Archimedes' Dilemma: The Misunderstood Concept of Pi = 4

  • Thread starter Thread starter JaredJames
  • Start date Start date
  • Tags Tags
    Archimedes Pi
Click For Summary
SUMMARY

The forum discussion centers on the erroneous claim that Pi equals 4, stemming from a misunderstanding of geometric principles. Participants clarify that this result arises from using inappropriate methods to approximate Pi, specifically by averaging the perimeters of inscribed and circumscribed squares. The correct approach involves using limits and proper geometric shapes to derive accurate values for Pi, which is approximately 3.14159. The conversation also touches on the concept of infinite series and limits, particularly in relation to the equality of 0.999... and 1.

PREREQUISITES
  • Understanding of basic geometry, including inscribed and circumscribed shapes
  • Familiarity with limits and infinite series in calculus
  • Knowledge of mathematical notation and concepts such as 0.999... = 1
  • Basic understanding of numerical approximation techniques
NEXT STEPS
  • Research the concept of limits in calculus, particularly in relation to infinite series
  • Study the methods for approximating Pi using polygons and other geometric shapes
  • Explore the mathematical proof that 0.999... equals 1
  • Learn about the historical context and significance of Archimedes' work on Pi
USEFUL FOR

Mathematicians, educators, students in mathematics or physics, and anyone interested in the foundations of geometry and numerical analysis.

  • #61
jreelawg said:
Pi does = 4. Don't you understand relativity? Curvature affects the metric and makes distances seam shorter. Sure a circle appears to be 3.14... because the circle is experiencing curvature. In the frame of reference of the square, pi is 4.

I hope this is a joke lol.
 
Mathematics news on Phys.org
  • #62
It's sort of interesting. The perimeter of a digital circle is 8r, and the surface area is approximately 6pir^2.
 
Last edited:
  • #63
Mathnomalous said:
Btw, I, too, would have a problem if my name was Archimedes; what kind of parent names his kid Archimedes!?

Continuing the necro spirit :biggrin:

Archimedes in ancient Greek translates into "the one who gives leading advice" :wink:
 

Similar threads

New Subforum for GD : Science and Technology News
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Optimization problem with multiple outputs: impossible?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad How to evaluate the enclosed area of this implicit curve?
  • · Replies 2 ·
Replies
2
Views
3K
Logic behind the Lifting Water problem
  • · Replies 6 ·
Replies
6
Views
2K
Physics Over what field I'm going to choose
  • · Replies 3 ·
Replies
3
Views
2K
Graduate In light of new evidence, what might be behind the Casimir Effect?
  • · Replies 46 ·
2
Replies
46
Views
5K
Graduate Regarding angular momentum axial thrust force etc. space stations
  • · Replies 5 ·
Replies
5
Views
4K
Thermodynamics of a Single-Component Ideal Gas
  • · Replies 1 ·
Replies
1
Views
1K
How Can Concept Maps Enhance Understanding in Advanced Mathematics?
  • · Replies 5 ·
Replies
5
Views
47K
PF Fan Fiction: Mathematicians in Love
  • · Replies 2 ·
Replies
2
Views
4K