((https://www.codersrevolution.com/blog/will-a-piece-of-paper-folded-42-times-reach-the-moon))

The Basic Principle:

First, let’s start with some assumptions:

• The average distance from the Earth to the Moon is about 384,400 km (or 384,400,000 meters).((https://spaceplace.nasa.gov/moon-distance/en/))
• A standard sheet of paper is about 0.1 mm thick (or 0.0001 meters).((https://www.uniquelycreative.com.au/blogs/news/what-is-gsm-for-paper-a-paper-thickness-and-weight-guide))

Each time you fold the paper, its thickness doubles. So, the thickness of the paper after n folds is given by 0.0001 × 2ⁿ meters.

We want to find out how many folds n it would take for the thickness to reach or exceed the distance to the moon. So, we must solve for n in the equation 0.0001 × 2ⁿ ≥ 384,400,000.

To reach the moon, you must fold a piece of paper approximately 41.81 times. Since you can’t fold a piece of paper a fraction of a time, rounding up, it would take 42 folds to reach or exceed the distance to the moon.((https://boundlessbrilliance.org/brilliant-blog/foldingpapertothemoon))

The exact distance it would cover depends on the original thickness of the paper and the precise distance to the moon, which varies slightly in its orbit around the Earth.

However, practically speaking, it’s impossible to fold a piece of paper this many times.((https://www.wtamu.edu/~cbaird/sq/2012/12/07/what-stops-a-piece-of-paper-from-being-folded-more-than-seven-times/)) The world record for the number of folds is much lower, primarily because each fold increases the difficulty exponentially.((https://www.guinnessworldrecords.com/world-records/494571-most-times-to-fold-a-piece-of-paper)) The paper quickly becomes too thick to fold any further, and even if it were possible, the size of the paper also becomes a limiting factor as it decreases with each fold.((https://www.livescience.com/how-many-times-can-paper-be-folded))

The concept is a great way to illustrate exponential growth – a concept used in various fields like finance (compound interest), population growth, and computer science (algorithmic complexity), among others.((https://www.sciencedirect.com/topics/engineering/exponential-growth)),((https://en.wikipedia.org/wiki/Exponential_growth))

Can You Fold A Paper More Than 8 Times?

The common belief that you can’t fold a piece of paper more than 7 or 8 times was widely accepted for a long time. However, this is not strictly true and depends on several factors, including the size and thickness of the paper and the method of folding.((https://www.sciencefocus.com/science/whats-the-maximum-number-of-times-that-you-can-fold-a-piece-of-paper))

• Traditional Folding: For a standard sheet of paper (like A4 or letter size), it’s incredibly difficult to fold it more than 7 or 8 times in half due to the exponential increase in thickness and decrease in foldable surface area with each fold.
• World Record: The current world record for the most folds in a piece of paper is much higher. In 2012, high school student Britney Gallivan folded a single toilet paper 12 times, following extensive mathematical calculations. This was achieved using a very long, thin piece of toilet paper.
• Paper Size and Type: The ability to fold paper more than 7 or 8 times increases significantly with larger and thinner pieces of paper. The larger the paper, the more folds can be made because the exponential growth takes longer to become prohibitive.

So, while it’s a practical challenge to fold standard paper more than 7 or 8 times, it’s not an absolute physical or mathematical limitation. With the right conditions (especially larger and thinner paper), more folds are indeed possible.((https://www.guinnessworldrecords.com/world-records/494571-most-times-to-fold-a-piece-of-paper))