Order of magnitude is a hell of a drug
Order of magnitude is a hell of a drug
Meme of two women fighting while a man smokes from a pipe in the background.
The women fighting are labeled "mathematicians defining pi" and "engineers just using 3 because it's within tolerance"
The man smoking is labeled "astrophysicists" and the pipe is labeled "pi = 1"
38 digits of pi can get the circumference of the visible universe to within a single hydrogen atom.
10 digits gets the diameter of the earth to within an inch.
Thank you for subscribing to Daily Spacey Math Facts
10 digits gets the diameter of the earth to within an inch.
Put another way, 10 digits means that your error will be caused by your imprecise model of the Earth's shape, rather than imprecision in the value of pi.
out of curiosity... does that first fact account for the continued expansion of the universe?
It works at the current 93 billion light years of observable universe (46ish in every direction)
The real comment mvp. You deserve every positive vote my post got
Thank you O'Brian!
I hope you have finally done the DTR with Bashir...Earth is shaped like potatoe pi accounts for that??
as an engineer, a lot of languages (even proprietary ones) have a built-in constant pi variable because it is so ubiquitous - its easier and more readable to use pi than 3........
And then you’re using C++ and they scold you for including cmath for just M_PI because it increases compilation times.
As a retired mechanical engineer, the joke is that we don't really remember the value of Pi, but we think it's somewhere around 3. But maybe we should use 4 just to be safe.
In any case, I have to remember 3.14 because one of my Daughters was born on Pi Day. Which, according her, is the second most important day of the year, just right behind Christmas Day, when she was growing up. So when she got into high school that meant that we had to bring enough pie to be served in each of her math classes on that day. (Oddly enough she prefers cheese cake over pie on her Birthday).
Now I'm not saying being born on Pi Day influenced her life any, but she has a PhD in Mech Engineering.
You sound like an involved and caring father. Rock on, dude
Theres a YouTube video where the presenter demonstrates DOOM running (or not) with varying values of Pi that's quite interesting: Non Euclidean DOOM
The last 4 years of my working life, I taught some math in my small rural local school. I introduced a tradition of calculating Pi from scratch by various "silly" means. All shamelessly stolen from Matt Parker of Standup Maths fame on Youtube. The students, (4th through 8th grade), were always highly entertained and may have accidentally learned some math.......
When you least expect it, Pi is there.
38 digits of pie gives youv an error of less then a hydrogen atom in the circumference of the known universe.
https://www.jpl.nasa.gov/edu/news/how-many-decimals-of-pi-do-we-really-need/
From the article for anyone who cares, NASA uses 15 digits (
3.141592653589793) because at Voyagers current distance from earth (~48 billion kilometers) that would give you an accuracy of less than half an inch.
As an Astrophysicist, I have never seen anybody use pi=1, you just leave the character, it's anyway better to read, is not like you do any calculations by hand anyway. More common is c=hbar=kB=1, but that is not an approximate, is a gauge in another unit system. Also... Astronomy is not astrophysics...
"is not like you do calculations by hand anyway"
... get off my lawn, whippersnapper.
Using 1 is fun. That means the circumference of a circle is equal to its diameter.
Isn't this functionally true for objects on the infinite focal plane? I.e. a star? Betelgeuse might actually be huge in absolute terms, but from earth, and even in a large telescope, it's still a pinpoint whose circumference is not meaningfully distinct from its diameter.
It would be the size of the telescope's diffraction artifacts probably. Meaning the shape you see on the picture is not related to the size of the star but only to the physical limits of the optical instrument. This diffraction pattern is proportional to the color your looking at and inversely proportional to the size of the telescope primary mirror. The bigger the telescope primary mirror, the smaller the diffraction pattern and the more chance you have that this artifact will not completely hide the object you are looking at. I didn't do the math, but I guess to image the actual disk of Betelgeuse, the size of the telescope you need is probably still science fiction, even with interferometry.
Euclidean geometry enjoyers in shambles
Computer science: pi is O(1)
Is it actually? I'll admit im pretty rusty on time complexity, but naively I'd think that pi being irrational would technically make even reading or writing it from memory an undecidable problem
If you're trying to calculate it, then it's quite difficult.
If you just want to use it in a computer program, most programming languages have it as a constant you can request. You get to pick whether you want single or double precision, but both are atomic (a single instruction) on modern computers.
It's a number and complexity refers to functions. The natural inclusion of numbers into functions maps pi to the constant function x -> pi which is O(1).
If you want the time complexity of an algorithm that produces the nth digit of pi, the best known ones are something like O(n log n) with O(1) being impossible.
It all depends on the precision you need. You could use an infinite series to get to the precision needed but for most use-cases it’s just a double baked into the binary itself, hence O(1)
It's usually a constant (or several ones with varying degrees of accuracy and size)
I heard once π²=10 is fairly accurate approx and thus g=π²=10 in astrophysics where people thinks in order of magnitude, not value.
But my engineering ass is telling assumptions with larger than 50% difference from actual value may cause issues on order of magnitude if the value is used multiple times and isnt it better be like 5=1/2×10?
That's because your engineering ass needs things to be physical and sane. Physics is a field for the mentally unwell to sink further into insanity while incoherently scribbling greek letters on every available flat surface.
On a more serious note, yeah you absolutely have to be careful about where you apply really ambitious simplifications like that. There are plenty of mathematical regimes where you can use natural units (this is the term to look up if your interest extends further) and simplify your reference frame by a hell of a lot though. Setting the speed of light to 1 is also a hell of a drug, and brother I've got an addiction
Electrical engineer. Never used 3. Always 3.14. don't really get the joke.
I just use the pi from my calculator or numpy/matlab. But I'm often too lazy for vacuum speed of light and use 3e8 m/s.
Electrician over here is killing the buzz
Electrical engineer. I'm nowhere near as useful as an electrician.
Pi = 355/113
I think you need this symbol: ≈