June 29th, 2002, 06:21 AM
four impossible math problems
Problem One: draw or illustrate how you would draw a line of infinte length enclosed in finite space.
normally its the simplest problems in mathematics that provide us with the best problems. or worst, depending on what your stand point is. take for example arithmetic, and the multiplicative structure of the integers 1, 2, 3......... from this comes the idea of the prime number (a number that can not be obtained by multipling two smaller numbers, except for itself and one.) yet even with the discovery and development of mathematics like chaos theory or knot theory, there is still no known formula to determine if a number is prime.
the largest known prime is 2^13466917 - 1 (that is - two to the power of thirteen million four hundread and sixty six thousand, nine hundread and seventeen minus one) found on 14-november-2001.
Problem Two: write a program or equation to find the largest prime number...?
Problem Three: write a program or equation to find primality, for all x.
...or just go playing about with it and make your processor work for the money you paid for it.
the greeks used a method known as 'the sieve of Erathosthenese' which for all x|Z, basically boils down to multiplying all combinations of integers <x and not getting x.
heres the source for more primes. click here if you want to see a previous largest prime (2^6,972,593 - 1) written out in decimal?
as you all know, a compiler converts a program written in high level language into an equivalent program in machine language then the linker resolves symbolic refferences and generates a file that can be loaded into memory and executed. therefor the program exists in the hardware electronic signals that are interprited as one's and zero's. when a computation is performed its the threads of binary that are run through the processor.
Problem Four: write a program whose binary output is random or write down a binary string that is random and prove its random.
note: a random sequence has no pattern. hence a not random sequence has a pattern. so a sequence has a pattern if it can be computed by a shorter sequence. so by definition a random sequence can not be computed by a shorter definition because it has no pattern.
one of the above was actually done i believe.eof(max)
Hmm...theres something a little peculiar here. Oh i see what it is! the sentence is talking about itself! do you see that? what do you mean? sentences can\'t talk! No, but they REFER to things, and this one refers directly-unambigeously-unmistakably-to the very sentence which it is!
June 29th, 2002, 06:43 AM
OpenBSD as pretty darn good pseudo random number generator (not that I can personnaly prove it).
This article on PRNGs and TCP ISNs was pretty interesting (disclaimer: might fry your brain
Credit travels up, blame travels down -- The Boss
June 29th, 2002, 10:47 AM
Problem 1: There is no sutch thing as infinte, you can have infinatly growing, but to messure something's length it must be static, and once the line start's to fold onto it self, it become's a solid shape, and not a line......so the question is impossible my consept, not by math's....
Problem 2: I'll get around to it....shouldn't be that difficult, the only problem is it would consume huge amount's of resources....
With all the subtlety of an artillery barrage / Follow blindly, for the true path is sketchy at best. .:Bring OS X to x86!
Og ingen kan minnast dei linne drag i dronningas andlet den fagre dag Då landet her kvilte i heilag fred og alle hadde kjærleik å elske med.
June 29th, 2002, 12:17 PM
um, no. a random number dosnt not have patern...... a random number has........ that is random....... how do i say this. um what your note describes is an inrealistic number, not a random number, by your definition pi would be random but it is a mathmatical formula and can be repeted an infanite number of times and you will get the EXACT same answer, thus pi is not random, thus that isnt the definition
June 29th, 2002, 12:51 PM
once i wrote a vb program that find prime numbers from X to Y, it worked well but i have some ideas about how to make this program even faster.
Oh and btw my ICQ number is a prime number
June 29th, 2002, 02:02 PM
in linux theres a program called primes that takes input of numbers and pulls up all the prime numbers between those.......
steroid > cool, my ICQ number is even, so there. infact ill bet you that about half of the ICQ UINs are even..... he he he, im a master of the obvius!
June 29th, 2002, 06:12 PM
"Problem One: draw or illustrate how you would draw a line of infinte length enclosed in finite space. "
i'm not clear on the definitions used, so i'm just throwing out some possibilities:
- a circle if the line can exist as a shape
- if not, then a decaying radius that never completely expires.
- decimal increments represented between 0 and 1.0, or 0 and .1, or 0 and .00000000000000000000000000000000001, etc.
June 29th, 2002, 07:04 PM
IF they're impossible then why did you post them?
June 29th, 2002, 07:11 PM
heres an infinite line drawn in a finite space
June 29th, 2002, 09:25 PM
problem 1. is not impossible... if you take any two number say 1 and 2 there are an infinite number of interger(numbers) between them. the numbers 1 and 2 represent finite space and the numbers inbetween them .5, .80, .75 are infinite.
just my way of looking at it