diff --git a/content/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.omdoc.xz b/content/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.omdoc.xz index c3052a5adcb5b18f9e3febaa5659740798f64202..77e82dbba5a503d463ebeee6fa74265be208222e 100644 Binary files a/content/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.omdoc.xz and b/content/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.omdoc.xz differ diff --git a/content/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.omdoc.xz b/content/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.omdoc.xz index 4178ed545c97fa640915a6826366829bdd666cc0..ac60e586d19170c0a559ed5791ab9fa625558ad5 100644 Binary files a/content/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.omdoc.xz and b/content/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.omdoc.xz differ diff --git a/content/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem.omdoc.xz b/content/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem.omdoc.xz new file mode 100644 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b/content/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Angle$At$B.omdoc.xz differ diff --git a/content/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Right$Angle$At$C.omdoc.xz b/content/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Right$Angle$At$C.omdoc.xz new file mode 100644 index 0000000000000000000000000000000000000000..380f0d8fceafd6af434eb64375f234b0d2c57ec1 Binary files /dev/null and b/content/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Right$Angle$At$C.omdoc.xz differ diff --git a/errors/mmt-omdoc/Scrolls/TriangleScrolls.mmt.err b/errors/mmt-omdoc/Scrolls/TriangleScrolls.mmt.err index a003a310ddaac2945e140ceaaaa6d7e3db90d6b4..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 100644 --- a/errors/mmt-omdoc/Scrolls/TriangleScrolls.mmt.err +++ b/errors/mmt-omdoc/Scrolls/TriangleScrolls.mmt.err @@ -1,2 +0,0 @@ -<errors> -</errors> diff --git a/narration/Scrolls/TriangleScrolls.omdoc b/narration/Scrolls/TriangleScrolls.omdoc index 9f6f7d5711365e02fedd14dcf72757cc90fa538c..92f8e4a48cd6368eb5a72f314d0bea12dc2762a6 100644 --- a/narration/Scrolls/TriangleScrolls.omdoc +++ b/narration/Scrolls/TriangleScrolls.omdoc @@ -1,5 +1,5 @@ <?xml version="1.0" encoding="UTF-8"?> -<omdoc base="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#0.0.0:4666.135.3"/><meta property="http://cds.omdoc.org/?metadata?importedby"><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMLIT type="http://www.openmath.org/cd?OpenMath?OMSTR" value="mmt-omdoc"/></om:OMOBJ></meta></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#0.0.0:47.0.47"/></metadata>Modular scrolls having to do with triangles</opaque><instruction text="namespace http://mathhub.info/FrameIT/frameworld"/><instruction text="fixmeta http://mathhub.info/FrameIT/frameworld?FrameworldMeta"/><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#128.5.0:322.14.0"/></metadata>A blueprint problem theory for triangle scrolls +<omdoc base="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#0.0.0:4946.141.3"/><meta property="http://cds.omdoc.org/?metadata?importedby"><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMLIT type="http://www.openmath.org/cd?OpenMath?OMSTR" value="mmt-omdoc"/></om:OMOBJ></meta></metadata><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#0.0.0:47.0.47"/></metadata>Modular scrolls having to do with triangles</opaque><instruction text="namespace http://mathhub.info/FrameIT/frameworld"/><instruction text="fixmeta http://mathhub.info/FrameIT/frameworld?FrameworldMeta"/><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#128.5.0:322.14.0"/></metadata>A blueprint problem theory for triangle scrolls B /| / | @@ -7,6 +7,6 @@ /___| A C - (nicer image: https://en.wikipedia.org/wiki/Right_triangle#/media/File:Rtriangle.svg)</opaque><mref name="[http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem]" target="http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#324.15.0:359.15.35"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#511.21.0:667.23.77"/></metadata>A blueprint problem theory for triangle scrolls that require a right angle + (nicer image: https://en.wikipedia.org/wiki/Right_triangle#/media/File:Rtriangle.svg)</opaque><mref name="[http://mathhub.info/FrameIT/frameworld?TriangleProblem]" target="http://mathhub.info/FrameIT/frameworld?TriangleProblem"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#324.15.0:345.15.21"/></metadata></mref><opaque format="text"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#497.21.0:653.23.77"/></metadata>A blueprint problem theory for triangle scrolls that require a right angle - We use ?TriangleScroll_GeneralProblem and demand the angle at C to be 90°</opaque><mref name="[http://mathhub.info/FrameIT/frameworld?TriangleScroll_RightAngledProblem]" target="http://mathhub.info/FrameIT/frameworld?TriangleScroll_RightAngledProblem"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#669.24.0:708.24.39"/></metadata></mref><mref name="[http://mathhub.info/FrameIT/frameworld?AngleSum]" target="http://mathhub.info/FrameIT/frameworld?AngleSum"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#941.33.0:955.33.14"/></metadata></mref><mref name="[http://mathhub.info/FrameIT/frameworld?OppositeLen]" target="http://mathhub.info/FrameIT/frameworld?OppositeLen"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#2240.68.0:2257.68.17"/></metadata></mref></omdoc> \ No newline at end of file + We use ?TriangleScroll_GeneralProblem and demand the angle at C to be 90°</opaque><mref name="[http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC]" target="http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#655.24.0:690.24.35"/></metadata></mref><mref name="[http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA]" target="http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#988.33.0:1018.33.30"/></metadata></mref><mref name="[http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB]" target="http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#1277.42.0:1307.42.30"/></metadata></mref><mref name="[http://mathhub.info/FrameIT/frameworld?AngleSum]" target="http://mathhub.info/FrameIT/frameworld?AngleSum"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#1521.51.0:1535.51.14"/></metadata></mref><mref name="[http://mathhub.info/FrameIT/frameworld?OppositeLen]" target="http://mathhub.info/FrameIT/frameworld?OppositeLen"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.mmt#2574.77.0:2591.77.17"/></metadata></mref></omdoc> \ No newline at end of file diff --git a/relational/Scrolls/TriangleScrolls.rel b/relational/Scrolls/TriangleScrolls.rel index fff48a866de028137e0f6abb13458d88f7de560f..05c2bf85a4eccdaed220441bbc28c37b4c040424 100644 --- a/relational/Scrolls/TriangleScrolls.rel +++ b/relational/Scrolls/TriangleScrolls.rel @@ -1,5 +1,7 @@ document http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc -Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem -Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?TriangleScroll_RightAngledProblem +Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?TriangleProblem +Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC +Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA +Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?AngleSum Declares http://mathhub.info/FrameIT/frameworld/Scrolls/TriangleScrolls.omdoc http://mathhub.info/FrameIT/frameworld?OppositeLen diff --git a/relational/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.rel b/relational/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.rel index 531b143ac24cee9e7fd92444517a5ca1f84cac60..8d4c439e751c7aa34b1dc8d97c2a8c50f5e0c138 100644 --- a/relational/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.rel +++ b/relational/http..mathhub.info/FrameIT/frameworld/$Angle$Sum.rel @@ -3,61 +3,39 @@ HasMeta http://mathhub.info/FrameIT/frameworld?AngleSum http://mathhub.info/Fram Declares http://mathhub.info/FrameIT/frameworld?AngleSum http://mathhub.info/FrameIT/frameworld?AngleSum?Problem theory http://mathhub.info/FrameIT/frameworld?AngleSum/Problem HasMeta http://mathhub.info/FrameIT/frameworld?AngleSum/Problem http://mathhub.info/FrameIT/frameworld?FrameworldMeta -Includes http://mathhub.info/FrameIT/frameworld?AngleSum/Problem http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem -Declares http://mathhub.info/FrameIT/frameworld?AngleSum/Problem http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC -constant http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/MitM/Foundation?Logic?ded?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/MitM/Foundation?Logic?prop?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/MitM/Foundation?Logic?prop?definition -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?A?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?C?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?B?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleBAC?type http://mathhub.info/MitM/Foundation?Logic?eq?type -Declares http://mathhub.info/FrameIT/frameworld?AngleSum/Problem http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC -constant http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?ded?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?prop?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?prop?definition -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?A?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?C?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?B?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?eq?type +Includes http://mathhub.info/FrameIT/frameworld?AngleSum/Problem http://mathhub.info/FrameIT/frameworld?TriangleProblem +Includes http://mathhub.info/FrameIT/frameworld?AngleSum/Problem http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA +Includes http://mathhub.info/FrameIT/frameworld?AngleSum/Problem http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB Declares http://mathhub.info/FrameIT/frameworld?AngleSum http://mathhub.info/FrameIT/frameworld?AngleSum?Solution theory http://mathhub.info/FrameIT/frameworld?AngleSum/Solution HasMeta http://mathhub.info/FrameIT/frameworld?AngleSum/Solution http://mathhub.info/FrameIT/frameworld?FrameworldMeta Includes http://mathhub.info/FrameIT/frameworld?AngleSum/Solution http://mathhub.info/FrameIT/frameworld?AngleSum/Problem -Declares http://mathhub.info/FrameIT/frameworld?AngleSum/Solution http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA -constant http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/MitM/Foundation?Logic?ded?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/MitM/Foundation?Logic?prop?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/MitM/Foundation?Logic?prop?definition -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?A?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?C?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?B?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?type http://mathhub.info/MitM/Foundation?Logic?eq?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?definition http://mathhub.info/MitM/Foundation?Logic?prop?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?definition http://mathhub.info/MitM/Foundation?Logic?ded?definition -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?definition http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch?type -DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleBCA?definition 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http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/Foundation?Logic?ded?definition +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://cds.omdoc.org/urtheories?Ded?DED?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/Foundation?Logic?eq?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://cds.omdoc.org/urtheories?Bool?BOOL?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/core/geometry?3DGeometry?point?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/Foundation?Logic?ded?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/core/arithmetics?RealArithmetics?subtraction?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://cds.omdoc.org/urtheories?Strings?string?type +DependsOn http://mathhub.info/FrameIT/frameworld?AngleSum/Solution?angleC?definition http://mathhub.info/FrameIT/frameworld?TriangleProblem?B?type diff --git a/relational/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.rel b/relational/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.rel index a678981ac33eed8539f0506e5f5dd93bf10c14cb..9b162282b5ddf7103234266253c8715579e725da 100644 --- a/relational/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.rel +++ b/relational/http..mathhub.info/FrameIT/frameworld/$Opposite$Len.rel @@ -3,7 +3,7 @@ HasMeta http://mathhub.info/FrameIT/frameworld?OppositeLen http://mathhub.info/F Declares http://mathhub.info/FrameIT/frameworld?OppositeLen http://mathhub.info/FrameIT/frameworld?OppositeLen?Problem theory http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem HasMeta http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem http://mathhub.info/FrameIT/frameworld?FrameworldMeta -Includes http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem http://mathhub.info/FrameIT/frameworld?TriangleScroll_RightAngledProblem +Includes http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC Declares http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC constant http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/MitM/core/geometry?Geometry/Common?metric?type @@ -11,22 +11,11 @@ DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC? DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/MitM/Foundation?Logic?ded?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/MitM/Foundation?Logic?prop?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/MitM/Foundation?Logic?prop?definition +DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?C?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?B?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/MitM/Foundation?Logic?eq?type -Declares http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC -constant http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?ded?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?prop?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?prop?definition -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?A?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?C?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?B?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type http://mathhub.info/MitM/Foundation?Logic?eq?type +DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?B?type +Includes http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB Declares http://mathhub.info/FrameIT/frameworld?OppositeLen http://mathhub.info/FrameIT/frameworld?OppositeLen?Solution theory http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution HasMeta http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution http://mathhub.info/FrameIT/frameworld?FrameworldMeta @@ -38,15 +27,16 @@ DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLin DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/MitM/Foundation?Logic?ded?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/MitM/Foundation?Logic?prop?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/MitM/Foundation?Logic?prop?definition -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?A?type +DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type +DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?C?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?type http://mathhub.info/MitM/Foundation?Logic?eq?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?distanceBC?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/Foundation?Trigonometry?tan?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/Foundation?Logic?prop?type +DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/Foundation?Logic?ded?definition -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/FrameIT/frameworld?OppositeLen/Problem?angleABC?type +DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://cds.omdoc.org/urtheories?Ded?DED?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/Foundation?Logic?eq?type @@ -55,7 +45,6 @@ DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLin DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/core/geometry?3DGeometry?point?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/Foundation?Logic?ded?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/core/arithmetics?RealArithmetics?multiplication?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?A?type +DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type -DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://mathhub.info/FrameIT/frameworld?TriangleScroll_GeneralProblem?C?type DependsOn http://mathhub.info/FrameIT/frameworld?OppositeLen/Solution?deducedLineCA?definition http://cds.omdoc.org/urtheories?Strings?string?type diff --git a/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem.rel b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem.rel new file mode 100644 index 0000000000000000000000000000000000000000..e83f644f75d14ed169ee9c302a1da421f7862850 --- /dev/null +++ b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem.rel @@ -0,0 +1,17 @@ +dataconstructor http://mathhub.info/FrameIT/frameworld?TriangleProblem?A +dataconstructor http://mathhub.info/FrameIT/frameworld?TriangleProblem?B +dataconstructor http://mathhub.info/FrameIT/frameworld?TriangleProblem?C +theory http://mathhub.info/FrameIT/frameworld?TriangleProblem +HasMeta http://mathhub.info/FrameIT/frameworld?TriangleProblem http://mathhub.info/FrameIT/frameworld?FrameworldMeta +Declares http://mathhub.info/FrameIT/frameworld?TriangleProblem http://mathhub.info/FrameIT/frameworld?TriangleProblem?A +constant http://mathhub.info/FrameIT/frameworld?TriangleProblem?A +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?definition +Declares http://mathhub.info/FrameIT/frameworld?TriangleProblem http://mathhub.info/FrameIT/frameworld?TriangleProblem?B +constant http://mathhub.info/FrameIT/frameworld?TriangleProblem?B +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem?B?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem?B?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?definition +Declares http://mathhub.info/FrameIT/frameworld?TriangleProblem http://mathhub.info/FrameIT/frameworld?TriangleProblem?C +constant http://mathhub.info/FrameIT/frameworld?TriangleProblem?C +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?definition diff --git a/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Angle$At$A.rel b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Angle$At$A.rel new file mode 100644 index 0000000000000000000000000000000000000000..f3e958276d3cf2c4a6fc0d3f16c0e07cecebf47b --- /dev/null +++ b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Angle$At$A.rel @@ -0,0 +1,16 @@ +dataconstructor http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA +theory http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA +HasMeta http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA http://mathhub.info/FrameIT/frameworld?FrameworldMeta +Includes http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA http://mathhub.info/FrameIT/frameworld?TriangleProblem +Declares http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA +constant http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/MitM/Foundation?Logic?ded?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/MitM/Foundation?Logic?prop?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/MitM/Foundation?Logic?prop?definition +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/MitM/Foundation?Logic?eq?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtA?angleA?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?B?type diff --git a/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Angle$At$B.rel b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Angle$At$B.rel new file mode 100644 index 0000000000000000000000000000000000000000..ecaa41815ed41e4d25e7cf412d05166f25df4298 --- /dev/null +++ b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Angle$At$B.rel @@ -0,0 +1,16 @@ +dataconstructor http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB +theory http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB +HasMeta http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB http://mathhub.info/FrameIT/frameworld?FrameworldMeta +Includes http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB http://mathhub.info/FrameIT/frameworld?TriangleProblem +Declares http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB +constant http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/MitM/Foundation?Logic?ded?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/MitM/Foundation?Logic?prop?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/MitM/Foundation?Logic?prop?definition +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/MitM/Foundation?Logic?eq?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_AngleAtB?angleB?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?B?type diff --git a/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Right$Angle$At$C.rel b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Right$Angle$At$C.rel new file mode 100644 index 0000000000000000000000000000000000000000..637218bc8604654e7ba723577fd7667c23622b82 --- /dev/null +++ b/relational/http..mathhub.info/FrameIT/frameworld/$Triangle$Problem_$Right$Angle$At$C.rel @@ -0,0 +1,17 @@ +dataconstructor http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC +theory http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC +HasMeta http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC http://mathhub.info/FrameIT/frameworld?FrameworldMeta +Includes http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC http://mathhub.info/FrameIT/frameworld?TriangleProblem +Declares http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC +constant http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/core/geometry?3DGeometry?point?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/Foundation?Logic?ded?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/Foundation?Logic?prop?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/Foundation?Logic?prop?definition +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?A?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/Foundation?Logic?ded?definition +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?C?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/Foundation?RealLiterals?real_lit?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/MitM/Foundation?Logic?eq?type +DependsOn http://mathhub.info/FrameIT/frameworld?TriangleProblem_RightAngleAtC?rightAngleC?type http://mathhub.info/FrameIT/frameworld?TriangleProblem?B?type diff --git a/source/Scrolls/TriangleScrolls.mmt b/source/Scrolls/TriangleScrolls.mmt index 94a9ec00fb2cd1f0bf3ad0121fde9d7060366b51..7b4843925f79a59ba38fe2a57a7137d6c57e32fb 100644 --- a/source/Scrolls/TriangleScrolls.mmt +++ b/source/Scrolls/TriangleScrolls.mmt @@ -13,7 +13,7 @@ fixmeta ?FrameworldMeta âš (nicer image: https://en.wikipedia.org/wiki/Right_triangle#/media/File:Rtriangle.svg) âš -theory TriangleScroll_GeneralProblem = +theory TriangleProblem = A: point ☠meta ?MetaAnnotations?label "A" â™ B: point ☠meta ?MetaAnnotations?label "B"â™ C: point ☠meta ?MetaAnnotations?label "C"â™ @@ -22,47 +22,56 @@ theory TriangleScroll_GeneralProblem = /T A blueprint problem theory for triangle scrolls that require a right angle We use ?TriangleScroll_GeneralProblem and demand the angle at C to be 90° âš -theory TriangleScroll_RightAngledProblem = - include ?TriangleScroll_GeneralProblem â™ - rightAngleBCA +theory TriangleProblem_RightAngleAtC = + include ?TriangleProblem â™ + rightAngleC : ⊦ ( ∠B,C,A ) ≠90.0 ☠- meta ?MetaAnnotations?label s"∟${lverb C}" ☠- meta ?MetaAnnotations?description s"Right angle at ${lverb C}" + meta ?MetaAnnotations?label s"⊾${lverb C} (${lverb A C} ⟂ ${lverb B C})" ☠+ meta ?MetaAnnotations?description s"Right angle at ${lverb C} as enclosed by legs ${lverb A C} and ${lverb B C}." â™ âš +theory TriangleProblem_AngleAtA = + include ?TriangleProblem â™ + angleA + : Σ α: â„. ⊦ ( ∠B,A,C ) ≠α ☠+ meta ?MetaAnnotations?label s"∠${lverb B A C}" ☠+ meta ?MetaAnnotations?description s"Angle at ${lverb A} as enclosed by legs ${lverb A B} and ${lverb A C}" + â™ +âš + +theory TriangleProblem_AngleAtB = + include ?TriangleProblem â™ + angleB + : Σ β: â„. ⊦ ( ∠A,B,C ) ≠β ☠+ meta ?MetaAnnotations?label s"∠${lverb A B C}" ☠+ meta ?MetaAnnotations?description s"Angle at ${lverb B}" + â™ +âš + theory AngleSum = meta ?MetaAnnotations?problemTheory ?AngleSum/Problem â™ meta ?MetaAnnotations?solutionTheory ?AngleSum/Solution â™ theory Problem = - include ?TriangleScroll_GeneralProblem â™ - - angleBAC - : Σ α: â„. ⊦ ( ∠B,A,C ) ≠α ☠- meta ?MetaAnnotations?label s"∠${lverb B A C}" ☠- meta ?MetaAnnotations?description s"Angle at ${lverb A}" - â™ - - angleABC - : Σ β: â„. ⊦ ( ∠A,B,C ) ≠β ☠- meta ?MetaAnnotations?label s"∠${lverb A B C}" ☠- meta ?MetaAnnotations?description s"Angle at ${lverb B}" - â™ + include ?TriangleProblem â™ + include ?TriangleProblem_AngleAtA â™ + include ?TriangleProblem_AngleAtB â™ âš theory Solution = include ?AngleSum/Problem â™ - meta ?MetaAnnotations?label "AngleSum" â™ - meta ?MetaAnnotations?description s"Given a triangle ${lverb A B C} and two known angles, we can deduce the missing angle by the sum of interior angles in triangles always being 180°" â™ - - angleBCA + angleC : Σ γ: â„. ⊦ ( ∠B,C,A ) ≠γ ☠- = ⟨180.0 - (Ï€l angleBAC) - (Ï€l angleABC), sketch "By sum of interior angles = 180° in triangles"⟩ ☠+ = ⟨180.0 - (Ï€l angleA) - (Ï€l angleB), sketch "By sum of interior angles = 180° in triangles"⟩ ☠meta ?MetaAnnotations?label s"∠${lverb B C A}" ☠- meta ?MetaAnnotations?description s"The deduced angle by calculating 180° - ${lverb angleBAC} - ${lverb angleABC}" + meta ?MetaAnnotations?description s"The deduced angle by calculating 180° - ${lverb angleA} - ${lverb angleB}" â™ + + // the description verbalizes angleC, hence must come after its declaration â™ + meta ?MetaAnnotations?label "AngleSum" â™ + meta ?MetaAnnotations?description s"Given a triangle â–³${lverb A B C} and two known angles, we can deduce the missing angle by: ${lverb angleC} = 180° - ${lverb angleA} - ${lverb angleB}." â™ âš âš @@ -71,33 +80,30 @@ theory OppositeLen = meta ?MetaAnnotations?solutionTheory ?OppositeLen/Solution â™ theory Problem = - include ?TriangleScroll_RightAngledProblem â™ + include ?TriangleProblem_RightAngleAtC â™ distanceBC : Σ x:â„ . ⊦ ( d- B C ) ≠x ☠meta ?MetaAnnotations?label s"${lverb B C}" ☠meta ?MetaAnnotations?description s"Length of leg ${lverb B C}" â™ - - angleABC - : Σ a:â„ . ⊦ ( ∠A,B,C ) ≠a ☠- meta ?MetaAnnotations?label s"∠${lverb A B C}" ☠- meta ?MetaAnnotations?description s"Angle at ${lverb B}" - â™ + + include ?TriangleProblem_AngleAtB â™ âš theory Solution = include ?OppositeLen/Problem â™ - - meta ?MetaAnnotations?label "OppositeLen" â™ - meta ?MetaAnnotations?description s"Given a triangle ${lverb A B C} right angled at ${lverb C}, the distance ${lverb A B} can be computed from the angle at ${lverb B} and the distance ${lverb B C}" â™ deducedLineCA : Σ x:â„ . ⊦ (d- C A) ≠x ☠- = ⟨(tan (Ï€l angleABC)) â‹… (Ï€l distanceBC), sketch "OppositeLen Scroll"⟩ ☠+ = ⟨(tan (Ï€l angleB)) â‹… (Ï€l distanceBC), sketch "OppositeLen Scroll"⟩ ☠meta ?MetaAnnotations?label s"${lverb C A}" ☠meta ?MetaAnnotations?description s"The deduced length of the line ${lverb C A}" â™ + + // the description verbalizes deducedLineCA, hence must come after its declaration â™ + meta ?MetaAnnotations?label "OppositeLen" â™ + meta ?MetaAnnotations?description s"Given a triangle â–³${lverb A B C} right-angled at ⊾${lverb C}, the distance ${lverb deducedLineCA} can be computed from the angle at ${lverb angleB} and the distance ${lverb B C}." â™ âš âš