feat(Geometry/Euclidean/Sphere/PolePolar): poles and polars#31892
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jsm28 wants to merge 35 commits intoleanprover-community:masterfrom
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feat(Geometry/Euclidean/Sphere/PolePolar): poles and polars#31892jsm28 wants to merge 35 commits intoleanprover-community:masterfrom
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… using polars Add further lemmas about `orthRadius` that are of use in setting up and using poles and polars. In particular, `ncard_inter_orthRadius_eq_two_of_dist_lt_radius` is the key part of showing that, in two dimensions, there are exactly two tangents to a circle from a point outside that circle (where the points of tangency lie on the polar of the point from which the two tangents are drawn). --- I think the extra imports are reasonable for this file, but if `Mathlib.Analysis.InnerProductSpace.TwoDim` turns out to be too heavy, it's only used for `FiniteDimensional.of_fact_finrank_eq_two` which could be moved to somewhere much more basic in mathlib.
Define poles and polars for spheres in Euclidean affine spaces, and set up some basic API, including in particular La Hire's theorem (`p₁` lies on the polar of `p₂` if and only if `p₂` lies on the polar of `p₁`). Poles and polars are actually meaningful for any quadric in a projective space over any field, but I think it's reasonable to set up this theory for spheres in the Euclidean context and potentially link it in future to more general projective geometry.
PR summary 6cad1b0fccImport changes for modified filesNo significant changes to the import graph Import changes for all files
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| Current number | Change | Type |
|---|---|---|
| 7424 | 1 | backward.isDefEq |
Current commit 34fdfd3dac
Reference commit 6cad1b0fcc
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- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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…_eq_two` Move `of_fact_finrank_eq_two` from `Mathlib.Analysis.InnerProductSpace.TwoDim` to `Mathlib.LinearAlgebra.FiniteDimensional.Defs` to avoid a large import in leanprover-community#31891 that was only in order to use that one lemma without needing the rest of `Mathlib.Analysis.InnerProductSpace.TwoDim`.
Co-authored-by: Ruben Van de Velde <[email protected]>
Co-authored-by: Eric Wieser <[email protected]>
Co-authored-by: Eric Wieser <[email protected]>
Co-authored-by: Eric Wieser <[email protected]>
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Define poles and polars for spheres in Euclidean affine spaces, and set up some basic API, including in particular La Hire's theorem (
p₁lies on the polar ofp₂if and only ifp₂lies on the polar ofp₁).Poles and polars are actually meaningful for any quadric in a projective space over any field, but I think it's reasonable to set up this theory for spheres in the Euclidean context and potentially link it in future to more general projective geometry.
of_fact_finrank_eq_two#32296