B How circular does it need to be?

AI Thread Summary
More accurate values of π do not necessarily lead to more circular constructions, as circles can be drawn accurately without knowing π. In engineering, while precision in calculations is important, practical applications like playgrounds can still achieve reasonable circularity without exact values. CERN's design requires precision because particles experience constant lateral acceleration; any deviation from a perfect circle would disrupt the particle beam's trajectory. However, the CERN accelerator is not a perfect circle but an oval shape with straight sections for collisions and detectors. The discussion highlights the distinction between theoretical accuracy and practical application in different contexts.
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Approximations of ##\pi##
1.PNG

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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