How circular does it need to be?

[Agent Smith]

TL;DR Summary

Approximations of $\pi$

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?

 

[Halc]

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.

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.

 

[berkeman]

Thread closed for Moderation.

 

[berkeman]

After a Mentor discussion, this thread will remain closed. @Agent Smith -- Please keep your questions about $\pi$ in your original thread: https://www.physicsforums.com/threads/a-pi-question.1064916/