Accuracy of Pi: Arguing with Dad

In summary, the conversation revolved around the accuracy of pi values. One person argued that the fraction 22/7 is always more accurate than any decimal representation of pi, while the other person argued that the value 3.14159265358979 is more accurate. The second person requested proof and further information on how pi values are measured. A helpful resource on pi was provided, along with a link to a proof of the irrationality of pi. Additionally, the value of 335/113 was mentioned as an accurate and easy to remember fraction for pi.
  • #1
miguel314
2
0
My dad and I got in an argument about accuracy of pi values. He said that the ratio 22/7 will always be more accurate than any decimal value of pi. I said that the value 3.14159265358979 is much more accurate. I'm 100% certain that I am correct, but I can't really think of how to prove this to him. I'd also like to know how those values are measured, exactly. Thank you for your time.
 
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  • #2
22/7 is an approximation to pi. It's not even accurate to three digits.

- Warren
 
  • #4
22/7= 3.142857143. As chroot said, not even to three digits.

(It is, however, the best approximate fraction with no more than 2 digits in the numerator.)
 
  • #5
To actually answer your question, you are looking for a proof of the irrationality of Pi. One such proof is http://www.lrz-muenchen.de/~hr/numb/pi-irr.html Google for "irrational pi proof" to see more.

Of course, in this context, the best "proof" would probably be to show him a calculator, press the Pi key, and then enter 22/7 for contrast.
 
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  • #6
thanks for the help, all... :approve:
 
  • #7

Related to Accuracy of Pi: Arguing with Dad

1. What is Pi and why is it important?

Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. It is important because it is a fundamental constant in mathematics and is used in various fields such as geometry, trigonometry, and physics.

2. Why is the accuracy of Pi a topic of argument?

The accuracy of Pi has been a topic of argument for many years because it is an irrational number, meaning it has an infinite number of digits after the decimal point. This makes it impossible to know its exact value, leading to debates and discussions about its accuracy.

3. How is the accuracy of Pi calculated?

The accuracy of Pi can be calculated using various methods such as the geometric method, the Monte Carlo method, or the converging series method. Each method uses a different approach to estimate the value of Pi.

4. What is the current known accuracy of Pi?

The current known accuracy of Pi is approximately 31.4 trillion digits after the decimal point. This was achieved through the use of powerful supercomputers and specialized algorithms.

5. How does the accuracy of Pi affect real-world applications?

The accuracy of Pi is crucial in real-world applications such as engineering, construction, and technology. Even small errors in the value of Pi can lead to significant miscalculations and affect the functionality and safety of structures and devices.

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