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Wednesday, August 17, 2005

A perfect sphear

This post is a random musing, so do not read it if you are looking for something witty or clever. I will never post something that I learned from a book or heard from a professor, but came up with on my own. I may have verified it before posting. But copying something that I got out of a book would evade the purpose of posting these random musings.

A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another.

Current therum dictats that it is impossible to draw or create a perfect circle. Let us consider some basic properties of a circle: A circle is a set of points on a plane, each equally distant from a center point. If we run a vertical line through the center, we divide the circle into two semicircles, each of which is the exact mirror image of the other. We can do the same using a horizontal line. If we use both, a vertical and a horizontal line, we divide the circle into four sections, all mirror images of the rest (the mirror can be horizontal, vertical, or both). That means if we draw a tangent to the circle at each point of intersection of our horizontal or vertical line with the circumference of the circle, the tangent itself will be either horizontal or vertical. If we are to emulate any of the quadrants with cubic Bézier curves, we need to draw a curve which has a starting point, an ending point, and two control points. If we connect the starting point with the nearest control point, and the ending point with its nearest control point, we will have drawn two line segments: One of them horizontal, the other vertical (depending on the quadrant). Further, both line segments will be of the same length l. There are an infinite number of curves that have these properties (since there are, at least in theory, an infinite number of lengths l we can use). None of them will yield a perfect circle.

I aim to disprove this, but this may be considered cheating. I theorize that when the laws of physics breaks down, it is infact possible to have a perfect circle exist in the universe. I will go a bit further to say, there can exist a perfect sphere. Interestingly enough, I believe you cannot have a perfect circle without having a sphere.

In order to escape the earth's gravity, (escape velocity), you need to move an object at 11.2 kilometers per second (about mach 5). Use this to imagin the escape velocity in a black hole. Let's say we have a black hole with the property of 1.8x1016 g/cm3 (that is 1,800,000,000,000,000 grams per cubic cetemeter). For our example, the black hole would be 1031 kilograms. The escape velocity would need to exceed the speed of light.

An object (we'll say a lead ball compressed into a singularity) would be pulled directly towards the center of the black hole. I surmise that it will quickly even out with the rest of the surface, for to stand above the surface by any amount, would mean that the object has the opposing force, greater than the force it would take to move this object the speed of light. Therefore, in a still, settled black hole, there will be no point that is higher than any other point on the curved plane.

A perfect sphere will ONLY occur if the black hole is not rotating. If a blackhole rotates (as Einstein theorized and Stephan Hawking reiterized in "A Brief History of Time") then it will bulge along the equador.

When the black hole is still, and no new stimuli are being added to it, once it settles, consider: if we create a plane through the center of the black hole, the mass on both sides of the plane will be qual.

Secondly, if we be able to draw an infinite amount of tangents on the sphere, and at each tangent-point, drawing a line to the center, the intersection would be perfectly perpendicular.

Q.E.F.

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