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angles_1.html
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{% extends arithmetic_template %}
{% block maincode %}
<script language=Javascript1.2><!--
var valueTable = {};
var explanationStack = new Array();
var usedRules = new Array();
var usedVariables = new Array();
var initCond = new Array();
var solved = false; //This is set to true once the choice variable is solved for
var solvedPaths = {};
var shortestPath = []
var initHash = {};
var goal = '';
var definedVariables = new Array();
var goalDrawn=false;
var type = 1;
var searchStack = new Array();
var xMin = 100;
var yMin = 100;
var xMax = 0;
var yMax = 0;
function initConditions(x, depth)
{
searchStack.push([x, depth, definedVariables.slice(), usedVariables.slice()]);
usedVariables.push(x);
if (depth==0)
{
definedVariables.push(x);
solveDependencies(definedVariables);
if (variables[x].type=='variableboolean')
{
initHash[x] = {value: true, reason: new Array()};
initHash[variables[x].dependent] = {value: variables[x].value, reason: new Array()};
initCond.push([variables[x].dependent, variables[x].value]);
}
else if (variables[x].type=='boolean')
{
initHash[x] = {value: true, reason: new Array()};
initCond.push([x, true]);
}
else if (variables[x].type=='line')
{
initHash[x] = {value: variables[x].value, reason: new Array()};
initCond.push([x,variables[x].value]);
}
else
{
var maxVal = 14;
var epsilon = .99;
var val = Math.round(KhanAcademy.random()*(maxVal-1+epsilon) - epsilon/2);
var newValue = Math.round(variables[x].seed-maxVal/2+val);
initHash[x] = {value: newValue, reason: new Array()};
initCond.push([x,newValue]);
}
}
else
{
var posRules = findRulesWithVariable(x);
var rulesUsed = 0;
if (posRules.length>0)
{
var curRule = randomArrayEntry(posRules);
usedRules.push(curRule[0]);
var unusedVars = curRule[1];
searchStack.push([unusedVars, 1,1,1]);
var r = randomIndices(unusedVars.length);
for(var i=0; i<unusedVars.length; i++)
{
if (inArray(unusedVars[r[i]], usedVariables)!=true && inArray(unusedVars[r[i]], definedVariables)!=true)
{
//alert(unusedVars[r[i]]);
rulesUsed++;
//solveDependencies();
if (variables[unusedVars[r[i]]].type=='variableboolean' || variables[unusedVars[r[i]]].type=='boolean')
{
initConditions(unusedVars[r[i]], 0);
}
else
{
initConditions(unusedVars[r[i]], depth-1);
}
}
}
}
if (rulesUsed==0)
{
initConditions(x,0);
}
}
}
function findPathsToGoal(path, definedVars)
{
var r = randomIndices(rules.length);
for(var i=0; i<rules.length; i++)
{
var index = r[i];
curRule = rules[index];
var x = canBeSolved(curRule, definedVars);
if (x!=null)
{
var newPath = path.slice();
newPath.push(index);
var newDefinedVars = definedVars.slice();
newDefinedVars.push(x);
if ((newPath.length < shortestPath.length) || shortestPath.length==0)
{
if (x==goal)
{
shortestPath = newPath;
//alert(shortestPath);
}
else
{
findPathsToGoal(newPath, newDefinedVars);
}
}
}
}
}
var usedInitCond = new Array();
function getExplanation()
{
usedVariables = [];
for(var i=0; i<shortestPath.length; i++)
{
var curRule = rules[shortestPath[i]];
for(var j=0; j<(curRule.length-1); j++) //Have to map the variables before the explanation is generated
{
if (variables[curRule[j]].type=='angle' && variables[curRule[j]].mapping==null)
variables[curRule[j]].mapping = mapVars.pop();
if (variables[curRule[j]].type=='variableboolean' && variables[curRule[j]].dependent.mapping==null)
{
variables[variables[curRule[j]].dependent].mapping = mapVars.pop();
//alert(variables[curRule[j]].dependent+' : '+variables[curRule[j]].dependent.mapping+' : '+mapVars.pop());
}
}
var x = solvable(curRule, initHash);
performOperation(shortestPath[i], initHash);
explanationStack.push([x, initHash[x].reason]);
for(var j=0; j<(curRule.length-1); j++) //Go through all the variables in the rule currently being used
{
usedVariables.push(curRule[j]);
for(var k=0; k<initCond.length; k++)
{
if (initCond[k][0]==curRule[j] && inArray(initCond[k], usedInitCond)==false)
{
usedInitCond.push(initCond[k]);
}
else if (variables[curRule[j]].type=='variableboolean')
{
if (initCond[k][0]==variables[curRule[j]].dependent && initCond[k][1]==variables[curRule[j]].value && inArray(initCond[k], usedInitCond)==false)
usedInitCond.push(initCond[k]);
}
}
}
}
}
function solveDependencies(definedVars)
{
//alert('solveSideEffects()');
var ruleApplied=true;
while(ruleApplied==true)
{
ruleApplied=false;
for(var i=0; i<rules.length; i++)
{
curRule = rules[i];
var x = canBeSolved(curRule, definedVars);
if (x!=null)
{
definedVars.push(x);
ruleApplied=true;
}
}
}
}
function canBeSolved(ruleArray, definedVars)
{
var variable = null;
var foundFalse = false;;
var nullCount = 0;
for(var i=0; i<ruleArray.length-1; i++)
{
if (inArray(ruleArray[i], definedVars)!=true)
{
variable=ruleArray[i];
nullCount++;
}
}
if (nullCount!=1)
variable = null;
return variable;
}
function solvable(ruleArray, valHash)
{
//alert('solvable('+ruleArray+')');
var variable = null;
var foundFalse = false;;
var nullCount = 0;
for(var i=0; i<ruleArray.length-1; i++)
{
if (valHash[ruleArray[i]]==null)
{
variable=ruleArray[i];
nullCount++;
}
else if (valHash[ruleArray[i]].value==false) //A truth that was found to be false
{
foundFalse = true;
}
}
if (nullCount!=1 || foundFalse==true)
variable = null;
return variable;
}
function drawVariable(a)
{
if (variables[a].type=='angle' && (a!=goal || goalDrawn==false))
{
var vertex = points[variables[a].points[1]].coor;
var p1 = points[variables[a].points[0]].coor;
var p2 = points[variables[a].points[2]].coor;
var slope1 = getSlope(vertex, p1);
var slope2 = getSlope(vertex, p2);
var startX;
var startY;
var endX;
var endY;
var textX;
var textY;
var radius=(xMax-xMin)/15;
var radIncrement = radius/2;
if(vertexDrawn[vertex]==null)
{
vertexDrawn[vertex]=1;
}
else
{
radius = radius + vertexDrawn[vertex]*radIncrement;
vertexDrawn[vertex]++;
}
var angle1 = (Math.atan(slope1)+(2*Math.PI))%(2*Math.PI);
var angle2 = (Math.atan(slope2)+(2*Math.PI))%(2*Math.PI);
if (p1[0]<vertex[0])
angle1 = (angle1 + Math.PI)%(2*Math.PI);
if (p2[0]<vertex[0])
angle2 = (angle2 + Math.PI)%(2*Math.PI);
if ((angle1-angle2)>Math.PI)
angle1= angle1-(2*Math.PI);
if ((angle2-angle1)>Math.PI)
angle2= angle2-(2*Math.PI);
if (angle1>angle2)
{
startX = vertex[0] + radius*Math.cos(angle2);
startY = vertex[1] + radius*Math.sin(angle2);
endX = vertex[0] + radius*Math.cos(angle1);
endY = vertex[1] + radius*Math.sin(angle1);
}
else
{
endX = vertex[0] + radius*Math.cos(angle2);
endY = vertex[1] + radius*Math.sin(angle2);
startX = vertex[0] + radius*Math.cos(angle1);
startY = vertex[1] + radius*Math.sin(angle1);
}
var textAngle = ((angle2+angle1)/2)%(2*Math.PI);
textX = vertex[0] + radius*Math.cos(textAngle);
textY = vertex[1] + radius*Math.sin(textAngle);
var textPos = 'above';
if ((textAngle*180/Math.PI)>337.5 || (textAngle*180/Math.PI)<22.5)
textPos = right;
else if ((textAngle*180/Math.PI)<67.5)
textPos =aboveright;
else if ((textAngle*180/Math.PI)<112.5)
textPos =above;
else if ((textAngle*180/Math.PI)<157.5)
textPos =belowleft;
else if ((textAngle*180/Math.PI)<202.5)
textPos =left;
else if ((textAngle*180/Math.PI)<247.5)
textPos =belowleft;
else if ((textAngle*180/Math.PI)<292.5)
textPos = below;
else if ((textAngle*180/Math.PI)<=337.5)
textPos =belowright;
present.stroke = variables[a].color;
present.fontfill = variables[a].color;
present.fontsize=15;
present.fontstyle ="italic";
present.fontweight="normal";
//fontfamily="arial";
present.arc([startX, startY], [textX, textY], radius);
present.arc([textX, textY], [endX, endY], radius);
//present.arc([startX, startY], [endX, endY], radius);
if (a==goal)
{
if(goalDrawn==false)
{
present.text([textX, textY], variables[a].mapping+'=?', textPos);
goalDrawn=true;
}
}
else
present.text([textX, textY], variables[a].mapping+'='+initHash[a].value, textPos);
} else if (variables[a].type=='line' && (a!=goal || goalDrawn==false))
{
present.stroke = variables[a].color;
present.line(points[variables[a].points[0]].coor, points[variables[a].points[1]].coor);
}
else if (variables[a].type=='boolean' && (a!=goal || goalDrawn==false))
{
if (variables[a].var1!=null)
drawVariable(variables[a].var1);
if (variables[a].var2!=null)
drawVariable(variables[a].var2);
}
}
function writeVariable(x, value)
{
var returnString;
var valueString = '';
if (value!=null)
valueString = '='+value;
if (variables[x].type=='angle')
{
returnString = '<font color='+variables[x].color+'><b>`∠`'+variables[x].mapping+valueString+'</b></font>';
}
else if (variables[x].type=='line')
{
returnString = '<font color='+variables[x].color+'><b>'+overline(x)+valueString+'</b></font>';
}
else if (variables[x].type=='variableboolean')
{
valueString = '='+x.value;
returnString = '<font color='+variables[x.dependent].color+'><b>'+overline(x)+valueString+'</b></font>';
}
else if (variables[x].type=='boolean')
{
returnString = writeVariable(variables[x].var1)+variables[x].relation+writeVariable(variables[x].var2);
}
return returnString;
}
function getSlope(p1, p2)
{
return ((p1[1]-p2[1])/(p1[0]-p2[0]));
}
var supAngles = function supplementaryAngles(ruleArray, valueHash) //Assumes that one of them has not been solved for in the valueHash and that the other two have
{
//alert("supplementaryAngles("+ruleArray+","+valueHash+")");
var answer = null;
var input1 = null;
for(var i=0; i<ruleArray.length-1;i++)
{
if (valueHash[ruleArray[i]]==null)
{
answer = ruleArray[i];
input1 = ruleArray[((i+1)%2)];
}
}
var in1 = valueHash[input1].value;
valueHash[answer]= {value: (180 - in1), reason: new Array()};
valueHash[answer].reason.push('Solve for '+writeVariable(answer)+' using '+writeVariable(input1));
valueHash[answer].reason.push(writeVariable(answer)+' and '+writeVariable(input1)+' are supplementary');
valueHash[answer].reason.push(writeVariable(answer)+'+'+writeVariable(input1)+'=180');
valueHash[answer].reason.push('Since '+writeVariable(input1, in1)+', '+writeVariable(answer,(180 - in1)));
}
var oppAngles = function oppositeAngles(ruleArray, valueHash) //Assumes that one of them has not been solved for in the valueHash and that the other two have
{
//alert("supplementaryAngles("+ruleArray+","+valueHash+")");
var answer = null;
var input1 = null;
for(var i=0; i<ruleArray.length-1;i++)
{
if (valueHash[ruleArray[i]]==null)
{
answer = ruleArray[i];
input1 = ruleArray[((i+1)%2)];
}
}
var in1 = valueHash[input1].value;
valueHash[answer]= {value: in1, reason: new Array()};
valueHash[answer].reason.push('Solve for '+writeVariable(answer)+' using '+writeVariable(input1));
valueHash[answer].reason.push(writeVariable(answer)+' and '+writeVariable(input1)+' are opposite angles');
valueHash[answer].reason.push('So :'+writeVariable(answer)+'='+writeVariable(input1)+' and '+writeVariable(input1,in1));
valueHash[answer].reason.push('Since '+writeVariable(input1, in1)+', '+writeVariable(answer,in1));
}
var corAngles = function corresspondingAngles(ruleArray, valueHash) //Assumes that one of them has not been solved for in the valueHash and that the other two have
{
//alert("supplementaryAngles("+ruleArray+","+valueHash+")");
var answer = null;
var input1 = null;
for(var i=0; i<ruleArray.length-1;i++)
{
if (valueHash[ruleArray[i]]==null)
{
answer = ruleArray[i];
input1 = ruleArray[((i+1)%3)];
input2 = ruleArray[((i+2)%3)];
}
}
if (answer.length<4)//We know that the answer will be an angle as opposed to a truth
{
var known;
if(input1.length <4)
{
known = input1;
reason = input2;
}
else
{
known = input2;
reason = input1;
}
var knownVal = valueHash[known].value;
valueHash[answer]= {value: knownVal, reason: new Array()};
valueHash[answer].reason.push('Solve for '+writeVariable(answer)+' using '+writeVariable(known));
valueHash[answer].reason.push('Since '+reason+', '+writeVariable(answer)+' and '+writeVariable(known)+' are corresponding angles');
valueHash[answer].reason.push('So:'+writeVariable(answer)+'='+writeVariable(known)+'; '+writeVariable(known,knownVal));
valueHash[answer].reason.push(writeVariable(answer,knownVal));
}
else
{
var in1 = valueHash[input1].value;
var in2 = valueHash[input2].value;
if (in1==in2)
{
valueHash[answer] = {value: true, reason: new Array()};
valueHash[answer].reason.push('Since '+writeVariable(input1)+'='+writeVariable(input2)+' and they are corresponding angles, we know that '+answer);
}
else
{
valueHash[answer] = {value: false, reason: new Array()};
valueHash[answer].reason.push('Since '+writeVariable(input1)+' does not equal '+writeVariable(input2)+', it cannot be true that '+answer);
}
}
}
var pyth = function pythTriangle(ruleArray, valueHash) //Assumes the arguments come in the order A, B, C, X=90 where A2+B2=C2
{
//alert('pythTriangle(['+ruleArray+'],{'+valueHash+'})');
var answer = null;
var inputs = {};
var solvingFor;
var A={name: ruleArray[0], value: null};
var B={name: ruleArray[1], value: null};
var C={name: ruleArray[2], value: null};
var angleRule={name: ruleArray[3], value: null};
if (valueHash[ruleArray[0]]!=null)
A.value= valueHash[ruleArray[0]].value;
if (valueHash[ruleArray[1]]!=null)
B.value= valueHash[ruleArray[1]].value;
if (valueHash[ruleArray[2]]!=null)
C.value= valueHash[ruleArray[2]].value;
if (valueHash[ruleArray[3]]!=null)
angleRule.value= valueHash[ruleArray[3]].value;
for(var i=0; i<ruleArray.length-1;i++)
{
if (valueHash[ruleArray[i]]==null)
{
answer = ruleArray[i];
inputs[0] = {name: ruleArray[((i+1)%4)], value: valueHash[ruleArray[((i+1)%4)]]};
inputs[1] = {name: ruleArray[((i+2)%4)], value: valueHash[ruleArray[((i+2)%4)]]};
inputs[2] = {name: ruleArray[((i+3)%4)], value: valueHash[ruleArray[((i+3)%4)]]};
solvingFor = i;
}
}
if (A.value==null)
{
valueHash[A.name]= {value: variables[A.name].value, reason: new Array()};
valueHash[A.name].reason.push('<b>'+writeVariable(A.name)+'<sup>2</sup>+'+writeVariable(B.name)+'<sup>2</sup>='+writeVariable(C.name)+'<sup>2</sup></b>');
valueHash[A.name].reason.push('<b>'+writeVariable(A.name)+'<sup>2</sup>+'+B.value+'<sup>2</sup>='+C.value+'<sup>2</sup></b>');
valueHash[A.name].reason.push('<b>'+writeVariable(A.name)+'`=sqrt('+Math.pow(variables[A.name].value,2)+')`</b>');
valueHash[A.name].reason.push(writeVariable(A.name,valueHash[A.name].value));
}
if (B.value==null)
{
valueHash[B.name]= {value: variables[B.name].value, reason: new Array()};
valueHash[B.name].reason.push('<b>'+writeVariable(B.name)+'<sup>2</sup>+'+writeVariable(A.name)+'<sup>2</sup>='+writeVariable(C.name)+'<sup>2</sup></b>');
valueHash[B.name].reason.push('<b>'+writeVariable(B.name)+'<sup>2</sup>+'+A.value+'<sup>2</sup>='+C.value+'<sup>2</sup></b>');
valueHash[B.name].reason.push('<b>'+writeVariable(B.name)+'`=sqrt('+Math.pow(variables[B.name].value,2)+')`</b>');
valueHash[B.name].reason.push(writeVariable(B.name,valueHash[B.name].value));
}
if (C.value==null)
{
valueHash[C.name]= {value: variables[C.name].value, reason: new Array()};
valueHash[C.name].reason.push('<b>'+writeVariable(B.name)+'<sup>2</sup>+'+writeVariable(A.name)+'<sup>2</sup>='+writeVariable(C.name)+'<sup>2</sup></b>');
valueHash[C.name].reason.push('<b>'+A.value+'<sup>2</sup>+'+B.value+'<sup>2</sup>='+writeVariable(C.name)+'<sup>2</sup></b>');
valueHash[C.name].reason.push('<b>'+writeVariable(C.name)+'=`sqrt('+Math.pow(variables[C.name].value,2)+')`</b>');
valueHash[C.name].reason.push('<b>'+writeVariable(C.name,valueHash[C.name].value)+'</b>');
}
if (angleRule.value==null)
{
valueHash[angleRule]= {value: true, reason: new Array()};
valueHash[angleRule].reason.push('`'+writeVariable(A.name)+'<sup>2</sup>+'+writeVariable(B.name)+'<sup>2</sup>='+writeVariable(C.name)+'^<sup>2</sup>`, so '+writeVariable(angleRule));
valueHash[variables[angleRule].dependent]= {value: 90, reason: new Array()};
}
}
var angSum = function angleSum(ruleArray, valueHash) //Assumes the first two angles add up to the third
{
//alert("angleSum("+ruleArray+","+valueHash+")");
var answer = null;
var input1 = null;
var input2 = null;
var solvingBigAngle = false; //start with the assumption that we are solving for one of the smaller angles
for(var i=0; i<ruleArray.length-1;i++)
{
if (valueHash[ruleArray[i]]==null)
{
answer = ruleArray[i];
if (i==2)
{
solvingBigAngle = true; //We are solving for the sum of the two smaller angles
input1 = ruleArray[0];
input2 = ruleArray[1];
}
else
{
input1 = ruleArray[((i+1)%2)];
input2 = ruleArray[2];
}
}
}
var in1 = valueHash[input1].value;
var in2 = valueHash[input2].value;
if (solvingBigAngle)
{
valueHash[answer]= {value: (in2 + in1), reason: new Array()};
valueHash[answer].reason.push('Solve for '+writeVariable(answer)+' using '+writeVariable(input1)+' and '+writeVariable(input2));
valueHash[answer].reason.push(writeVariable(input2)+'+'+writeVariable(input1)+'='+writeVariable(answer)+' and '+writeVariable(input1,in1)+', '+writeVariable(input2,in2));
valueHash[answer].reason.push('So '+writeVariable(answer,(in2+in1)));
}
else
{
valueHash[answer]= {value: (in2 - in1), reason: new Array()};
valueHash[answer].reason.push('Solve for '+writeVariable(answer)+' using '+writeVariable(input1)+' and '+writeVariable(input2));
valueHash[answer].reason.push(writeVariable(answer)+'+'+writeVariable(input1)+'='+writeVariable(input2)+' and '+writeVariable(input1,in1)+', '+writeVariable(input2,in2));
valueHash[answer].reason.push('So '+writeVariable(answer)+'='+in2+'-'+in1);
valueHash[answer].reason.push(writeVariable(answer,(in2 - in1)));
}
}
var triAngSum = function triangleAngleSum(ruleArray, valueHash) //Assumes that one of them has not been solved for in the valueHash and that the other two have
{
//alert("triangleAngleSum("+ruleArray+","+valueHash+")");
var answer = null;
var input1 = null;
var input2 = null;
for(var i=0; i<ruleArray.length-1;i++)
{
if (valueHash[ruleArray[i]]==null)
{
answer = ruleArray[i];
input1 = ruleArray[((i+1)%3)];
input2 = ruleArray[((i+2)%3)];
}
}
var in1 = valueHash[input1].value;
var in2 = valueHash[input2].value;
valueHash[answer]= {value: (180 - in1 - in2), reason: new Array()};
valueHash[answer].reason.push('Solve for '+writeVariable(answer)+' using '+writeVariable(input1)+' and '+writeVariable(input2));
//valueHash[answer].reason.push("The sum of the angles of a triangle = 180");
valueHash[answer].reason.push(writeVariable(answer)+'+'+writeVariable(input1)+'+'+writeVariable(input2)+'=180');
valueHash[answer].reason.push(writeVariable(input1,in1)+', '+writeVariable(input2,in2));
valueHash[answer].reason.push(writeVariable(answer)+'=180-'+in1+'-'+in2);
valueHash[answer].reason.push(writeVariable(answer,(180 - in1 - in2)));
}
function performOperation(rIndex, valueHash)
{
var rule = rules[rIndex];
rule[rule.length-1](rules[rIndex], valueHash);
}
function inArray(x, a)
{
var answer = false;
for(var i=0; i<a.length; i++)
{
if (x==a[i])
{
answer=true;
i=a.length;
}
}
return answer;
}
function varInRule(x, rule)
{
var j=0;
var foundMatch = false;
while (j<(rule.length-1) && foundMatch==false)
{
if (rule[j]==x)
{
foundMatch = true;
}
j++;
}
return foundMatch;
}
function assignRandom(x)
{
//alert("assignRandom("+x+")");
if (valueTable[x]==null)
{
var maxVal;
if (isAngle(x))
{
maxVal = 14;
}
else if (isLength(x))
{
maxVal = 5;
}
var epsilon = .99;
var val = Math.round(KhanAcademy.random()*(maxVal-1+epsilon) - epsilon/2);
var newValue = Math.round(variables[x].seed-maxVal/2+val);
valueTable[x] = {value: newValue, reason: new Array()};
initCond.push([x,newValue]);
solveSideEffects();
}
}
function isAngle(x)
{
return (x.length==3);
}
function isTruth(x)
{
return (x.length>3);
}
function isLength(x)
{
return (x.length==2);
}
function randomIndices(length)
{
var startArray = new Array();
var endArray = new Array();
for(var i=0; i<length; i++)
startArray.push(i);
while(startArray.length>0)
{
var epsilon = .99;
var maxVal = startArray.length-1;
var index = Math.round(KhanAcademy.random()*(maxVal+epsilon) - epsilon/2);
endArray.push(startArray.splice(index,1)[0]);
}
return endArray;
}
function findRulesWithVariable(v)
{
//alert("findRulesWithVariable("+v+")");
var matchingRules = new Array();
for(var i=0; i<rules.length; i++)
{
if (varInRule(v, rules[i]) && inArray(i, usedRules)!=true && ((v!=goal && varInRule(goal, rules[i])!=true)|| v==goal)) //The variable is in the rule and the rule has not been used yet
{
var unusedVars = new Array(); //figure out all of the variables that have not been used or defined (ALL defined variables are used but not the other way around)
for(var j=0; j<rules[i].length-1; j++)
{
if (inArray(rules[i][j], usedVariables)!=true) //If the jth element of rule i is not a usedVariables
unusedVars.push(rules[i][j]);
}
if (unusedVars.length>0)
{
matchingRules.push([i, unusedVars]);
}
}
}
return matchingRules;
}
function randomArrayEntry(a) //returns a random entry from the array a
{
var epsilon = .99;
var index = Math.round(KhanAcademy.random()*(a.length-1+epsilon) - epsilon/2);
return a[index];
}
function overline(x)
{
return ('<font style=\"text-decoration: overline;\">'+x+'</font>');
}
function draw_next_step() {
if (explanationStack.length <= steps_given) return;
drawVariable(explanationStack[steps_given][0]);
steps_given++;
show_step();
}
function graph_update() {
for (key in points)
{
xMin = Math.min(xMin, points[key].coor[0]);
xMax = Math.max(xMax, points[key].coor[0]);
yMin = Math.min(yMin, points[key].coor[1]);
yMax = Math.max(yMax, points[key].coor[1]);
}
var xPadding = 0.05*(xMax - xMin);
var yPadding = 0.05*(yMax - yMin);
goalDrawn = false;
present.initPicture(xMin-xPadding, xMax+xPadding, yMin-yPadding, yMax+yPadding);
present.fontstyle = "normal";
present.fontsize = "10";
present.stroke = "#AAAAAA";
present.strokewidth = "2";
if (type==1)
updateType1();
else
updateType2();
for(key in points)
{
if (points[key].label!=null)
{
present.text(points[key].coor, key, points[key].label);
}
}
for(var i=0; i<usedInitCond.length; i++)
{
drawVariable(usedInitCond[i][0]);
}
drawVariable(goal);
}
function updateType1()
{
present.line(points.A.coor, points.C.coor);
present.line(points.C.coor, points.D.coor);
present.line(points.D.coor, points.B.coor);
present.line(points.B.coor, points.A.coor);
present.line(points.B.coor, points.C.coor);
present.line(points.B.coor, points.E.coor);
present.line(points.I.coor, points.B.coor);
present.line(points.H.coor, points.I.coor);
present.line(points.F.coor, points.G.coor);
}
function updateType2()
{
for (x in variables)
{
if (variables[x].type=='line')
{
var p1 = points[variables[x].points[0]].coor;
var p2 = points[variables[x].points[1]].coor;
present.line(p1,p2);
}
}
}
function getReasonString(reason)
{
var reasonString = reason[0]+':<UL>';
for(var i = 1; i < reason.length; i++)
reasonString+='<li>'+reason[i]+'</li>';
reasonString+='</ul>';
return reasonString;
}
function type1()
{
variables['BAC'] = {type: 'angle', points:['B','A','C'], seed:60, color: '#D9A326'};
variables['ABC'] = {type: 'angle', points:['A','B','C'], seed:60, color: '#E8887D'};
variables['ACB'] = {type: 'angle', points:['A','C','B'], seed:60, color: '#9CC9B7'};
variables['CBD'] = {type: 'angle', points:['C','B','D'], seed:30, color: '#AE9CC9'};
variables['BCD'] = {type: 'angle', points:['B','C','D'], seed:120, color: '#CC6699'};
variables['BDC'] = {type: 'angle', points:['B','D','C'], seed:30, color: '#FF6347'};
variables['ABD'] = {type: 'angle', points:['A','B','D'], seed:90, color: '#8E2323'};
variables['EBD'] = {type: 'angle', points:['E','B','D'], seed:90, color: '#CD9B9B'};
variables['IBE'] = {type: 'angle', points:['I','B','E'], seed:60, color: '#E47833'};
variables['IBD'] = {type: 'angle', points:['I','B','D'], seed:150, color: '#777777'};
variables['ABI'] = {type: 'angle', points:['A','B','I'], seed:120, color: '#AA5303'};
variables['BIF'] = {type: 'angle', points:['B','I','F'], seed:120, color: '#CDBA96'};
variables['CBE'] = {type: 'angle', points:['C','B','E'], seed:120, color: '#D9A326'};
variables['HIF'] = {type: 'angle', points:['H','I','F'], seed:60, color: '#6B8E23'};
variables['GIH'] = {type: 'angle', points:['G','I','H'], seed:120, color: '#668B8B'};
variables['GIC'] = {type: 'angle', points:['G','I','C'], seed:60, color: '#00CED1'};
variables['GF'] = {type: 'line', points:['G','F'], value:10, color: '#CDBA96'};
variables['AE'] = {type: 'line', points:['A','E'], value:10, color: '#FF6347'};
variables['AB'] = {type: 'line', points:['A','B'], value:pythSide[0], color: '#E8887D'};
variables['BD'] = {type: 'line', points:['B','D'], value:pythSide[1], color: '#9370DB'};
variables['AD'] = {type: 'line', points:['A','D'], value:pythSide[2], color: '#DB70DB'};
variables['ABD=90'] = {type: 'variableboolean', dependent:'ABD', value:90};
variables['line GF is parrallel to line AE'] = {type: 'boolean', relation: ' is parallel to ', var1: 'GF', var2: 'AE'};
points.A = {coor: [-5,0], label: left};
points.B = {coor: [-2,6], label: above};
points.C = {coor: [0,0], label: below};
points.D = {coor: [5,0], label: right};
points.E = {coor: [1, 12], label: right};
points.F = {coor: [-2,12], label: right};
points.G = {coor: [-8,0], label: below};
points.H = {coor: [-4, 12], label: left};
points.I = {coor: [-16/5, 48/5], label: left};
rules = [ ['BAC', 'ABC', 'ACB', triAngSum],
['ABC', 'CBD', 'ABD', angSum], //Assumes the first n items make up the last item (before the function call)
['CBD', 'EBD', 'CBE', angSum],
['IBE', 'EBD', 'IBD', angSum],
['BAC', 'ABD', 'BDC', triAngSum],
['ACB', 'BCD', supAngles],
['CBE', 'ABC', supAngles],
['CBE', 'IBE', supAngles],
['IBE','ABC', oppAngles],
['GIH', 'BIF', oppAngles],
['HIF', 'GIC', oppAngles],
['ABI','CBE', oppAngles],
['IBE','ABI', supAngles],
['ABC','ABI', supAngles],
['ABD','EBD', supAngles],
['GIH', 'GIC', supAngles],
['HIF', 'BIF', supAngles],
['BIF', 'GIC', supAngles],
['IBE','HIF', 'line GF is parrallel to line AE', corAngles],
['BIF','CBE', 'line GF is parrallel to line AE', corAngles],
['ABI','GIH', 'line GF is parrallel to line AE', corAngles],
['ABC','GIC', 'line GF is parrallel to line AE', corAngles],
['CBD','IBD', supAngles],
['AB', 'BD', 'AD', 'ABD=90', pyth],
['BDC','BCD','CBD', triAngSum]];
}
function intersection(p1,p2,p3,p4)
{
var m1 = (points[p1].coor[1]-points[p2].coor[1])/(points[p1].coor[0]-points[p2].coor[0]);
var m2 = (points[p3].coor[1]-points[p4].coor[1])/(points[p3].coor[0]-points[p4].coor[0]);
var b1 = points[p1].coor[1] - m1*points[p1].coor[0];
var b2 = points[p3].coor[1] - m2*points[p3].coor[0];
var x = (b2-b1)/(m1-m2);
var y = m1*x+b1;
return [Math.round(x*100)/100,Math.round(y*100)/100];
}
function getLine(p1, p2)
{
var m = Math.round(getSlope(p1, p2)*100)/100;
var b = Math.round((p1[1]-p1[0]*m)*1000)/1000;
return [m,round2Dig(b)];
}
function equalLines(line1, line2)
{
return (line1[0]==line2[0] && line1[1]==line2[1]);
}
function round2Dig(x)
{
var s = xMax-xMin;
s = s/200;
return (Math.round(x*s)/s);
}
var colors = ['#D9A326', '#E8887D', '#9CC9B7', '#AE9CC9', '#CC6699', '#FF9999', '#CD9B9B', '#E47833', '#777777', '#CDBA96','#FFCC11','#6B8E23','#668B8B'];
var curColor = 0;
function getColor()
{
curColor = (curColor+1)%colors.length;
return colors[curColor];
}