From fb1565ff8c457cfe36c97d7078f19015138c9f3c Mon Sep 17 00:00:00 2001 From: Navid Roux <navid.roux@fau.de> Date: Wed, 14 Jul 2021 12:18:39 +0000 Subject: [PATCH] Update TriangleScrolls.mmt --- source/Scrolls/TriangleScrolls.mmt | 284 ++++++++++++++--------------- 1 file changed, 142 insertions(+), 142 deletions(-) diff --git a/source/Scrolls/TriangleScrolls.mmt b/source/Scrolls/TriangleScrolls.mmt index 80086b5..253bb55 100644 --- a/source/Scrolls/TriangleScrolls.mmt +++ b/source/Scrolls/TriangleScrolls.mmt @@ -1,142 +1,142 @@ -/T Modular scrolls having to do with triangles âš - -namespace http://mathhub.info/FrameIT/frameworld âš -fixmeta ?FrameworldMeta âš - -/T A blueprint problem theory for triangle scrolls - B - /| - / | - / | - /___| - A C - - (nicer image: https://en.wikipedia.org/wiki/Right_triangle#/media/File:Rtriangle.svg) -âš -theory TriangleProblem = - A: point ☠meta ?MetaAnnotations?label "A" â™ - B: point ☠meta ?MetaAnnotations?label "B"â™ - C: point ☠meta ?MetaAnnotations?label "C"â™ -âš - -/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 TriangleProblem_RightAngleAtC = - include ?TriangleProblem â™ - rightAngleC - : ⊦ ( ∠B,C,A ) ≠90.0 ☠- meta ?MetaAnnotations?label s"⊾${lverb C}" ☠- meta ?MetaAnnotations?description s"${lverb A C} ⟂ ${lverb B C}: 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 ${lverb B}" - â™ -âš - -theory AngleSum = - meta ?MetaAnnotations?problemTheory ?AngleSum/Problem â™ - meta ?MetaAnnotations?solutionTheory ?AngleSum/Solution â™ - - theory Problem = - include ?TriangleProblem â™ - include ?TriangleProblem_AngleAtA â™ - include ?TriangleProblem_AngleAtB â™ - âš - - theory Solution = - include ?AngleSum/Problem â™ - - angleC - : Σ γ: â„. ⊦ ( ∠B,C,A ) ≠γ ☠- = ⟨180.0 - (Ï€l angleA) - (Ï€l angleB), sketch "By sum of interior angles = 180° in triangles"⟩ ☠- meta ?MetaAnnotations?label s"∠${lverb B C A}" ☠- meta ?MetaAnnotations?description s"The deduced angle by calculating 180° - ${lverb 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} - ${lverb angleB}." â™ - âš -âš - -theory OppositeLen = - meta ?MetaAnnotations?problemTheory ?OppositeLen/Problem â™ - meta ?MetaAnnotations?solutionTheory ?OppositeLen/Solution â™ - - theory Problem = - include ?TriangleProblem_RightAngleAtC â™ - - distanceBC - : Σ x:â„ . ⊦ ( d- B C ) ≠x ☠- meta ?MetaAnnotations?label s"${lverb B C}" ☠- meta ?MetaAnnotations?description s"Length of leg ${lverb B C}" - â™ - - include ?TriangleProblem_AngleAtB â™ - âš - - theory Solution = - include ?OppositeLen/Problem â™ - - deducedLineCA - : Σ x:â„ . ⊦ (d- C A) ≠x ☠- = ⟨(tan (Ï€l angleB)) â‹… (Ï€l distanceBC), sketch "OppositeLen Scroll"⟩ ☠- meta ?MetaAnnotations?label s"${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 opposide side has length ${lverb deducedLineCA} = tan(${lverb angleB}) â‹… ${lverb B C}." â™ - âš -âš - -// Doesn't typecheck, not sure why âš -// theory Pythagoras = - meta ?MetaAnnotations?problemTheory ?Pythagoras/Problem â™ - meta ?MetaAnnotations?solutionTheory ?Pythagoras/Solution â™ - - theory Problem = - include ?TriangleScroll_RightAngledProblem â™ - - distanceAC - : Σ x:â„. ⊦ (d- A C) ≠x ☠- meta ?MetaAnnotations?description "Length of leg AC" - â™ - - distanceBC - : Σ x:â„. ⊦ (d- B C) ≠x ☠- meta ?MetaAnnotations?description "Length of leg BC" - â™ - âš - - // theory Solution = - include ?Pythagoras/Problem â™ - - meta ?MetaAnnotations?label "Pythagoras" â™ - meta ?MetaAnnotations?description "Given a ABC right-angled at C and lengths of both legs, we can compute the length of the hypotenuse via Pythagora's theorem" â™ - - deducedHypotenuse - : Σ x:â„. ⊦ (d- A B) ≠x ☠- = ⟨√ ((Ï€l distanceAC) â‹… (Ï€l distanceAC) + (Ï€l distanceBC) â‹… (Ï€l distanceBC)), - sketch "By Pythagora's theorem"⟩ ☠- meta ?MetaAnnotations?description "Deduced length of hypotenuse AB" - â™ - âš -// âš \ No newline at end of file +/T Modular scrolls having to do with triangles âš + +namespace http://mathhub.info/FrameIT/frameworld âš +fixmeta ?FrameworldMeta âš + +/T A blueprint problem theory for triangle scrolls + B + /| + / | + / | + /___| + A C + + (nicer image: https://en.wikipedia.org/wiki/Right_triangle#/media/File:Rtriangle.svg) +âš +theory TriangleProblem = + A: point ☠meta ?MetaAnnotations?label "A" â™ + B: point ☠meta ?MetaAnnotations?label "B"â™ + C: point ☠meta ?MetaAnnotations?label "C"â™ +âš + +/T A blueprint problem theory for triangle scrolls that require a right angle + + We use ?TriangleScroll_GeneralProblem and demand the angle at C to be 90° âš +theory TriangleProblem_RightAngleAtC = + include ?TriangleProblem â™ + rightAngleC + : ⊦ ( ∠B,C,A ) ≠90.0 ☠+ meta ?MetaAnnotations?label s"⊾${lverb C}" ☠+ meta ?MetaAnnotations?description s"${lverb A C} ⟂ ${lverb B C}: 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 ${lverb B}" + â™ +âš + +theory AngleSum = + meta ?MetaAnnotations?problemTheory ?AngleSum/Problem â™ + meta ?MetaAnnotations?solutionTheory ?AngleSum/Solution â™ + + theory Problem = + include ?TriangleProblem â™ + include ?TriangleProblem_AngleAtA â™ + include ?TriangleProblem_AngleAtB â™ + âš + + theory Solution = + include ?AngleSum/Problem â™ + + angleC + : Σ γ: â„. ⊦ ( ∠B,C,A ) ≠γ ☠+ = ⟨180.0 - (Ï€l angleA) - (Ï€l angleB), sketch "By sum of interior angles = 180° in triangles"⟩ ☠+ meta ?MetaAnnotations?label s"∠${lverb B C A}" ☠+ meta ?MetaAnnotations?description s"The deduced angle by calculating 180° - ${lverb 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} - ${lverb angleB}." â™ + âš +âš + +theory OppositeLen = + meta ?MetaAnnotations?problemTheory ?OppositeLen/Problem â™ + meta ?MetaAnnotations?solutionTheory ?OppositeLen/Solution â™ + + theory Problem = + include ?TriangleProblem_RightAngleAtC â™ + + distanceBC + : Σ x:â„ . ⊦ ( d- B C ) ≠x ☠+ meta ?MetaAnnotations?label s"${lverb B C}" ☠+ meta ?MetaAnnotations?description s"Length of leg ${lverb B C}" + â™ + + include ?TriangleProblem_AngleAtB â™ + âš + + theory Solution = + include ?OppositeLen/Problem â™ + + deducedLineCA + : Σ x:â„ . ⊦ (d- C A) ≠x ☠+ = ⟨(tan (Ï€l angleB)) â‹… (Ï€l distanceBC), sketch "OppositeLen Scroll"⟩ ☠+ meta ?MetaAnnotations?label s"${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 opposite side has length ${lverb deducedLineCA} = tan(${lverb angleB}) â‹… ${lverb B C}." â™ + âš +âš + +// Doesn't typecheck, not sure why âš +// theory Pythagoras = + meta ?MetaAnnotations?problemTheory ?Pythagoras/Problem â™ + meta ?MetaAnnotations?solutionTheory ?Pythagoras/Solution â™ + + theory Problem = + include ?TriangleScroll_RightAngledProblem â™ + + distanceAC + : Σ x:â„. ⊦ (d- A C) ≠x ☠+ meta ?MetaAnnotations?description "Length of leg AC" + â™ + + distanceBC + : Σ x:â„. ⊦ (d- B C) ≠x ☠+ meta ?MetaAnnotations?description "Length of leg BC" + â™ + âš + + // theory Solution = + include ?Pythagoras/Problem â™ + + meta ?MetaAnnotations?label "Pythagoras" â™ + meta ?MetaAnnotations?description "Given a ABC right-angled at C and lengths of both legs, we can compute the length of the hypotenuse via Pythagora's theorem" â™ + + deducedHypotenuse + : Σ x:â„. ⊦ (d- A B) ≠x ☠+ = ⟨√ ((Ï€l distanceAC) â‹… (Ï€l distanceAC) + (Ï€l distanceBC) â‹… (Ï€l distanceBC)), + sketch "By Pythagora's theorem"⟩ ☠+ meta ?MetaAnnotations?description "Deduced length of hypotenuse AB" + â™ + âš +// âš -- GitLab