How circular does it need to be?

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Discussion Overview

The discussion revolves around the relationship between the accuracy of the value of ##\pi## and the construction of circular objects, particularly in engineering contexts. It also touches on the differences in circularity requirements between engineering applications, such as those at CERN, and more casual constructions like a playground.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question whether more accurate values of ##\pi## lead to the construction of more circular objects, suggesting that it is possible to draw a circle accurately without knowing ##\pi##.
  • Others argue that while a playground may not be perfectly circular, having a rough estimate of the shape and diameter is sufficient for practical tasks, such as estimating materials needed.
  • One participant explains that CERN's requirement for circularity is due to the physics of particle acceleration, where deviations from a perfect circle would necessitate unequal acceleration or cause the particle beam to intersect the sides.
  • A clarification is made that the CERN accelerator is actually oval-shaped, with straight portions, indicating that it is not designed to be a perfect circle.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of accurate values of ##\pi## for constructing circular objects, with no consensus reached on the implications of this accuracy in practical applications.

Contextual Notes

The discussion does not resolve the assumptions regarding the implications of ##\pi## accuracy in various contexts, nor does it clarify the specific requirements for circularity in engineering versus casual applications.

Agent Smith
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TL;DR
Approximations of ##\pi##
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The above was part of a conversation on ##\pi## and the implication seems to be that the more accurate the value of ##\pi## in our calculations in an engineering context, the more circular our construction.

Questions:

1. Is this true? More accurate values of ##\pi## allow for construction of more circular objects? How exactly?

2. Why does CERN have to be more circular than a circular playground?
 
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Agent Smith said:
1. Is this true? More accurate values of ##\pi## allow for construction of more circular objects? How exactly?
No, not at all. I can draw a circle quite accurately with a compass, all without having any idea what pi is.

As for the playground, it probably won't be perfectly circular, but if you're going to line the edge with bricks, a rough idea of the shape and diameter will give a reasonable estimate of the number of bricks that will be needed for the task.

Agent Smith said:
2. Why does CERN have to be more circular than a circular playground?
Because particles going around the loop are subject to constant lateral acceleration and any deviation from a perfect circle would either require unequal acceleration or would cause the particle beam to intersect the sides.

For the same reasons, linear accelerators don't have bends in them.

Edit: The CERN accelerator is actually oval shaped, with straight portions on (at least) two sides, which is where the collisions take place, and where the detectors all are. Point is, it isn't designed to be a perfect circle.
 
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