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The red and blue paths are geodesics (the straightest possible paths, like great circles on a sphere) …
The red and blue paths are geodesics (the straightest possible paths, like great circles on a sphere) …
Refreshed, new and hallucinated: tourists book trips to nonexistent hot springs.
www.abc.net.au/news/2026-01...
Refreshed, new and hallucinated: tourists book trips to nonexistent hot springs.
www.abc.net.au/news/2026-01...
Link: www.abc.net.au/news/2026-01...
Link: www.abc.net.au/news/2026-01...
Let’s start by looking at the effect of curvature in a very simple situation. Two meridians on a sphere, like the red and blue ones in the diagram, will come together and move apart …
Let’s start by looking at the effect of curvature in a very simple situation. Two meridians on a sphere, like the red and blue ones in the diagram, will come together and move apart …
There’s a whole family of them hiding in plain sight:
x^2 – k^2 (x^2 + y^2 + z^2)^3 = 0
These are the surfaces of equal electrostatic potential for a dipole pointing along the x-axis!
There’s a whole family of them hiding in plain sight:
x^2 – k^2 (x^2 + y^2 + z^2)^3 = 0
These are the surfaces of equal electrostatic potential for a dipole pointing along the x-axis!
But the upshot is that we can find a curve in the space of eccentricities for two meridians of the ellipsoid, say e_xz and e_yz, in two orthogonal planes.
But the upshot is that we can find a curve in the space of eccentricities for two meridians of the ellipsoid, say e_xz and e_yz, in two orthogonal planes.
The answer is that you *can’t* pull off this trick for a generic tri-axial ellipsoid, with any old a, b and c.
The answer is that you *can’t* pull off this trick for a generic tri-axial ellipsoid, with any old a, b and c.
However, by adding just enough spin the shapes can be made the same.
However, by adding just enough spin the shapes can be made the same.
Initially, it will form an oblate spheroid, with two equal semi-axes shorter than its axis of rotation.
Initially, it will form an oblate spheroid, with two equal semi-axes shorter than its axis of rotation.
But what about the 3D equivalent?
Start with an ellipse and a hyperbola in orthogonal planes, with each curve’s vertices being the other’s foci.
But what about the 3D equivalent?
Start with an ellipse and a hyperbola in orthogonal planes, with each curve’s vertices being the other’s foci.
Congratulations to Georgina Steytler, who just won a wildlife photography award for this extraordinary image!
www.abc.net.au/news/2025-10...
Congratulations to Georgina Steytler, who just won a wildlife photography award for this extraordinary image!
www.abc.net.au/news/2025-10...
“Spare Parts for the Mind”
“Spare Parts for the Mind”