Is Special Relativity the Key to Understanding Shrinking Circles?

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SUMMARY

The discussion centers on the implications of special relativity on the geometry of a spinning circle, represented by the equation (x-h)²+(y-k)²=r², where (h,k) is the center and r is the radius. As the circle spins about an axis perpendicular to its plane, the distance between points on the circumference decreases due to gravitational effects, challenging the constancy of π, defined as π=c/(2r). This paradox highlights the relationship between acceleration, gravity, and the geometric properties of space, suggesting that the circle may transform into a cone under these conditions. The conversation connects this phenomenon to Einstein's exploration of non-Euclidean geometries.

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  • Basic knowledge of geometric equations, particularly circles
  • Comprehension of the equivalence principle in physics
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yourdadonapogostick
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am i missing something here?
we have a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center and r is the radius. we now spin the circle about an axis that is perpendicular to the plane on which the circle lies and it runs through the center of said circle. gravity contracts length (and my the equivelance principle, so does acceleration), so as the 1-sphere spins about the axis, the distance between any two points on it decreases while the radius stays the same. since [tex]\pi=\frac{c}{2r}[/tex], where c is circumference and r is radius, [tex]\pi[/tex] no longer is a constant. the circle shrinks, but the radius stays the same. what is going on? does the circle turn into a cone?
 
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i just found out that the equivelence princliple doesn't apply here.
 
You have stumbled upon a fanatastic paradox of special relativity

As it appears in the history books, this is the very same case that lead Einstein to consider non-euclidean geometries in the physical universe.
 

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