Undergrad Understanding the Physical Meaning of Pi in a Circle

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SUMMARY

The discussion centers on the physical meaning of π (pi) in relation to circles, emphasizing that π is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. Participants clarify that while π has an infinite decimal representation, it is a finite, irrational number, not infinite itself. The conversation also addresses misconceptions about the nature of π, asserting that perfect circles exist despite the non-terminating nature of π's decimal expansion. Understanding π is crucial for interpreting measurements in geometry and physics.

PREREQUISITES
  • Basic understanding of geometry, specifically circles and their properties.
  • Familiarity with the concept of irrational numbers.
  • Knowledge of mathematical constants and their applications.
  • Ability to interpret decimal representations and their significance in mathematics.
NEXT STEPS
  • Study the properties of irrational numbers and their implications in mathematics.
  • Explore the derivation of the circumference formula: C = πD.
  • Learn about the significance of π in various fields, including physics and engineering.
  • Investigate methods for approximating π, such as using fractions like 22/7 or series expansions.
USEFUL FOR

Mathematicians, physics students, educators, and anyone interested in the foundational concepts of geometry and the significance of mathematical constants like π.

  • #31
akashpandey said:
yes .14159 and so on :nb) .
please can you explain ?

What exactly do you want explained? Have you understood anything that's been said in this thread so far?
 
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  • #33
akashpandey said:
what is exact measurement of that last part since the measurement of that last part is .142 so on is infinite so its length is also .142 and so on

The exact length is three less than pi: π-3 = 0.14159...
 
  • #34
but how the length .142 is exact??
 
  • #35
means .142...
 
  • #36
akashpandey said:
but how the length .142 is exact??

How isn't it?
 
  • #37
akashpandey said:
but how the length .142 is exact??

Drakkith said:
How isn't it?

To clarify, I'm asking so that I understand your thinking and level of knowledge on this.
 
  • #38
akashpandey said:
https://www.physicsforums.com/attac...1/?temp_hash=586afacbbfb47e99be368397d4138bd7.
can somebody explain me the measurement of last part of the circle i.e .3142 and so on.
means what is the exact measurement of that last part?
All I see in your picture is a circle with the diameter marked (but numerical value given) and a small section marked off, labeled ".14159...". There does not seem to be any reason given for that section to be marked or any explanation of what that means. I might guess that the ".14159", simply because it is the first 5 decimal places \pi, is supposed to be the decimal part of \pi, 3- \pi but I have no idea what it is really intended to show
 
  • #39
akashpandey said:
but how the length .142 is exact??
0.14159 (and so on) is a definite number between 0 and 1. Just because there's a decimal, it doesn't mean that it's not "real" or that it's "infinite" like you've said along this thread.
 

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