… that NASA-JPL (Jet Propulsion Laboratory) scientists and engineers use 3.141592653589793 as an approximation for π?
“… [f]or JPL’s highest accuracy calculations, which are for interplanetary navigation, we use 3.141592653589793. Let’s look at this a little more closely to understand why we don’t use more decimal places. I think we can even see that there are no physically realistic calculations scientists ever perform for which it is necessary to include nearly as many decimal points as you present. Consider these examples:
- The most distant spacecraft from Earth is Voyager 1. It is about 12.5 billion miles away. Let’s say we have a circle with a radius of exactly that size (or 25 billion miles in diameter) and we want to calculate the circumference, which is pi times the radius times 2. Using pi rounded to the 15th decimal, as I gave above, that comes out to a little more than 78 billion miles. 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. 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. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches. Think about that. We have a circle more than 78 billion miles around, and our calculation of that distance would be off by perhaps less than the length of your little finger.
- We can bring this down to home with our planet Earth. It is 7,926 miles in diameter at the equator. The circumference then is 24,900 miles. That’s how far you would travel if you circumnavigated the globe (and didn’t worry about hills, valleys, obstacles like buildings, rest stops, waves on the ocean, etc.). How far off would your odometer be if you used the limited version of pi above? It would be off by the size of a molecule. There are many different kinds of molecules, of course, so they span a wide range of sizes, but I hope this gives you an idea. Another way to view this is that your error by not using more digits of pi would be 10,000 times thinner than a hair!
- Let’s go to the largest size there is: the visible universe. The radius of the universe is about 46 billion light years. Now let me ask 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)? The answer is that you would need 39 or 40 decimal places. If you think about how fantastically vast the universe is — truly far beyond what we can conceive, and certainly far, far, far beyond what you can see with your eyes even on the darkest, most beautiful, star-filled night — and think about how incredibly tiny a single atom is, you can see that we would not need to use many digits of pi to cover the entire range.”
15 decimal digits!
… today is π Day?
Do you want to know at what π digit you can find your birthday?
Use Wolfram Alpha search www.mypiday.com.
Today’s date is ONLY at digit 91,355.
… you can create art with a programming language?
Clayton Shonkwiler, a mathematics professor at Colorado State University, uses the Wolfram Language to create AMAZING animations and static images.
Fall In by Clayton Shonkwiler
Caught by Clayton Shonkwiler
Please view his work at http://flotsam.sellingwaves.com.
… the number of ways to arrange 128 balls?
It exceeds the 1080 atoms in the universe! We know the answer because of the work of Stefano Martiniani and his colleagues at the University of Cambridge in the UK.
Follow this link to a New Scientist article about how they arrived at this result.
… someone has photographed an atom?
The photo taken by David Natlinger is titled Single Atom In An Ion Trap. The image of a single atom of strontium suspended in a strong electric field was captured using an ordinary digital camera on a long exposure shot. The radii of a strontium atom is just around 215 billionths of a millimeter!
View this stunning photo in this article from the New Scientist.
… where zero comes from?
Brahmagupta was one of India’s prominent mathematicians and astronomers. His major treatise Brahmasphutasiddhanta (“Correctly Established Doctrine of Brahma”), published in 628 AD, addressed various mathematical concepts, like rules for summing series (for example, 12 + 22 + 32 + … + n2 = n(n + 1)(2n + 1)/6), or rules for operations on negative numbers (for example, 5 – 7 = -2). He also described methods of multiplication based on the place-value system similar to the multiplication algorithm we use today.
But first and foremost: Brahmasphutasiddhanta is the oldest known text to define zero as a number resulting from subtracting a number from itself, like 9 – 9 = 0. Brahmagupta called it sunya. He also defined zero’s role by explaining the rules for operations in a base-ten number system. Can we imagine how cumbersome a number system without zero would be? Think Roman numerals!
Recognizing the superiority of the system described by Brahmagupta, Arab mathematicians translated his work into Arabic, and changed sunya into zifr. From Arabic, European mathematicians translated it into Latin and renamed zifr as zephirium. In English it later became cipher or zero.
Thank you for the zero, Brahmagupta!
… there was a pancake calculator?
Students at the University of Sheffield in the UK have developed a formula to prepare the perfect pancake. Yum!
For mixture recipe and pancake calculator (aka Excel spreadsheet) click here.
… February 11 is the International Day of Women and Girls in Science?
Poster by Ana Barrett
This date was voted by the United Nations General Assembly as a day to celebrate the work of women scientists and re-energize our efforts towards gender equality and full participation in science for women and girls.
Watch video on YouTube: Marie Curie – Mini Biography.