Lesson plan
Toroidal coordinates
about the axis separating its two foci. The foci are located at a distance 1 from the vertical z-axis. The portion of the red sphere that lies above the xy -plane is the σ = 30° isosurface, the blue torus is the τ = 0.5 isosurface, and the yellow half-plane is the φ = 60° isosurface. The green half-plane marks the x-z plane, from which φ is measured. The black point is located at the intersection of the red, blue and yellow isosurfaces, at Cartesian coordinates roughly (0.996, −1.725, 1.911). Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci F_1 and F_2 in bipolar coordinates become a ring of radius a in the xy plane of the toroidal coordinate system; the z -axis is the axis of rotation. The focal ring is also known as the reference circle.
Article summary
about the axis separating its two foci. The foci are located at a distance 1 from the vertical z-axis. The portion of the red sphere that lies above the xy -plane is the σ = 30° isosurface, the blue torus is the τ = 0.5 isosurface, and the yellow half-plane is the φ = 60° isosurface. The green half-plane marks the x-z plane, from which φ is measured. The black point is located at the intersection of the red, blue and yellow isosurfaces, at Cartesian coordinates roughly (0.996, −1.725, 1.911). Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci. Thus, the two foci F_1 and F_2 in bipolar coordinates become a ring of radius a in the xy plane of the toroidal coordinate system; the z -axis is the axis of rotation. The focal ring is also known as the reference circle.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.