Have you ever heard the claim that folding a newspaper 42 times can make it reach the moon? Most of you might be thinking, No way! But it’s a mind-blowing truth, and in this article, we’ll dive into the magic of exponential growth.
The Astonishing Truth: Folding a Newspaper 42 Times Reaches the Moon
Let’s start by proving the claim. Assuming the thickness of a newspaper is 0.1mm, if you fold it 42 times, its height would be:
\(\displaystyle 0.1×2^{42}=439804651110.4\)
Understanding the Growth
Want to see how the thickness grows with each fold? Here’s a breakdown:
| Folds | Thickness (in meters) | Notes |
|---|---|---|
| 1 | 0.000 | – |
| 2 | 0.000 | – |
| 3 | 0.001 | – |
| 4 | 0.002 | – |
| 5 | 0.003 | – |
| 6 | 0.006 | – |
| 7 | 0.013 | – |
| 8 | 0.026 | – |
| 9 | 0.051 | – |
| 10 | 0.10 | – |
| 11 | 0.20 | – |
| 12 | 0.41 | – |
| 13 | 0.82 | – |
| 14 | 1.64 | Equivalent to human height |
| 15 | 3.28 | – |
| 16 | 6.55 | – |
| 17 | 13 | – |
| 18 | 26 | – |
| 19 | 52 | – |
| 20 | 105 | – |
| 21 | 210 | – |
| 22 | 419 | Taller than Tokyo Tower (333m) |
| 23 | 839 | – |
| 24 | 1,678 | – |
| 25 | 3,355 | – |
| 26 | 6,711 | Higher than Mount Fuji (3,776m) |
| 27 | 13,422 | Surpasses Mount Everest (8,849m) |
| 28 | 26,844 | – |
| 29 | 53,687 | – |
| 30 | 107,374 | – |
| 31 | 214,748 | – |
| 32 | 429,497 | Beyond the altitude of Himawari satellite |
| 33 | 858,993 | – |
| 34 | 1,717,987 | – |
| 35 | 3,435,974 | – |
| 36 | 6,871,948 | – |
| 37 | 13,743,895 | – |
| 38 | 27,487,791 | – |
| 39 | 54,975,581 | – |
| 40 | 109,951,163 | – |
| 41 | 219,902,326 | – |
| 42 | 439,804,651 | Reaches the moon |
And visually, the growth looks something like this:
As you can see, as the number of folds increases, the thickness explodes.
Another Jaw-Dropping Fact
So, we’ve seen that folding a newspaper 42 times gets us to the moon. But what happens if we fold it 101 times? Hold onto your hats: it would reach the edges of the universe.
How We Calculated It
The distance from the center to the edge of the universe is 13.8 billion light years. Given that 1 light year is approximately 9.5 trillion km, the radius of the universe can be found as:
\(\displaystyle 13,800,000,000×9,500,000,000,000=1.311×10^{23}\)
The radius of the universe is roughly 1.311×10^23 km. So, to figure out how many times we need to fold the newspaper to reach the universe’s edge (keeping our calculations in meters):
\begin{align}
0.1×10^{-3}×2^x&=1.311×10^{23}×10^3\\
2^x&=\frac{1.311×10^{23}×10^3}{0.1×10^{-3}}\\
2^x&=1.311×10^{30}\\
log_22^x&=log_2(1.311×10^{30})\\
xlog_22&=log_2(1.311×10^{30})\\
x&=\frac{log_2(1.311×10^{30})}{log_22}\\
x&=100.0485105＜101
\end{align}
With 101 folds, the newspaper’s thickness surpasses the universe’s radius. Meaning, if we imagine the universe as a sphere, a 101-folded newspaper would reach any point on the universe’s edge. The power of exponential growth is truly beyond our wildest imagination!
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