Oblate Circle

Robust · 05-04-2005

Except for the few die-hards, we know that that there can be no such thing as the perfect citcle, earth dimensions giving a prine example. The figure I give for disparity of the static circle is 1.001129 adinfinitum. Atmospheric scientists say that is a very close figure to describing earth's oblateness, the varying moisture content of its upper atmosphere perhaps accounting for the slight difference.

Knowing then dimensions of the static circle, which would be the configuration to annouced plans for the eventual navigation of a probe beyond our solar system, might be seen as essential. The next essential (if not the first) would be in knowing the distance between each angular degree on circumference of the intended trajectory. And indeed we do now have all those figures - so up and away, folks....let's do it!

C1ay · 05-04-2005

Quote:

Originally Posted by Robust

Except for the few die-hards, we know that that there can be no such thing as the perfect citcle, earth dimensions giving a prine example. The figure I give for disparity of the static circle is 1.001129 adinfinitum.

A circle is the set of points in a plane that are equidistant from a given point O. If you disagree, prove it.

maddog · 05-04-2005

Quote:

Originally Posted by Robust

Except for the few die-hards, we know that that there can be no such thing as the perfect citcle, earth dimensions giving a prine example. The figure I give for disparity of the static circle is 1.001129 adinfinitum. Atmospheric scientists say that is a very close figure to describing earth's oblateness, the varying moisture content of its upper atmosphere perhaps accounting for the slight difference.

Knowing then dimensions of the static circle, which would be the configuration to annouced plans for the eventual navigation of a probe beyond our solar system, might be seen as essential. The next essential (if not the first) would be in knowing the distance between each angular degree on circumference of the intended trajectory. And indeed we do now have all those figures - so up and away, folks....let's do it!

???

"A perfect circle is a construct". It is simple to make.

x^2 + y^2 = cos^2 theta + sin^2 theta = 1 or for complex numbers

z^2 = 1 = [e^(i * theta)/2*pi + e^ - (i * theta)/2*pi]/2 + [e^(i * theta)/2*pi - e^ - (i * theta)/2*pi]/2

This is EXACTLY a perfect circle in either coordinate system.

maddog

Robust · 05-04-2005

Quote:

Originally Posted by maddog

???

"A perfect circle is a construct". It is simple to make.

x^2 + y^2 = cos^2 theta + sin^2 theta = 1 or for complex numbers

z^2 = 1 = [e^(i * theta)/2*pi + e^ - (i * theta)/2*pi]/2 + [e^(i * theta)/2*pi - e^ - (i * theta)/2*pi]/2

This is EXACTLY a perfect circle in either coordinate system.

maddog

maddog: One can probaby arrive at any conclusion they want by the application of mathematics. Proving it empirically is another ballgame entirely. We know that there is no such thing as the perfect circle by empirical application. If you can show otherwise, there are great awards awating you.