// Numbas version: finer_feedback_settings {"name": "\u00dcbungen (Lektion 4)", "metadata": {"description": "

Grichische Antike 1

", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Griechische Zahlzeichen", "extensions": [], "custom_part_types": [], "resources": [["question-resources/greeknumbers.png", "/srv/numbas/media/question-resources/greeknumbers.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "

Milesisches Zahlzeichensystem

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Unten ist eine Zahl in einem der beiden antiken griechischen Zahlzeichensysteme, dem sogenannten milesischen oder alphabetischen Zahlzeichensystem dargestellt, in dem griechische Buchstaben als Ziffern/Zahlen verwendet werden.

\n

$\\begin{matrix}\\var{latex(T2[digits[0]])}\\var{latex(O2[digits[1]])}\\\\\\LARGE{\\mathrm{M}}&\\LARGE{'\\var{latex(O[digits[2]])}\\var{latex(H[digits[3]])}\\var{latex(T[digits[4]])}\\var{latex(O[digits[5]])}}\\end{matrix}$

\n

\n

", "advice": "

Über dem $\\mathrm{M}$ stehen die Zehntausender und Hunderttausender, also $\\var{latex(T2[digits[0]])}\\var{latex(O2[digits[1]])}$ ergibt $\\var{digits[0]*100000+digits[1]*10000}$.

\n

Dahinter folgen mit $'\\var{latex(O[digits[2]])}\\var{latex(H[digits[3]])}\\var{latex(T[digits[4]])}\\var{latex(O[digits[5]])}$ Tausender, Hunder, Zehner und Einer. Hier ergibt sich $\\var{digits[2]*1000+digits[3]*100+digits[4]*10+digits[5]}$.

\n

Das ergibt als Zahl dann insgesamt $\\var{number}$

\n

Tabelle der Zahlzeichen:

\n

\n

", "rulesets": {}, "variables": {"O": {"name": "O", "group": "Ungrouped variables", "definition": "['0','\\\\mathrm\\{A\\}','\\\\mathrm\\{B\\}','\\\\Gamma','\\\\Delta','\\\\mathrm\\{E\\}','6','\\\\mathrm\\{Z\\}','\\\\mathrm\\{H\\}','\\\\Theta']\n", "description": "", "templateType": "anything"}, "T": {"name": "T", "group": "Ungrouped variables", "definition": "['0','\\\\mathrm\\{I\\}','\\\\mathrm\\{K\\}','\\\\Lambda','\\\\mathrm\\{M\\}','\\\\mathrm\\{N\\}','\\\\Xi','\\\\mathrm\\{O\\}','\\\\Pi','90']\n", "description": "", "templateType": "anything"}, "H": {"name": "H", "group": "Ungrouped variables", "definition": "['0','\\\\mathrm\\{P\\}','\\\\Sigma','\\\\mathrm\\{T\\}','\\\\Upsilon','\\\\Phi','\\\\mathrm\\{X\\}','\\\\Psi','\\\\Omega','900']\n", "description": "", "templateType": "anything"}, "digits": {"name": "digits", "group": "Ungrouped variables", "definition": "[random(1..8),random(1,2,3,4,5,7,8,9),random(1,2,3,4,5,7,8,9),random(1..8),random(1..8),random(1,2,3,4,5,7,8,9)]", "description": "", "templateType": "anything"}, "number": {"name": "number", "group": "Ungrouped variables", "definition": "digits[0]*10^5+digits[1]*10^4+digits[2]*10^3+digits[3]*10^2+digits[4]*10^1+digits[5]*10^0", "description": "", "templateType": "anything"}, "O2": {"name": "O2", "group": "Ungrouped variables", "definition": "['0','\\\\alpha','\\\\beta','\\\\gamma','\\\\delta','\\\\epsilon','6','\\\\zeta','\\\\eta','\\\\theta']", "description": "", "templateType": "anything"}, "T2": {"name": "T2", "group": "Ungrouped variables", "definition": "['0','\\\\iota','\\\\kappa','\\\\lambda','\\\\mu','\\\\nu','\\\\xi','\\\\mathrm\\{o\\}','\\\\pi','90']", "description": "", "templateType": "anything"}, "H2": {"name": "H2", "group": "Ungrouped variables", "definition": "['0','\\\\rho','\\\\sigma','\\\\tau','\\\\upsilon','\\\\varphi','\\\\chi','\\\\psi','\\\\omega','900']", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["O", "T", "H", "digits", "number", "O2", "T2", "H2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Um welche Zahl handelt es sich?

", "minValue": "{number}", "maxValue": "{number}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Salaminische Tafel", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "

Darstellen von Zahlen an einem Felderabakus (noch ohne Anzeige der Lösung)

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

An der Salaminischen Tafel (ca. 500 v. Chr., auch als griechischer Felderabakus bezeichnet) können bis zu drei Zahlen dargestellt werden:

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Je eine Zahl links oberhalb und links unterhalb der horizontalen Linie und eine rechts.

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Auf den vertikalen Linien liegen dabei die Einer (Zehner, Hunderter, usw.), zwischen den Linien die Fünfer (Fünfziger, Fünfhunderter, usw.).

", "advice": "

Lösung: {a} oben, {b} unten:

\n

{app2}

", "rulesets": {}, "variables": {"app": {"name": "app", "group": "Setup", "definition": "geogebra_applet('https://www.geogebra.org/m/ykpkawkw')", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Setup", "definition": "random(100..899)*10+random(1..9)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Setup", "definition": "random(1..9)*100+random(0,5)*10+random(0..9)", "description": "", "templateType": "anything"}, "app2": {"name": "app2", "group": "Setup", "definition": "geogebra_applet('https://www.geogebra.org/m/rp8bapvy',defs)", "description": "", "templateType": "anything"}, "a_sol": {"name": "a_sol", "group": "Points", "definition": "[floor(mod(a,10000)/1000),floor(mod(a,1000)/100),floor(mod(a,100)/10),mod(a,10)]", "description": "", "templateType": "anything"}, "b_sol": {"name": "b_sol", "group": "Points", "definition": "[floor(mod(b,1000)/100),floor(mod(b,100)/10),mod(b,10)]", "description": "", "templateType": "anything"}, "a_3": {"name": "a_3", "group": "Points", "definition": "switch(a_sol[3]=0,[],\n a_sol[3]=1,[['S_1',vector(13,5)]],\n a_sol[3]=2,[['S_1',vector(13,5)],['S_2',vector(13,4)]],\n a_sol[3]=3,[['S_1',vector(13,5)],['S_2',vector(13,4)],['S_3',vector(13,3)]],\n a_sol[3]=4,[['S_1',vector(13,5)],['S_2',vector(13,4)],['S_3',vector(13,3)],['S_4',vector(13,2)]],\n a_sol[3]=5,[['S_1',vector(12,5)]],\n a_sol[3]=6,[['S_1',vector(12,5)],['S_2',vector(13,5)]],\n a_sol[3]=7,[['S_1',vector(12,5)],['S_2',vector(13,5)],['S_3',vector(13,4)]],\n a_sol[3]=8,[['S_1',vector(12,5)],['S_2',vector(13,5)],['S_3',vector(13,4)],['S_4',vector(13,3)]],\n a_sol[3]=9,[['S_1',vector(12,5)],['S_2',vector(13,5)],['S_3',vector(13,4)],['S_4',vector(13,3)],['S_5',vector(13,2)]],\n 0)", "description": "", "templateType": "anything"}, "a_2": {"name": "a_2", "group": "Points", "definition": "switch(a_sol[2]=0,[],\n a_sol[2]=1,[['S_6',vector(11,5)]],\n a_sol[2]=2,[['S_6',vector(11,5)],['S_7',vector(11,4)]],\n a_sol[2]=3,[['S_6',vector(11,5)],['S_7',vector(11,4)],['S_8',vector(11,3)]],\n a_sol[2]=4,[['S_6',vector(11,5)],['S_7',vector(11,4)],['S_8',vector(11,3)],['S_9',vector(11,2)]],\n a_sol[2]=5,[['S_6',vector(10,5)]],\n a_sol[2]=6,[['S_6',vector(10,5)],['S_7',vector(11,5)]],\n a_sol[2]=7,[['S_6',vector(10,5)],['S_7',vector(11,5)],['S_8',vector(11,4)]],\n a_sol[2]=8,[['S_6',vector(10,5)],['S_7',vector(11,5)],['S_8',vector(11,4)],['S_9',vector(11,3)]],\n a_sol[2]=9,[['S_6',vector(10,5)],['S_7',vector(11,5)],['S_8',vector(11,4)],['S_9',vector(11,3)],['S_9',vector(11,2)]],\n 0)", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Points", "definition": "a_3+a_2+a_1+a_0+b_2+b_1+b_0", "description": "", "templateType": "anything"}, "a_1": {"name": "a_1", "group": "Points", "definition": "switch(a_sol[1]=0,[],\n a_sol[1]=1,[['S_10',vector(9,5)]],\n a_sol[1]=2,[['S_10',vector(9,5)],['S_11',vector(9,4)]],\n a_sol[1]=3,[['S_10',vector(9,5)],['S_11',vector(9,4)],['S_12',vector(9,3)]],\n a_sol[1]=4,[['S_10',vector(9,5)],['S_11',vector(9,4)],['S_12',vector(9,3)],['S_13',vector(9,2)]],\n a_sol[1]=5,[['S_10',vector(8,5)]],\n a_sol[1]=6,[['S_10',vector(8,5)],['S_11',vector(9,5)]],\n a_sol[1]=7,[['S_10',vector(8,5)],['S_11',vector(9,5)],['S_12',vector(9,4)]],\n a_sol[1]=8,[['S_10',vector(8,5)],['S_11',vector(9,5)],['S_12',vector(9,4)],['S_13',vector(9,3)]],\n a_sol[1]=9,[['S_10',vector(8,5)],['S_11',vector(9,5)],['S_12',vector(9,4)],['S_13',vector(9,3)],['S_14',vector(9,2)]],\n 0)", "description": "", "templateType": "anything"}, "a_0": {"name": "a_0", "group": "Points", "definition": "switch(a_sol[0]=0,[],\n a_sol[0]=1,[['S_15',vector(7,5)]],\n a_sol[0]=2,[['S_15',vector(7,5)],['S_16',vector(7,4)]],\n a_sol[0]=3,[['S_15',vector(7,5)],['S_16',vector(7,4)],['S_17',vector(7,3)]],\n a_sol[0]=4,[['S_15',vector(7,5)],['S_16',vector(7,4)],['S_17',vector(7,3)],['S_18',vector(7,2)]],\n a_sol[0]=5,[['S_15',vector(6,5)]],\n a_sol[0]=6,[['S_15',vector(6,5)],['S_16',vector(7,5)]],\n a_sol[0]=7,[['S_15',vector(6,5)],['S_16',vector(7,5)],['S_17',vector(7,4)]],\n a_sol[0]=8,[['S_15',vector(6,5)],['S_16',vector(7,5)],['S_17',vector(7,4)],['S_18',vector(7,3)]],\n a_sol[0]=9,[['S_15',vector(6,5)],['S_16',vector(7,5)],['S_17',vector(7,4)],['S_18',vector(7,3)],['S_19',vector(7,2)]],\n 0)", "description": "", "templateType": "anything"}, "b_2": {"name": "b_2", "group": "Points", "definition": "switch(b_sol[2]=0,[],\n b_sol[2]=1,[['S_20',vector(13,-5)]],\n b_sol[2]=2,[['S_20',vector(13,-5)],['S_21',vector(13,-4)]],\n b_sol[2]=3,[['S_20',vector(13,-5)],['S_21',vector(13,-4)],['S_22',vector(13,-3)]],\n b_sol[2]=4,[['S_20',vector(13,-5)],['S_21',vector(13,-4)],['S_22',vector(13,-3)],['S_23',vector(13,-2)]],\n b_sol[2]=5,[['S_20',vector(12,-5)]],\n b_sol[2]=6,[['S_20',vector(12,-5)],['S_21',vector(13,-5)]],\n b_sol[2]=7,[['S_20',vector(12,-5)],['S_21',vector(13,-5)],['S_22',vector(13,-4)]],\n b_sol[2]=8,[['S_20',vector(12,-5)],['S_21',vector(13,-5)],['S_22',vector(13,-4)],['S_23',vector(13,-3)]],\n b_sol[2]=9,[['S_20',vector(12,-5)],['S_21',vector(13,-5)],['S_22',vector(13,-4)],['S_23',vector(13,-3)],['S_24',vector(13,-2)]],\n 0)", "description": "", "templateType": "anything"}, "b_0": {"name": "b_0", "group": "Points", "definition": "switch(b_sol[0]=0,[],\n b_sol[0]=1,[['S_25',vector(9,-5)]],\n b_sol[0]=2,[['S_25',vector(9,-5)],['S_26',vector(9,-4)]],\n b_sol[0]=3,[['S_25',vector(9,-5)],['S_26',vector(9,-4)],['S_27',vector(9,-3)]],\n b_sol[0]=4,[['S_25',vector(9,-5)],['S_26',vector(9,-4)],['S_27',vector(9,-3)],['S_28',vector(9,-2)]],\n b_sol[0]=5,[['S_25',vector(8,-5)]],\n b_sol[0]=6,[['S_25',vector(8,-5)],['S_26',vector(9,-5)]],\n b_sol[0]=7,[['S_25',vector(8,-5)],['S_26',vector(9,-5)],['S_27',vector(9,-4)]],\n b_sol[0]=8,[['S_25',vector(8,-5)],['S_26',vector(9,-5)],['S_27',vector(9,-4)],['S_28',vector(9,-3)]],\n b_sol[0]=9,[['S_25',vector(8,-5)],['S_26',vector(9,-5)],['S_27',vector(9,-4)],['S_28',vector(9,-3)],['S_29',vector(9,-2)]],\n 0)", "description": "", "templateType": "anything"}, "b_1": {"name": "b_1", "group": "Points", "definition": "switch(b_sol[1]=0,[],\n b_sol[1]=1,[['S_30',vector(11,-5)]],\n b_sol[1]=5,[['S_30',vector(10,-5)]],\n 0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Setup", "variables": ["app", "a", "b", "app2"]}, {"name": "Points", "variables": ["defs", "a_sol", "b_sol", "a_3", "a_2", "a_1", "a_0", "b_2", "b_0", "b_1"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "extension", "useCustomName": false, "customName": "", "marks": 1, "scripts": {"constructor": {"script": "this.marks=4", "order": "after"}}, "customMarkingAlgorithm": "studenta:\n value(app,\"a\")\n\nstudentb:\n value(app,\"b\")\n\nmark:\n if(studenta=a,add_credit(1/2,'Obere Zahl korrekt'),negative_feedback(\"Obere Zahl falsch: $\\\\var{latex(app,'a')}$\")); \n if(studentb=b,add_credit(1/2,'Untere Zahl korrekt'),negative_feedback(\"Untere Zahl falsch: $\\\\var{latex(app,'b')}$.\"))\n \ninterpreted_answer:\n vector(studenta,studentb)", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Bitte etwas Geduld beim Laden des Applets.

\n

{app}

\n

Stellen Sie oben links die Zahl {a} und unten links die Zahl {b} dar, indem Sie die entsprechende Anzahl Punkte von oben auf bzw. zwischen die Linien der Salaminischen Tafel verschieben!

"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Thales von Milet", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "

Konstruktion und Beweis zu einem Vermessungsverfahren nach Thales von Milet

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Thales soll ein Verfahren zur Bestimmung der Entfernung von Schiffen zum Ufer unter Verwendung des Kongruenzsatzes WSW erfunden haben.

\n

Eine mögliche Methode wäre folgende (s. Abb.): Sei $A$ ein Punkt an Land und $S$ ein Schiff (alle weiteren Punkte sind auch an Land).

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Wir wählen zunächst einen weiteren Punkt $C$ an Land, so dass $AC$ normal auf $SA$ steht.

\n

Bitte etwas Geduld, während das Applet lädt.

", "advice": "

Konstruktion:

\n

{app2}

\n

Beweis:

\n

Es ist $AB=BC$  ($B$ ist der Mittelpunkt) und die Winkel $\\measuredangle SAB\\cong\\measuredangle DCB$ (Scheitelwinkel) und $\\measuredangle ABS\\cong\\measuredangle CBD$ (beides rechte Winkel).

\n

", "rulesets": {}, "variables": {"app": {"name": "app", "group": "Setup", "definition": "geogebra_applet('https://www.geogebra.org/m/etsqtheh',defs)", "description": "", "templateType": "anything"}, "S": {"name": "S", "group": "Setup", "definition": "vector(random(8..12)/2,4)", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "Setup", "definition": "vector(0,-1*random(2..4)/2)", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Setup", "definition": "[['S',S],['C',C]]", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Setup", "definition": "(vector(0,4)+C)/2", "description": "", "templateType": "anything"}, "D": {"name": "D", "group": "Setup", "definition": "vector(-S[0],C[1])", "description": "", "templateType": "anything"}, "defs2": {"name": "defs2", "group": "Setup", "definition": "defs+[['B',B],['D',D]]", "description": "", "templateType": "anything"}, "app2": {"name": "app2", "group": "Setup", "definition": "geogebra_applet('https://www.geogebra.org/m/uum4bwqc',defs)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Setup", "variables": ["app", "S", "C", "defs", "B", "D", "defs2", "app2"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Konstruktion", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Beweis", "rawLabel": "", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": true}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Konstruktion erstellen", "prompt": "

{app}

\n

Führen Sie nun die folgenden Konstruktionsschritte durch:

\n
    \n
  1. Bestimmen Sie den Mittelpunkt $B$ der Strecke $AC$.
    2. \n
  2. Erstellen Sie eine Normale zu $AC$ durch den Punkt $C$
    3. \n
  3. Ermitteln Sie denjenigen Punkt $D$ auf der Normale, der auch auf der Geraden $SB$ liegt.
    4. \n
\n

Hinweis: Die konstruierten Punkte müssen $B$ und $D$ heißen, sonst kann Ihre Lösung nicht als korrekt erkannt werden. Sie können die Punkte falls erforderlich umbenennen, indem Sie diese anklicken und \"Umbenennen\" auswählen.

\n

Um Fortzufahren (egal, ob Sie eine Lösung konstruiert haben oder nicht), klicken Sie nach der Konstruktion auf \"Abschnitt einreichen\", dann erscheint eine Schaltfläche \"Weiter zum Beweis\".

\n

[[0]]

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Es soll nun gezeigt werden, dass $CD$ und $AS$ gleich lange Strecken sind und zwar über den Kongruenzsatz WSW.

\n

{app2}

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Kreuzen Sie die für den Beweis zu verwendenden Winkel (4 Stück) und zu verwendenden Seiten (2 Stück) an.

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