Take any scientific calculator and follow these steps:
- Ensure the calculator is in degrees mode.
- Enter some number of 5's (more than 4 is ideal).
- Take the reciprocal of step 2.
- Take the sine of step 3.
You should find that the result is an approximation of $\pi$ (that becomes more accurate as more 5's are entered), multiplied by a negative exponent of 10.
Why does this occur?
Attribution: I found this puzzle on Numberphile.