The date 3/14 reminds everyone that the Greek letter π, always representing the ratio between any circle’s circumference to its diameter, is about 3.14.
Pi or π which has infinite digits (3.1415926…). Some of us number lovers have memorized π to 100 decimal places, which is useless but sort of fun.
How Many Digits of Pi Do We Really Need?
How many digits have we actually found? And how many do we need?
A few years ago, Jet Propulsion Lab answered a student’s question about how many digits of pi they use when calculating spacecraft trajectories.
NASA, he explained, certainly doesn’t need trillions of digits for its calculations. They get by with just using 15 digits, and calculated with a value of 3.141592653589793. Why not more?
Well, they explained on their website, “Consider Earth. It is 7,926 miles in diameter at the equator. How far off would you be if you calculated our planet’s circumference with only 15 digits of pi instead of using a few more? You’d be wrong by the size of a molecule.”
So, what could be the purpose of using (or knowing) 100 digits? None whatsoever. It’s strictly a numbers fascination.
How Far Can We Count?
Kids often ask how far they can count. In astronomy, we certainly use enormous numerals. But it wasn’t always this way!
The word “million” didn’t come into general use until the 13th century. Before then, the largest number was a myriad, equal to ten thousand.
A million seemed huge when we were kids. It became less intimidating only when we realized it was possible to count to a million in a few days.
In astronomy, we use “million” mainly in relation to the Sun, which is nearly a million miles wide and sits 93 million miles away. Millions also express the distance to the nearer planets. Venus is 26 such units, Mars 34.
A bit less useful, astronomically, is the billion, which is a thousand million. Saturn is nearly a billion miles away from us, and Uranus, Neptune and Pluto are a couple of billion. And the visible universe offers for our inspection about 500 billion galaxies. It’s also convenient for expressing Earth’s worldwide census of seven billion people, some of whom may contemplate the accumulated wisdom of the 60 to 100 billion people who have ever walked the face of this forgiving planet.
So we jump to a trillion. This is a million millions, a most valuable unit for government economists and astronomers. There are almost a trillion stars in our galaxy and about the same number of planets. The lightyear is equal to six trillion miles. Grasping what a trillion represents is like having a floodlight illuminate the path to understanding the cosmos.
One way to appreciate the enormity of a trillion is to count it out. Unfortunately, at the rate of five numbers a second, without stopping to eat or sleep, this exercise would still require three thousand years.
Strange Number Connections
Like Peter the Great, who had his wife’s lover beheaded and kept that head in a bottle of alcohol in her bedroom for her to contemplate, nature’s numbers can also be perverse.
- Why does each cell in our body have 90 trillion atoms, roughly the same as the number of stars in our home cluster of galaxies?
- Why is there the same number of Earth-sun distances in a lightyear as there are inches to the mile?
- And the number of atoms in a lungful of air is the same as the number of breaths of air in our atmosphere.
Such strange connections are always interesting. I’m sure you know some interesting number phenomenon, too.
Anyway, even a trillion is tiny compared with the sum total of all subatomic particles in the universe. That figure is a one followed by 86 zeroes. Yet, despite such vastness, the actual material in the universe is infinitesimally tiny when compared with the vastness of space. If the whole universe were a cube 20 miles wide, 20 miles long, and 20 miles high, all the matter it contained would be as a single grain of sand.
Happy pi day, my friends.
Source: Farmer's Almanac - Everything