Ah, ok...got it. Thanks all.
The mentioned wikipage also states "While that series is easy to write and calculate, it is not immediately obvious why it yields π.".
Does that mean there no proof for the Pi series equation?
These are estimations. My question is when they say the value of Pi is accurate to so and so number of digits with respect to the reference value of Pi, how did they come up with the reference value of Pi.
When we say we know the value of Pi upto - say 1 billion position accuracy -, how exactly they calculate it? Is it as simple as Circumference / diameter and the whole accuracy of the value of Pi is completely dependent on the accuracy to measure circumference and diameter?
It's different from art. In art a computer cannot sort out a good picture from garbage. In case of mathematical theorems proof, a computer can clearly rule out the invalid ones. Using it to derive all the mathematical proofs will be nearly impossible. But for a given specific problem, a computer...
If we feed all the existing mathematical axioms to a powerful computer, it should be able to give us all the proofs and theorems that can be derived using the axioms. Is there anything wrong with this logic?
I need to convert x (ranging between 0 - 1,000,000) to y (ranging between 0 - (2^32)-1).
so y = (x * 2^32)/1M => (x << 32)/ 1M
We, the software guys have no problem doing it. But the microcode group says they don't have division operation.
I was trying to provide a solution by converting (x <<...
The order is from left to right.
Now, that brings me to another question. In Arabic (or any natural language which reads from right to left), do they follow a right to left ordering convention for mathematics?
The difference is calculators that uses RPN (Reverse Polish Notation) or not.
Can a sudoku generator determine the complexity, without trying to solve it?
[EDIT] Probably not. My thinking is as follows.
A puzzle may have different paths to reach the unique solution. The less number of paths means it's a harder puzzle.
Make any sense?
Ah...Thanks uart and MooOfDoom. I should have found it myself :(.
I was trying to think of a possible variation of sudoku - 2 people play, start with no initial numbers, each player adds a number alternately: player A tries to solve the puzzle and win, player B aims to prevent player A from...
That's the puzzle here. Let's say I created a software program to generate a Sudoku puzzle. Now I need the same software to tell me to tell the difficulty of the puzzle.
By valid, I simply mean, there is no initial numbers that contradict itself (same numbers in the same row/column/box). I...
I can't find a solution to these questions. Can someone help?
1. An algorithm to determine if a Sudoku puzzle is easy, medium, hard, or evil.
2. For every valid Sudoku puzzle, there exist at least one valid solution. True or false? Proof?
Is there a proof for complex number to exist? Can I just make a statement the imaginary part of a complex number can have a real part and imaginary' part and goes on infinitely recursively. What makes the maths world to accept the definition of complex numbers to be the current one, and reject...