pie calcualation project, almost done, just need some help

hey whats up cboard, my teacher gave me a project to do. She wants us to write a program that will calculate this equation: pi *4*(1-1/3+1/5+1/7+1/9-1/11+1/13-1/(2*i)+1/(2*100+i))

she said to calculate for i = 100, 1000, and 100000

I have to use a while loop, and when i do it it works for 100, but for 1000 and 100000 it says inf, is there a way to fix this?

this is what i get in cmd:

PI1 = 5.0482e+060
PI2 = 1.#INF
PI3 = 1.#INF
Press any key to continue . . .

any help is appreciated, i can show my code if requested.

Go ahead and show the code.

gg

You're going to have to show your code. You say that it works for 100, but 5.0482e+60 is not particularly close to 3.14etcetera, having an error of ... well, a lot.

Do you know what the formula means (i.e., it alternates, and you have to run from i = 1 to 100 or whatever)?

Code:

---

#include <iostream>
using namespace std;

int main (){


double pi1 = 3.1415;
double pi2 = 3.1415;
double pi3 = 3.1415;
double a = 0;
double b = 0;
double c = 0;
double i1 = 100;
double i2 = 1000;
double i3 = 100000;
double equation1 = 4*(1-1/3+1/5+1/7+1/9-1/11+1/13-1/(2*100)+1/(2*100+1));
double equation2 = 4*(1-1/3+1/5+1/7+1/9-1/11+1/13-1/(2*100)+1/(2*100+1));
double equation3 = 4*(1-1/3+1/5+1/7+1/9-1/11+1/13-1/(2*100)+1/(2*100+1));

while (a!=i1){
        pi1 *= equation1 ;
        a++;
       
}
while (b!=i2){
        pi2 *= equation2 ;
        b++;
       
}
while (c!=i3){
        pi3 *= equation3 ;
        c++;
       
}



double total1 = pi1;
double total2 = pi2;
double total3 = pi3;

cout << "PI1 = " << total1 << endl;
cout << "PI2 = " << total2 << endl;
cout << "PI3 = " << total3 << endl;


        return 0;

}

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And now that I see the code, I see your steno error : pi equals 4*(1-1/3+1/5-1/7+ ... +1/(2i+1) + ...).

Your while loop should add up the alternating bits (the 1, 1/3, etc.) until i reaches the target number, then multiply by 4.

so what do i need to do/replace?

Quote:

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Originally Posted by pjr5043

so what do i need to do/replace?

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Quote:

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Originally Posted by tabstop

Your while loop should add up the alternating bits (the 1, 1/3, etc.) until i reaches the target number, then multiply by 4.

---

You don't want any *= in your code, maybe +=.

PI1 = 403.142
PI2 = 4003.14
PI3 = 400003
Press any key to continue . .

alrite i tried the += .. this is what i got ^^
how can i find out if they are correct or not?

the correct value? you mean pi?
3.1415926?

no i mean for the 400, 4003, 400003 .. i can't tell if its doing teh calcualtions correctly

1/11 will definitely not do what you intend - It is integer and therefor == 0

Your loop need to sum up the individual elements of that series. Start with a sum variable initialized to 0. Next, add 1/1 to that, then subtract 1/3, then add 1/5, etc... this is the part where your loop comes into play, the summation of these individual pieces. Once you've run your loop the desired number of times (100, 1000, 100000) then you multiply the sum by 4 which will then be your result. You need to figure out how to do that loop part. All of this should be in a function that you can call along with passing in a value (how many times you want the loop to iterate), then you can just call this function the three times with the various values (100, 1000, 100000) and have the function return this value which you then output for the user. As already hinted at, the summation/division part should not use integers but rather double since division of integer values is not going to give you correct values. The function should return a type double value, the result of the calculation, and accept an integer which is the number of times to do the loop part.

Quote:

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Originally Posted by pjr5043

i can't tell if its doing teh calcualtions correctly

---

You've been tasked to calculate the value of pi which is 3.14159... If you are getting anything that isn't remotely close to that then you are obviously not doing it correctly. 403.142 is nowhere near 3.14159...

[edit]Have you tried a search of the message board for this topic before posting?[/edit]

i guess i have to fix that equation, i know what pie is .. i have to find out this pie value using that equation, so i figured that would be a lot higher than pie

Quote:

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i guess i have to fix that equation, i know what pie is .. i have to find out this pie value using that equation, so i figured that would be a lot higher than pie

---

That is an approximation of pi using Taylor series. What I find suspect is "-1/(2*i)+1/(2*100+i)", but if you follow the pattern you will be fine.

Quote:

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Originally Posted by pjr5043

i guess i have to fix that equation, i know what pie is .. i have to find out this pie value using that equation, so i figured that would be a lot higher than pie

---

Actually, pie is something you eat, and has nothing to do with pi which is the ratio of the circumference of a circle to its diameter.
If you want to find pie, look in the supermarket!

What on earth made you think you should calculate pi by starting with a number very close to pi and constantly multiplying that by some other number? Surely you can see that all this does is increase that number quadratically? Even if it could work it would be cheating since you almost start with the answer anyway.

pjr5043,

This is not a simple formula that you can plug into your program, but rather an infinite series. (To be honest, I don't understand the notation your teacher gave you.) You can't make a calculation with an infinite number of elements, but with a computer, you can easily carry this series out to 100 or 100,000 elements.

Here is a reference.

The series is equal to one-quarter of PI, and it looks like this:
1 - 1/3 + 1/5 - 1/7 + 1/9 -1/13 +1/17...

Can you see what's next? ...-1/19 +1/21 -1/23...

You need to write a loop does this automatically for 100, 1,000 or 100,000 elements. Each time you go through the loop, you will be adding-and-subtracting smaller-and-smaller fractions. In other words, your program will be figuring-out the fractions... For example, you won't see "1\13" or any of those fractions anywhere in your C++ code... You might see "1/i". Does that make sense?

I assume you know how to write a loop that increments a number, or adds 5 to a number every time through the loop... If you don't know how to do that, you need to re-study loops before you jump into this project.

Quote:

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Originally Posted by iMalc

What on earth made you think you should calculate pi by starting with a number very close to pi and constantly multiplying that by some other number? Surely you can see that all this does is increase that number quadratically? Even if it could work it would be cheating since you almost start with the answer anyway.

---

I think the equation was written wrong. It should be:

pi = 4 * (1 - 1/3 + 1/5 - 1/7...)

(Which is true, by the way)

And it looks like an assignment, not something that was thought up.

Make Pi a define(ed) value in your program, and then don't touch it until right at the end when you compare your value for Pi, to the real (close approximation) of Pi. You know your equation is goofed, I believe. You should be having - then a +, then another - and +, throughout the series, iirc.

All the rest of your program except one line of the series equation, is rubbish - junk it.

Use the while loop to work with the digits after the decimal place, and only do the multiplication, (* 4), right at the end.

very naive method of finding pi :(
see my output . . .

Code:

---

>>> mpi(10)
pi 3.04183961893
>>> mpi(100)
pi 3.13159290356
>>> mpi(1000)
pi 3.14059265384
>>> mpi(10000)
pi 3.14149265359
>>> mpi(100000)
pi 3.14158265359
>>> mpi(1000000)
pi 3.14159165359
>>> mpi(10000000)
pi 3.14159255359
>>>

---

It's slow as a dog, but if you carry the arithmetic out far enough, it does find the correct digits.

It's just S-L-O-W as a snail if you want a lot of digits, compared to many other algorithms to find Pi.

pjr5043,

I had another idea that might help you through this...

Start with a program that simply "calculates" 1/3 by using an infinite series in a loop. As you know, 1/3 is represented in decimal by the infinite series 0.3333... So, the series looks like this:
3/10 + 3/100 + 3/1,000 + 3/10,000... (Or, like this: 0.3 + 0.03 + 0.003 + 0.0003... But, you should use fractions... I should say division... in your program.)

The first time though the loop, you will get 0.3*. The 5th time through the loop you will get 0.33333*, etc.

Once you get that working, you can modify the code inside you loop to calculate the Taylor series.


* You won't get these exact numbers, due to the way floats and doubles are stored in binary. So, don't worry if you see something like 0.33299999999999 instead of 0.333.

4*(1- 1/2i-1 + 1/2i+1) .. thats the equation, i just need to figure out how to implement it.. this stuff is pretty hard

Quote:

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Originally Posted by pjr5043

4*(1- 1/2i-1 + 1/2i+1) .. thats the equation, i just need to figure out how to implement it.. this stuff is pretty hard

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That is by no means the equation. The equation is: pi = 4*(1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... + (-1)^i/(2*i+1) + ...). In summation notation, the right hand side is (bad ASCII art alert):

Code:

---

  inf
  -----
  \      (-1)^i
4* >    ------
  /      2i+1
  -----
  i=0

---

Summations are trivially easy to code up using for-loops (start with the sum equal to 0; each time through the loop add up the bit off to the right). Multiplication by 4 is not that hard either. Of course, we won't be able to stop the loop at infinity; we'll have to settle for the first hundred (or thousand, etc.) terms as given in your assignment.

alrite guys, i'm super confused with all of this right now.

This is what my teacher told me today:
She said that this "4*(1- 1/2i-1 + 1/2i+1)" was the equation i needed to use. She then said that this equation needed to go to a loop and add by increments of 2 each time, so i figured make a variable like c, then do c+2. I really can't get it to work.

To be honest, if someone on here can just give me an equation to use, i'll paypal you $5, that's how bad i need this right now, i have so much other work to do, and i'm just never going to understand this project.


This is the exact description i was given:

Description : You can approximate π by using the following series :
π = 4 * (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ........ - 1/(2i - 1) + 1/(2i + 1) )

Write a program that displays the π value for i = 100, 1000 and 100000

note : find the pattern in the series.

We've put the equation up here six times, and you just posted it yourself. Note how this:

Quote:

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4*(1- 1/2i-1 + 1/2i+1)

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and this

Quote:

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π = 4 * (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ........ - 1/(2i - 1) + 1/(2i + 1) )

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are not in fact the same thing, which is what we've been trying to tell you all along.

One last time:
when i is 1: 1/(2i-1) - 1/(2i+1) = 1 - 1/3
when i is 3: 1/(2i-1) - 1/(2i+1) = 1/5 - 1/7
when i is 5: 1/(2i-1) - 1/(2i+1) = 1/9 - 1/11

So to get 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... + 1/(2i-1) - 1/(2i+1) you should do ..............

i would need to have i equal all numbers from 1 to 100? than 1000 and 100000?

Quote:

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Originally Posted by pjr5043

i would need to have i equal all numbers from 1 to 100? than 1000 and 100000?

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If you're going to do two at a time (with a + and a -), then you have to go by twos. You can let i be every number, but then you'll have to take care of the alternating + and - yourself (with sign = -1*sign or whatever).

alrite, so i can put like int i+2 in the loop right? .. but then what should my command line be for the loop .. right now i have c!=100 is that right?

Quote:

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Originally Posted by pjr5043

alrite, so i can put like int i+2 in the loop right? .. but then what should my command line be for the loop .. right now i have c!=100 is that right?

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No and no. If you're doing a for loop you would need to
(1) start with i = 1
(2) keep going unless i exceeds 100
(3) and add 2 to i each time

i really don't know, i'm never going to get this right because my teacher is a terrible at teaching, i already submitted my file, but honestly i'm being straight with you, if one of you were to just tweak my original code to make this thing work, i could see what you did, and that is the best way i learn things, i'm absolutely horrible and things like this right now, i need to see what i did and what i should of did, thats how my brain works

Quote:

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Originally Posted by pjr5043

i really don't know, i'm never going to get this right because my teacher is a terrible at teaching, i already submitted my file, but honestly i'm being straight with you, if one of you were to just tweak my original code to make this thing work, i could see what you did, and that is the best way i learn things, i'm absolutely horrible and things like this right now, i need to see what i did and what i should of did, thats how my brain works

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The only thing providing you with code will do is give you a template to copy from without understanding for future assignments. As to telling you what you should have done, we've been doing that all this time -- look at all that telling you things in this thread! My last post told you how your for-loop should have gone: this is your response. My post before that pointed out that there is a difference between 1, 2, 3, 4, 5 and 1, 3, 5, which led to your odd question about loops. It's hard to point out what errors are in your code when you don't seem to have any -- at least, you've never shown us any beside that original post. And, despite -- twenty-odd posts in this thread all together? -- you still have never managed to write the problem down correctly; and how important can the answer be if you don't seem to care about the question? I'm not saying you can't be taught, and I obviously can't speak for your instructor, but I can say that right now in this thread you are refusing to learn.