3f:null 40:["$","title",null,{"children":"A visual representation of the GCD | Silvas Workspapce | Observable"}] 46:Te74,function drawGCD(){ const context = DOM.context2d(width, width); context.canvas.width = width; context.canvas.height = width; const cf = continuedFraction(A,B) const rez = A>B?width/A:width/B; // draw a grid of squares of size 1 for (let row=0; rows*rez); cf.quotients.forEach((quotient, i)=>{ // the current y coordinate of the squares // sum quotients[j]*sizes[j] for j%4=1 up to i-1. let oddOneIndSum=0; let j=1; while(j<=i-1){ oddOneIndSum+=cf.quotients[j]*scaledsizes[j]; j+=4; } // sum quotients[j]*sizes[j] for j%4=3 up to i-1. let oddThreeIndSum=0; let l=3; while(l<=i-1){ oddThreeIndSum+=cf.quotients[l]*scaledsizes[l]; l+=4; } // the current x coordinate of the squares // sum quotients[k]*sizes[k] for k%4=0 up to i-1. let eveZeroIndSum=0; let k=0; while(k<=i-1){ eveZeroIndSum+=cf.quotients[k]*scaledsizes[k]; k+=4; } // sum quotients[k]*sizes[k] for k%4=2 up to i-1. let eveTwoIndSum=0; let m=2; while(m<=i-1){ eveTwoIndSum+=cf.quotients[m]*scaledsizes[m]; m+=4; } let ind=0; //var to keep track of number of square of a specific size switch (i%4) { case 0: if(i==0){ while (indB?A*w/A:A*w/B;\n const svg = d3\n .create(\"svg\")\n .attr('width', w)\n .attr('height', h);\n \n // Set up the SVG background\n const mapbg = DOM.uid('mapbg');\n\n svg\n .append(\"defs\")\n .append('pattern')\n .attr('id', mapbg.id)\n .attr('patternUnits', 'userSpaceOnUse')\n .attr('width', w)\n .attr('height', h)\n .append(\"image\")\n .attr(\"xlink:href\", drawGCD())\n .attr('width', w)\n .attr('height', w)\n\n svg\n .append(\"rect\")\n .attr(\"x\", 0)\n .attr(\"y\", 0)\n .attr(\"width\", w)\n .attr(\"height\", h)\n .attr(\"fill\", mapbg);\n\n return svg.node();\n}\n ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"The drawing above shows the rectangle of size ${B+'x'+A} divided into:\n${sq_to_txt(continuedFraction(A,B))}\n\nHence the Greatest Common Divisor of ${A} and ${B} is ${tex`\\gcd(A,B)=`} ${continuedFraction(A,B).gcd}.\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":49,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"continuedFraction(A,B)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"\nfunction continuedFraction(a,b,r=-1,cf='undefined') {\n cf = cf==='undefined'?{quotients:[],remainders:[],gcd:a}:cf;\n\n let c = Math.floor(b/a);\n cf.quotients.push(c);\n \n if (r==-1) cf.remainders.push(a);\n \n r=b-c*a;\n if (r>0) {\n cf.remainders.push(r);\n cf.gcd = r;\n continuedFraction(r,a,r,cf);\n }\n return cf;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":122,"value":"function sq_to_txt(cf) {\n let text = '\\n';\n cf.quotients.forEach((q,i)=>{\n if (q!==0) {\n text+=`\\t ${q} square${q>1?'s':''} of size ${cf.remainders[i]}\\n`;\n }\n });\n return text;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W47","stdlib":"1"}} 45:"$44:body"