Using a twelve digit number system with no zeros, does pi come out 3.0?
No. [math]3.0_b = 3\cdot b^0 + 0\cdot b^{-1} = 3[/math] represents the same value (three) in every base [math]b[/math] number system, including base twelve, and [math]\pi \ne 3[/math].Keep in mind that using a different number system does not change the facts of mathematics, such as the values of mathematical constants. It only changes the way you write them.In base 12, [math]\pi = 3.184809493b918\dots_{12}[/math] (where [math]a_{12}[/math] and [math]b_{12}[/math] are the digits for ten and eleven).
Why doesn't Pi have a 0 in its first 30 digits?
While [math]\pi[/math] goes a while without a 0 (in base 10), the number [math]2\pi[/math] does not:[math]2\pi = 6.283185307179...[/math]There really isn’t much that makes [math]\pi[/math] a more special number than [math]2\pi[/math]. In fact, one could easily make the case that 6.28318530… (the ratio between the circumference of a circle and its radius) should have been the number to get the special Greek letter, not 3.14159265… (the ratio between the circumference of a circle and its diameter). In fact, there’s a saying:The Greeks were smart, so they discovered pi. But if they were really smart, they would have discovered two pi.Since [math]2\pi[/math] doesn’t wait that long for a 0 (again, in base 10), the fact that [math]\pi[/math] does is probably not connected to any interesting properties about it. Thus, a coincidence.There’s a few other coincidences to find as well. Note the number of times we get an “xyx” pattern in the first batch of digits:3.14159265358979323846264338395…
How many digits of pi could be stored on a 1 TB drive in a usable format (in decimal, not compressed, etc.)?
If you’re storing decimal digits in a text file with no attempt at compression then, frankly, it doesn’t matter one iota if those are the digits of the decimal expansion of [math]\pi[/math], the digits of the decimal expansion of [math]1/17[/math], a trillion [math]0[/math]’s, or the phone numbers of everyone in the world, concatenated and repeated as needed.Storing one decimal digit per byte is pretty wasteful, but it’s definitely easy to view. I don’t know that I’d call it “usable” since I’m not sure what utility a trillion such digits might have, but whatever you need to do with those digits, you can probably do it with ASCII encoding of one digit per byte.This will likely give you somewhere between 900 billion and a trillion digits, depending on the file system, hard drive overhead and so on.You can easily gain a factor of [math]2[/math] by storing two decimal digits per byte, since a decimal digit can comfortably fit in four bits. You’d simply store the digit-pair 00 as 00000000 and 99 as 10011001. Depending on what you actually want to do with the data, this may be perfectly convenient or a bit of a nuisance, but it’s not hard to read and manipulate in any reasonable system.Now you’re up to something like 1.9 trillion digits, give or take.Triplets of decimal digits have 1,000 combinations, which is almost perfect for 10 bits of storage. Since 10 bits don’t align nicely with 8 bits per byte, we are now getting into pretty cumbersome encoding territory, but it’s still not what I would call “compression”, just a pretty awkward encoding aimed at retaining the “decimal” requirement of the question.Every five bytes now accommodate twelve decimal digits, so you can get something like 2.3–2.4 trillion digits using this scheme, which is a pretty modest gain for the hassle. I’d probably stick with two decimal digits per byte, if I managed to dream up a good reason to try this at all.
What was the maximum number of digits of pi or e used in an application in the physical world? Why did they do it?
Using an 39 digit approximation for [math]\pi[/math] is enough to calculate the volume of the observable universe with a prescision of one atom.
How can you distinguish a Pi Galaxy that sends out digits of Pi from an E universe that sends out digits of E?
Since galaxies don’t “send out numbers”, you’re asking about intelligent species of sentient beings.If their mathematical knowledge is sufficient to understand one of these constants (e and/or pi), then I would expect they also know the other.The question remains as to how they express the value. Do they use decimal digits? Binary digits? Octal? Duodecimal? Some weird radix. Or do they use “digits” at all???It is entirely possible that alien mathematicians have developed ways to express numbers without using digits at all. Since the fundamental law of arithmetic says that any integer may be expressed as a unique product of the primes raised to integer powers, it is sufficient to give the sequence of powers.Irrational numbers may be approximated with rational fractions, or (better yet!) with a sequence of rational values that diminish toward zero and whose the sum of approaches pi or e as a limit.A remaining question is how they “send out” these numbers or expressions; I doubt they would use Morse Code!
A pizza is cut into twelve pieces. Describe the steps you would take to find the area of one slice of the pizz?
We are studying this in class, This was an example my teacher gave me. I left the room so I didn't get the notes. Im not sure how to find it ether...Anyone help?!!?! I need to know how to do this before state testing ]':
Can Pi be represented in a finite number of digits in any number system?
If you mean in a integer base then it´s impossible because the resultant number will be rational and pi is not rational. If you refer to any other base pi can be expressed in base pi (1), however rational numbers can´t be expressed in base pi because pi is trascendent (pi is not the root of a polynomial with rational coefficients). It is interesting though to ask for which real numbers pi can be expressed in base such a number.
Whats bigger two 12 inch pizzas or one 16 inch?
two 12 inch, cuz it's 24 inches
Do the digits of pi contain every possible combination of numbers from 0 to 9?
If we consider pi to contain infinite digits then this question reduces to a classical mathematical question "Given a sequence of completely random digits, how many digits of the sequence would you have to go through to find a specific sequence of a given length?". Though, equating our problem to this question makes one assumption that digits of pi are completely random.When mathematicians study the first trillion or so digits of pi on a computer, they find that the digits appear to be statistically random in the sense that the probability of each digit occurring appears to be independent of what digits came just before it. Furthermore, each digit (0 through 9) appears to occur essentially one tenth of the time, as would be expected if the digits had been generated uniformly at random..Frequency of Each Digit of PiWhile tests performed on samples can never unequivocally prove that a sequence is random (in fact, we know the digits of pi are not random, since we know formulas to generate them) the apparent randomness in pi is consistent with the idea that it contains all finite sequences (or, at least, all fairly short ones).In theory, if we generate a number from an infinite stream of digits selected uniformly at random, then there is a probability of 100% that such a number contains each and every finite sequences of digits, and pi has the appearance of being statistically random. That being said, to this day it has not even been proven whether every single digit from 0 to 9 occurs an unlimited number of times in pi’s decimal representation (it may happen that after some point it may only contain 3's and 6's). Though mathematically in theory we can say that it may also contain a binary representation of entire human DNA.For some more rigorous mathematical explanations, look at the answer to this question.Finding a specific sequence of digits in piand also Normal numberYou won't find any continuous sequence of digits in pi like 0123456789 ( using the maximum digits of pi that have been calculated till now ) Though you can find the string 12345678 occurs at position 186557266.The string 23456789 occurs at position 995998.How to know this?Pretty simple, just go to this website and explore pi in detail. The Pi-Search PageHave Fun.