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Diff — Triangle

Revision #1640 → #2258 · back to history

modifiedTriangle236e9af2bcfd
FieldFrom #1640To #2258
mathlib.declAffine.Triangle
mathlib.match_kindexact
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Simplex.Basic
noteAffine.Triangle abbreviates `Affine.Simplex k P 2`, a bundled triple of affinely independent points.
statusformalized
modifiedSum of angles equals straight angle10e647e6b05e
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.angle_add_angle_add_angle_eq_pi
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Triangle
noteProves ∠p₁p₂p₃ + ∠p₂p₃p₁ + ∠p₃p₁p₂ = π for three points in a Euclidean affine space.
statusformalized
modifiedArea equals half base times height24a1c70f3a59
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `Affine.Triangle.area` (or simplex analogue with the ½·base·height formula) appears in Mathlib.
statusnot_formalized
modifiedThree non-collinear points determine a triangled4ef29f02a80
FieldFrom #1640To #2258
mathlib.declAffine.Triangle
mathlib.match_kindexact
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Simplex.Basic
noteThe structure `Affine.Triangle` bundles exactly three affinely independent (i.e. non-collinear) points.
statusformalized
addedTetrahedrond1a9916474fe
addedSpherical and hyperbolic triangles (non-Euclidean)cc40605372fb
modifiedGeodesic triangle1a0ddcdebdad
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteMathlib has no notion of geodesic triangle on a surface or in a metric space.
statusnot_formalized
modifiedCurvilinear trianglec35f5118be51
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo definition of curvilinear triangle exists in Mathlib.
statusnot_formalized
modifiedTriangle (sides and vertices)fb494d910ada
FieldFrom #1640To #2258
mathlib.declAffine.Triangle
mathlib.match_kindexact
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Simplex.Basic
noteTriangles in Mathlib are bundled as three affinely independent vertices, with `Polygon.toTriangle` linking to the three-segment view.
statusformalized
modifiedEquilateral, isosceles, scalene trianglesf5557d89390b
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.Equilateral
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Analysis.Normed.Affine.Simplex
note`Affine.Simplex.Equilateral` and `Affine.Simplex.Scalene` exist for simplices, but Mathlib has no `Isosceles` predicate.
statuspartial
modifiedRight, acute, obtuse trianglesd26ad9729740
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.AcuteAngled
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Geometry.Euclidean.Simplex
noteOnly `AcuteAngled` (with `Affine.Triangle.acuteAngled_iff_angle_lt`) is in Mathlib; no `Right` or `Obtuse` triangle predicate.
statuspartial
addedDeltahedron901fffd796dd
addedSimplex (generalized triangle)c8b2963d477e
modifiedCeva's theorem02eb51094fd4
FieldFrom #1640To #2258
mathlib.declAffine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMap
mathlib.match_kindexact
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Ceva
noteMathlib has Ceva's theorem for triangles in several equivalent forms (weights, divisions, distances).
statusformalized
modifiedMenelaus' theorema4f870cf4f5c
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteGrep over Mathlib finds no occurrence of Menelaus.
statusnot_formalized
modifiedPerpendicular bisector2502b3e23891
FieldFrom #1640To #2258
mathlib.declAffineSubspace.perpBisector
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.PerpBisector
note`perpBisector p₁ p₂` is the perpendicular bisector of the segment [p₁, p₂] as a bundled affine subspace.
statusformalized
modifiedCircumcenter from perpendicular bisectorse2a6c6caa38a
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.circumcenter
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Geometry.Euclidean.Circumcenter
noteCircumcenter is defined via uniqueness of an equidistant point; the explicit concurrence-of-perpBisectors theorem isn't stated as such.
statuspartial
addedCircumcircled9465424012e
modifiedThales' theorem (circumcenter on side)7e33379261b4
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.Sphere.thales_theorem
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Angle.Sphere
noteAn inscribed angle subtending a diameter is a right angle; aliased as `thales_theorem`.
statusformalized
modifiedCircumcenter location and triangle type16f2854c044f
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo lemma classifying triangle type by interior/exterior position of the circumcenter is in Mathlib.
statusnot_formalized
modifiedAltitude of a trianglefe7a848f807c
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.altitude
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Geometry.Euclidean.Altitude
noteAltitude of a simplex is defined as the line through a vertex orthogonal to the opposite face.
statusformalized
modifiedOrthocenter from altitudes2f55d550049d
FieldFrom #1640To #2258
mathlib.declAffine.Triangle.eq_orthocenter_of_forall_mem_altitude
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.MongePoint
note`orthocenter_mem_altitude` plus `eq_orthocenter_of_forall_mem_altitude` show the three altitudes concur at the orthocenter.
statusformalized
modifiedOrthocenter inside iff acute37a6e3bd928b
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteMathlib has the orthocenter and AcuteAngled but no lemma linking the orthocenter's interior position to acuteness.
statusnot_formalized
modifiedAngle bisectorfd0546b7265c
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo dedicated `angleBisector` definition appears in Mathlib's geometry library.
statusnot_formalized
modifiedIncenter from angle bisectors2ee9902a4aca
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.incenter
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Geometry.Euclidean.Incenter
noteIncenter is defined as the center of the insphere (tangent to the faces), not via concurrence of angle bisectors.
statuspartial
addedIncircle586a53147c44
modifiedExcircles and orthocentric system65621c6252a3
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.exsphere
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Geometry.Euclidean.Incenter
note`exsphere` covers excircles, and `EuclideanGeometry.OrthocentricSystem` formalises the orthocentric system.
statusformalized
modifiedNine-point circle18ff01a2a164
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.ninePointCircle
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.NinePointCircle
noteNine-point circle defined; lemmas like `faceOppositeCentroid_mem_ninePointCircle` and `altitudeFoot_mem_ninePointCircle` verify the nine points.
statusformalized
addedNine-point circle radius is half circumradiusf763d9301591
addedFeuerbach's theorem (nine-point circle touches incircle and excircles)a9b538321f42
modifiedEuler's line482d05f21781
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteCircumcenter, centroid and orthocenter all exist but the collinearity result `EulerLine` is not stated in Mathlib.
statusnot_formalized
addedDistances along Euler's line7ca6d05563d5
modifiedMedian of a triangle8a6747ab4880
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.median
mathlib.match_kindgeneralization
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Simplex.Centroid
note`median` is the line from a vertex of a simplex through the centroid of the opposite face; for a triangle this is the median through the midpoint.
statusformalized
modifiedCentroid from medians86d874ea8c89
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.eq_centroid_of_forall_mem_median
mathlib.match_kindgeneralization
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Simplex.Centroid
noteStates that any point lying on all medians of a simplex equals the centroid.
statusformalized
addedCentroid is center of mass4df51d9c70cc
modifiedCentroid cuts median 2:1837031c29f57
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.point_vsub_centroid_eq_smul_vsub
mathlib.match_kindgeneralization
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Simplex.Centroid
noteCommandino's theorem: vertex-to-centroid equals `n` times centroid-to-faceOppositeCentroid, giving the 2:1 ratio when n = 2.
statusformalized
modifiedSymmedian and symmedian pointaafac5de5bea
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo symmedian or symmedian point definition exists in Mathlib.
statusnot_formalized
modifiedSum of interior angles is 180°b9e51ac5d7cc
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.angle_add_angle_add_angle_eq_pi
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Triangle
noteSum of the three angle-at-point measures equals π.
statusformalized
addedAngle-sum equivalent to parallel postulate4a766053baf0
modifiedExterior angle theorem4527572f8c73
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.exterior_angle_eq_angle_add_angle
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Triangle
noteStated directly using `Sbtw` to place a point on the extension of a side.
statusformalized
modifiedSum of exterior angles is 360°58126f9123a9
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo statement summing the three exterior angles to 2π is present in Mathlib.
statusnot_formalized
modifiedTrigonometric functions in right triangles1c93b21a86ee
FieldFrom #1640To #2258
mathlib.declReal.sin
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Analysis.SpecialFunctions.Trigonometric.Basic
noteMathlib defines sin/cos analytically and has `cos_angle` in terms of inner products, but does not give the right-triangle ratio definition.
statuspartial
modifiedLaw of sines and cosines062e6192c4e9
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.law_cos
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Triangle
noteBoth `law_cos` and `law_sin` are proved (with vector-angle variants in InnerProductGeometry).
statusformalized
modifiedThree angles summing to 180° form a triangle1839d4db151d
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo converse-existence lemma constructing a triangle from three angles summing to π is in Mathlib.
statusnot_formalized
modifiedDegenerate triangleb0aa8f47ce41
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
note`Affine.Triangle` requires affine independence, so a degenerate-triangle predicate is not defined separately.
statusnot_formalized
modifiedSimilar triangles0b7ecd573adf
FieldFrom #1640To #2258
mathlib.declSimilar
mathlib.match_kindexact
mathlib.moduleMathlib.Topology.MetricSpace.Similarity
note`Similar` is the general indexed-family similarity used by the triangle similarity lemmas in `Mathlib.Geometry.Euclidean.Similarity`.
statusformalized
modifiedAA similarity9e380e19f216
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.similar_of_angle_angle
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Similarity
noteTwo pairs of equal angles imply similarity of the two triangles.
statusformalized
modifiedSAS similarityb1a4632a48d6
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.similar_of_side_angle_side
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Similarity
noteProportional adjacent sides with equal included angle imply similarity.
statusformalized
modifiedSSS similarity407034261b14
FieldFrom #1640To #2258
mathlib.declsimilar_of_side_side
mathlib.match_kindexact
mathlib.moduleMathlib.Topology.MetricSpace.Similarity
noteProportional sides imply similarity for the (a,b,c)/(a',b',c') triples.
statusformalized
modifiedCongruent trianglesfd6b7c4bd7e9
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.triangle_congruent_iff_dist_eq
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Congruence
noteTriangle congruence is the specialisation of the general `Congruent` predicate, characterised by pairwise equal distances.
statusformalized
modifiedSAS congruence postulateca715ce0dd1f
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.side_angle_side
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Congruence
noteTwo sides and the included angle equal ⇒ triangles congruent.
statusformalized
modifiedASA congruence719e124a4df9
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.angle_side_angle
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Congruence
noteTwo angles and the included side equal ⇒ triangles congruent (with a non-collinearity hypothesis).
statusformalized
modifiedSSS congruencea9ec7c2c49cd
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.side_side_side
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Congruence
noteThree equal pairs of sides ⇒ congruent, even for degenerate triangles.
statusformalized
modifiedAAS congruence48d4f73eceb3
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.angle_angle_side
mathlib.match_kindexact
mathlib.moduleMathlib.Geometry.Euclidean.Congruence
noteTwo angles and a non-included side equal ⇒ congruent.
statusformalized
modifiedArea as half base times altitude8277edfdb10b
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `triangle area = ½·base·height` lemma is present in Mathlib.
statusnot_formalized
modifiedArea from two sides and included angled79217ad3f65
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `½ a b sin C` triangle-area formula in Mathlib.
statusnot_formalized
modifiedHeron's formulaeb36da31cea6
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo Heron's-formula declaration appears in Mathlib (the `Heron`-named hits are all unrelated, e.g. `Harmonic`).
statusnot_formalized
modifiedAffine relative area39eb65af66c2
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteMathlib does not define a notion of relative/affine triangle area.
statusnot_formalized
modifiedShoelace formula for triangle areac5c78681fdd9
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteGrep for `shoelace`/`Shoelace` finds no Mathlib declaration.
statusnot_formalized
modifiedTriangle inequalityfe9566631302
FieldFrom #1640To #2258
mathlib.decldist_triangle
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Topology.MetricSpace.Pseudo.Defs
noteThe metric-space `dist_triangle` is the general form; `norm_add_le` is the vector version.
statusformalized
modifiedConverse of triangle inequality830921f2ca5e
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo constructive lemma producing a triangle from three side lengths satisfying the triangle inequality is in Mathlib.
statusnot_formalized
modifiedTriangle rigidity13ba6912fd15
FieldFrom #1640To #2258
mathlib.declEuclideanGeometry.side_side_side
mathlib.match_kindinvocation
mathlib.moduleMathlib.Geometry.Euclidean.Congruence
noteSSS congruence is the precise statement of triangle rigidity; no separate `rigidity` lemma exists.
statuspartial
modifiedPolygon triangulation count70b99121289b
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
notePolygon triangulation, Catalan-number counts, and simple-polygon decomposition are not formalised in Mathlib.
statusnot_formalized
modifiedTwo ears theoremdc26c7f575de
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteGrep finds no `TwoEar`/`ears`-theorem declaration in Mathlib.
statusnot_formalized
modifiedTrilinear coordinates6e35c8b5ab0a
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteMathlib mentions trilinear coordinates only in a docstring of `SignedDist`; no dedicated definition exists.
statusnot_formalized
modifiedBarycentric coordinates719774c14add
FieldFrom #1640To #2258
mathlib.declAffineBasis.coord
mathlib.match_kindgeneralization
mathlib.moduleMathlib.LinearAlgebra.AffineSpace.Basis.Defs
note`AffineBasis.coord` gives the ith barycentric coordinate map; lemmas like `coord_apply_combination` characterise it.
statusformalized
modifiedUnique incircle59d26382e9da
FieldFrom #1640To #2258
mathlib.declAffine.Simplex.insphere
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Geometry.Euclidean.Incenter
noteMathlib's insphere is uniquely defined for every simplex; specialised to a triangle it gives the unique incircle.
statusformalized
modifiedSteiner inellipse17cca5701672
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteGrep for `Steiner.*inellipse`/`SteinerInellipse` returns no matches.
statusnot_formalized
modifiedMarden's theorem1d45afd76896
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `Marden` declaration in Mathlib.
statusnot_formalized
addedSteiner inellipse has maximum areaa876dc23fe7a
modifiedMandart inellipse32722cd79009
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteGrep for `Mandart` returns no matches.
statusnot_formalized
modifiedPedal triangle and medial triangle87735ec9b6fd
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNeither `pedalTriangle` nor `medialTriangle` is defined in Mathlib.
statusnot_formalized
modifiedMedial triangle subdivides into four congruent triangles4d3209c3f568
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteWithout a medial-triangle definition, the corresponding subdivision lemma is not in Mathlib.
statusnot_formalized
modifiedIntouch triangle529ddfd67822
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `intouchTriangle` declaration; only the underlying `Simplex.touchpoint` exists.
statusnot_formalized
modifiedExtouch trianglef6d144e8df53
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `extouchTriangle` declaration in Mathlib.
statusnot_formalized
modifiedCalabi trianglece3b4775086f
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo Calabi triangle definition exists in Mathlib.
statusnot_formalized
modifiedInscribed squares by triangle type2de49ed23ff0
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo Mathlib lemma counts inscribed squares of a triangle by type.
statusnot_formalized
modifiedLemoine hexagon98fb603dd729
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `Lemoine` hexagon definition is present in Mathlib.
statusnot_formalized
modifiedConvex polygon inscribed in triangle area boundeef08703c1ed
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo area-bound theorem comparing inscribed convex polygons to the enclosing triangle is in Mathlib.
statusnot_formalized
addedEquality case: inscribed parallelogram3963d1dab959
modifiedTangential triangleba5b68cfe28c
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `tangentialTriangle` definition exists in Mathlib.
statusnot_formalized
modifiedSteiner circumellipsedf845ac94542
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteSteiner circumellipse is not defined or characterised in Mathlib.
statusnot_formalized
addedSteiner circumellipse has minimum area428d03d3dc47
modifiedKiepert hyperbolab8eabc430a54
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo Kiepert hyperbola is formalised in Mathlib.
statusnot_formalized
modifiedMaximum-area triangle in convex polygon2e114d6ecb96
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteAlgorithmic result on maximum-area inscribed triangles is not part of Mathlib.
statusnot_formalized
modifiedCircular trianglec1c6185ce9f7
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo circular-triangle definition appears in Mathlib.
statusnot_formalized
addedIntersection of three disks is a convex circular triangle7f4fbf591f70
modifiedReuleaux triangle36f37cb2d991
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteGrep for `Reuleaux` returns no matches.
statusnot_formalized
modifiedMohr–Mascheroni theorem52dba7200f1a
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo `Mohr` declaration in Mathlib (the `Mascheroni` hits are about the Euler–Mascheroni constant).
statusnot_formalized
modifiedPseudotriangleca725b91c49b
FieldFrom #1640To #2258
anchor.snippetForA pseudotriangle is a simply-connected subset of the plane lying between three mutually tangent convex regions
kindpropositiondefinition
labelPseudo-triangulation countsPseudotriangle
mathlib.decl
mathlib.match_kind
mathlib.module
noteMathlib has no notion of pseudotriangle.
statusnot_formalized
addedPseudo-triangulation counts6e0ffac79180
modifiedConvex hull of pseudotriangle is a trianglec0edc2d91bc2
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteWithout a pseudotriangle definition, no convex-hull lemma about them is in Mathlib.
statusnot_formalized
modifiedHyperbolic and spherical triangles6f7e16194078
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo hyperbolic or spherical triangle definition exists in Mathlib.
statusnot_formalized
modifiedAngle sum in hyperbolic and spherical triangles264543e78a1d
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteMathlib does not formalise angle sums in hyperbolic or spherical triangles.
statusnot_formalized
modifiedGirard's theorem2d0ae3059e95
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo Girard-theorem (spherical excess) declaration is in Mathlib.
statusnot_formalized
addedTriangle comparison theorems88288baf6609
modifiedCAT(k) space01a6e4f578b6
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteNo CAT(k) space definition exists in Mathlib.
statusnot_formalized
modifiedFractal triangles (Sierpiński, Koch)f9984e748a7f
FieldFrom #1640To #2258
mathlib.decl
mathlib.match_kind
mathlib.module
noteMathlib has no Sierpiński gasket or Koch snowflake construction.
statusnot_formalized
deletedPseudotriangleb967537f3bd4