Collapsing then Expanding the Equation for a Sphere

[caption id="attachment_8626" align="alignright" width="480"] How simple is a sphere?[/caption] Equation for the Simplest Sphere The equation for a sphere with its center at the origin is: x2 + y2 + z2 = c2 Where c is a positive constant. For simplicity, let's choose a positive constant, k, such that k = c2. Equation for a Circle by Collapsing a Sphere Collapsing it in one dimension generates the equation of one of three circles: x2 + y2 = k x2 + z2 = k y2 + z2 = k Equation for a Point by Collapsing a Circle Collapsing the three circles in one dimension generates two equations representing precisely two points for each of them: For x2 + y2 = k, x²2 = k y2 = k For x2 + z2…
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The Fabric of Space Time

[caption id="attachment_5108" align="alignright" width="440"] Fabric of Space Time -  GNU Free Documentation License Version 1.2 by LobStoR[/caption] This morning I read the Quantum Day article "Binary White Dwarf System J0651 Emits Gravitational Waves". It says just as sound waves require a medium such as air to travel through, gravitational waves as predicted by Einstein though as yet undetected would require a medium of travel as well. That medium would be the so-called fabric of space time. Quirky Ideas Though I am not certain such a fabric exists, I feel it is one of the more believable concepts in modern physics. I decided to speculate on the nature of that fabric. Is it absolutely continuous and smooth? Or might it only appear such, as air and water appear smooth, when they…
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