It’s fun to think about its truly endless sequence of digits, and it may be surprising how often it appears in the equations scientists and engineers use. Pi is an intriguing number with interesting mathematical properties. Image credit: NASA, ESA, CSA, STScI | + Expand image | › More about the image | Text description (PDF) The oldest-known galaxy identified in the image is 13.1 billion years old. If you were to hold a single grain of sand at arm's length, you could cover the entire area of space taken up by this image, which was captured by the James Webb Space Telescope and contains thousands of galaxies. Isn’t it amazing that we wouldn’t need to use many digits of pi at all to cover that entire unbelievable range? Now think about how incredibly tiny a single atom is. And the vastness of the universe is truly far, far, far beyond what we can even conceive. It’s yet farther beyond the extraordinary vision of the James Webb Space Telescope. It’s certainly far beyond what you can see with your eyes even on the darkest, most beautiful night of sparkling stars.
Think about how fantastically vast the universe is. Now let me ask (and answer!) a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, the simplest atom? It turns out that 37 decimal places (38 digits, including the number 3 to the left of the decimal point) would be quite sufficient. The radius of the universe is about 46 billion light years. Let's go to the largest size there is: the known universe.
We have a circle more than 94 billion miles (more than 150 billion kilometers) around, and our calculation of that distance would be off by no more than the width of your little finger. It turns out that our calculated circumference of the 30-billion-mile (48-billion-kilometer) diameter circle would be wrong by less than half an inch (about one centimeter). In other words, by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. We don't need to be concerned here with exactly what the value is (you can multiply it out if you like) but rather what the error in the value is by not using more digits of pi. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 94 billion miles (more than 150 billion kilometers). Now say we have a circle with a radius of exactly that size, 30 billion miles (48 billion kilometers) in diameter, and we want to calculate the circumference, which is pi times the radius times 2. Let’s be generous and call that 15 billion miles (24 billion kilometers). As of this writing, it’s about 14.7 billion miles (23.6 billion kilometers) away.
In fact, it was posed many years ago by a sixth-grade science and space enthusiast who was later fortunate enough to earn a doctorate in physics and become involved in space exploration. Thank you for your question! This isn't the first time I've heard a question like this. Here’s JPL’s Chief Engineer for Mission Operations and Science, Marc Rayman, with the answer: “Does JPL only use 3.14 for its pi calculations? Or do you use more decimals, like say ?” We received this question from a fan on Facebook who wondered how many decimals of the never-ending mathematical constant pi (π) NASA-JPL scientists and engineers use when making calculations: Image credit: NASA/JPL-Caltech | + Expand image This graphic shows more than 500 of the infinite number of decimals in pi.
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