Circle = Infinite Polygon, Ellipse = Infinite Polygon

 

Circle = Infinite Polygon, Ellipse = Infinite Polygon

Compression, Expansion

A circle becomes an ellipse through compression and expansion, and a regular polygon becomes a polygon through compression and expansion.

The minor axis of the ellipse is compressed relative to the major axis, and conversely, the minor axis is expanded by the same amount as the major axis.

In a circle, every angle point has a constant value, whereas in an ellipse, each angle has a different value. This can be explained using an octagon.

For a regular octagon, a=b; for an octagon, a≠b.

When side 'a' is divided infinitely, it becomes a point. In the case of a circle, however, every point has a constant value, creating the angle of the circular curve. Based on this principle, for a circle, you calculate one point and sum them all, but for an ellipse, you must calculate each one individually. Therefore, it is an NP problem. This is why calculating the circumference of an ellipse must be solved using a computer.

When side 'a' is divided infinitely, it becomes a point; in the case of a circle, all points have a constant value, creating the angle of the circular curve. Based on this principle, for a circle, one point is calculated and then summed, whereas for an ellipse, each point must be calculated individually. Therefore, it is an NP problem. This is why calculating the circumference of an ellipse must be solved using a computer.

 

Ellipses are difficult to solve as infinite polygons. However, they can be much easier than expected when solved in the following way.

 

Intersection point p

Two circles, A (small circle) and B (large circle), are divided and solved at the intersection point p.

 

For convenience in calculation, the problem is solved by dividing it into four equal parts.

 

If you have divided it into four equal parts, you need to separate the two circles.

 

You just need to divide it into two circular curves based on the intersection point p and substitute the curves.

 

However, finding the intersection point p is difficult. As such, you have to apply various ideas. For now, that is all for the ellipse circumference...

 

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Ellipses and the Shape of the Universe

What form does the universe we live in take? A sphere, or a donut shape, or perhaps Sky Butterfly's Up-Down Universe Theory? When a sphere is expanded in one direction, a cylinder is formed, and the top and bottom faces of the cylinder form a shape resembling a cone with empty space. This shape perfectly matches a sphere in both volume and surface area. Sky Butterfly's proof of the sphere is verified.

 

A rectangle is formed from the compression and expansion of a square. An ellipse is formed from the compression and expansion of a circle.