Nobody needs more than 37 digits

Every year on March 14, mathematicians celebrate World Pi Day. The circle number Pi plays a central role in mathematics and physics and not a few scientists are enthusiastic about the special properties of this number. Because the first digits of Pi are 3.14 and 3/14 is the US spelling of March 14, this date has been made a holiday for all Pi enthusiasts.

In fact, pi has infinitely many decimal places in decimal notation. The sequence of digits after the comma never ends. For years there has been a sport among mathematicians to calculate as many digits of Pi as possible using supercomputers.

The world record currently stands at 62.8 trillion decimal places. Swiss researchers set it up in 2021. In practice, however, far fewer digits of pi are needed and used for scientific calculations.

Take a look at your pocket calculator to see how many pi digits it uses: the accuracy of calculation results that is achieved with this approximation of pi is more than sufficient in everyday life.

However, more decimal places are required when it comes to cosmic questions - for example, the calculation of the trajectory of a space probe that is in space on an interplanetary journey. For calculations with the greatest required precision, NASA scientists use 15 decimal places - i.e. 3.141592653589793. Nobody else should need more digits of Pi.

Because Pi plays a role in every nook and cranny of space travel and space research, NASA announces a "Pi Challenge" every year, which is primarily aimed at students but certainly at everyone who is interested. The tasks can be found here.

The first task of the “Pi Challenge” is comparatively easy. It's about the NASA Mars rover "Perseverance", which uses a drill to take soil samples on the red planet. The inner diameter of this special drill is 13 millimeters. The length of the cavity, which is finally filled with a soil sample, is 60 millimeters.

NASA's question now is: How many cubic centimeters of Martian material is in the cylinder at the end? It is clear that the result can only be calculated using the number pi.

The second task is to compare the mirrors of the James Webb and Hubble space telescopes. The "James Webb" telescope has been in use since 2022 and provides images from space in the infrared wavelength range. "Hubble", on the other hand, is already a space veteran and has been delivering fantastic images in the visible wavelength range since 1990.

Hubble's primary mirror is 2.4 meters in diameter. The mirror by "James Webb" consists of 18 hexagonal elements, which together span an area of ​​26.4 square meters. The question of the "Pi Challenge" is: By what factor is the mirror surface of the Webb telescope larger than that of "Hubble"?

The third task, in which the density of the asteroid “Psyche” is to be calculated, is a bit more difficult. "Psyche" has the shape of an ellipsoid with the three axis lengths 290 kilometers, 245 kilometers and 170 kilometers.

By measuring gravitational effects, it is also known that the asteroid has a mass of around 2.7 times 10 to the power of 19 kilograms. From this, the density of "Psyche" can be calculated and then compared with the density of planet Earth in the next step.

The fourth and final task of the "Pi Challenge" deals with a solar eclipse that can be observed on October 14, 2023 in North and South America. If you are interested in solving these tasks, you will find all the information on the said Nasa page. The correct solutions should also be announced there from March 15th.

Although for all practical purposes knowledge of pi to 15 decimal places is sufficient, one can theoretically ask how many digits of pi one would need to calculate the circumference of the entire universe with an accuracy equal to that corresponds to the diameter of a hydrogen atom. If one assumes that the universe has a radius of 46 billion light years, 37 decimal places of pi would be sufficient for such a calculation.

"Aha! Ten minutes of everyday knowledge" is WELT's knowledge podcast. Every Tuesday and Thursday we answer everyday questions from the field of science. Subscribe to the podcast on Spotify, Apple Podcasts, Deezer, Amazon Music, among others, or directly via RSS feed.