Once again, the Maryland Science Center and the wonderful staff there helped celebrate π (Pi) Day, which falls on March 14 every year but this year has the added bonus of being in 2015, supplying the next two digits of the irrational number that represents the ratio between a circle’s circumference and diameter.
“π (1st 10,000 digits) in the Sky” on the planetarium dome, 360 digits per row
Events for kids included a show in the planetarium called “π in the Sky,” during which the presenter suggested that any possible sequence of digits you could think of existed somewhere in the digits of π. Many kids asked if their birthday was in the sequence, but because only the first 10,000 digits were displayed on the planetarium’s dome, the odds weren’t good that the digits would be visible.
However, one of the scientists on hand told them all exactly what decimal place of π their birthday’s digits started at. Because some of the requested sequences started at the millionth decimal place or higher, the announcements brought a few “Ah”s from the audience.
Most of what was shown had to do with patterns that could be seen in the first 10,000 digits. For example, the famous “Feynman Point,” named after theoretical physicist Richard Feynman, is a sequence of six 9s that begins at position 762 in the decimal representation of π. There’s no other digit that occurs six times in a row during the first 10,000 decimal places. Or five times in a row, for that matter.
Other π Day activities included a pie-eating contest, a π memorization contest, and the stringing along of the digits of π right up the main staircase.
“Baltimore Hoop Love” had kids of all ages dancing with circles.
Non-π-related stuff to do
The Maryland Science Center features lots for kids to explore, many exhibits being hands-on. This includes a dinosaur room where kids are encouraged to examine fossils and put together evidence to learn about dinosaurs.
A meat-eating and a much larger plant-eating dinosaur. Based on evidence, both lived in Maryland.
One of the most intriguing exhibits is the bed of nails: hundreds of nails support the weight of a person lying down on top of them. Because the nails make a nearly flat surface—and because the body is an amazing machine—no harm comes to the person lying on the bed of nails.
The more nails you use, the less painful it is to lie on the bed. Reduce the number to just one nail, as the parent of one young nail bed rider noted, and there would be much more pain involved.
Even though this wasn’t pointed out, the bed of nails perhaps comes closest, among the center’s regular exhibits, to telling us something about the history of π.
As shown here, the more sides a polygon has, the more closely its perimeter approximates the circumference of the circle in which it’s inscribed. Here we see a big difference between the perimeter of a square and the circumference of the circle, but the difference becomes less with a pentagon, and still less with a hexagon.
Now we use, at left, a polygon with 20 sides, known as an icosagon. I took the liberty of drawing it next to, not inscribed in, the circle in this case, because the sides of the regular icosagon make nearly a perfect circle.
So, as with the bed of nails, where the more nails you use, the closer the surface of the bed of nails approximates a flat surface, the more sides you draw in the polygon, the closer its perimeter comes to the circumference of a circle.
Frequency of digits in π
One student asked during the “π in the Sky” program, “How many of each digit are in the first 10,000 digits of π?” The presenter didn’t know the answer, but the Mathematica software can supply it quickly. Using the command “N [ Pi, 10000 ],” we get the first 10,000 decimal places of π. Then, we treat the value as a string and have the computer count how many 0s there are, how many 1s, and so on.
Here are my results. At next year’s π Day celebration (3/14/16), whoever presents the “π in the Sky” show can answer, with certainty, that each of the 10 digits occurs about as often as any other digit among the first 10,000 decimal places of π.
- 0: 968 occurrences
- 1: 1026 occurrences
- 2: 1021 occurrences
- 3: 975 occurrences
- 4: 1012 occurrences
- 5: 1046 occurrences
- 6: 1021 occurrences
- 7: 969 occurrences
- 8: 948 occurrences
- 9: 1014 occurrences