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Last active Dec 27, 2019

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Sum of First n Numbers

Demonstrates a proof of the formula for the sum of first n positive integers commonly attributed to Carl Friederich Gauss.

<!DOCTYPE html>
<meta charset="utf-8">
<style>
body{
width:900px;
}
svg text{
font-size:30px;
}
line{
stroke:black;
}
rect{
stroke:grey;
fill:red;
fill-opacity:0.2;
}
</style>
<body>
<svg width='900' height='600'></svg>
<script src="http://d3js.org/d3.v3.min.js">
</script>
<script>
var e=50+Math.floor(49*Math.random()),
ele = ['1','+','2','+','3','+','...','+',''+(e-2),'+',''+(e-1),'+',''+e,'=','S'];
var duration=2000;
function x(i){
return 120+i*40;
}
d3.select("svg").append("text").attr("id",'qstn').text('What is ')
.attr("x",0).attr("y",100);
d3.select("svg").append('g').attr("id","row1").selectAll('.ele')
.data(ele).enter().append("text").attr("class","ele")
.attr("x",function(d,i){ return x(i);}).attr("y",100)
.attr("text-anchor","middle")
.text(function(d,i){ return (i==ele.length-1 ? '??':d);});
setTimeout(function(){
d3.select("#qstn").transition().duration(1000).style("fill-opacity",0);
d3.select("#row1").selectAll('.ele').filter(function(d,i){ return i==ele.length-1;})
.transition().duration(1000).style("fill-opacity",0);
},duration
);
duration+=2000;
setTimeout(function(){
d3.select("#qstn").text('Let').transition().duration(1000).style("fill-opacity",1);
d3.select("#row1").selectAll('.ele').filter(function(d,i){ return i==ele.length-1;})
.text(function(d,i){ return d;})
.transition().duration(1000).style("fill-opacity",1);
},duration
)
duration+=2000;
setTimeout(function(){
d3.select("#qstn").transition().duration(1000).style("fill-opacity",0);
d3.select("svg").append("g").attr("id","row2").selectAll('.ele')
.data(ele).enter().append("text").attr("class","ele")
.attr("x",function(d,i){ return 120+i*40;}).attr("y",100)
.attr("text-anchor","middle")
.text(function(d,i){ return d;})
.style("fill-opacity",0).transition().duration(1000)
.attr('y',160).style('fill-opacity',1);
},duration
);
duration+=2000;
setTimeout(function(){
d3.select("#row2").selectAll(".ele").transition().duration(500)
.attr('y',function(d,i){ return (i==0||i==2|i==4 ? 130 : i==8||i==10||i==12? 190: 160);})
.transition().duration(2000)
.attr('x',function(d,i){ return (i==0||i==2|i==4||i==8||i==10||i==12 ? x(12-i) : x(i)); })
.transition().duration(500).attr('y',160);
},duration);
duration+=3500;
setTimeout(function(){
d3.select("svg").append("line").attr("x1",50).attr("x2",750).attr("y1",200).attr("y2",200);
},duration);
duration+=1500;
setTimeout(function(){
d3.select("svg").selectAll("rect").data([0,2,4,8,10,12,14]).enter().append("rect")
.attr("x",function(d,i){ return x(d)-25;}).attr("y",50)
.attr("width",50).attr("height",0)
.transition().delay(function(d,i){return i*500;}).duration(500)
.attr("height",150);
d3.select("svg").append("g").attr("id","row3").selectAll("ele")
.data(ele.map(function(d,i){ return (i==0||i==2||i==4||i==8||i==10||i==12 ? +ele[12]+1 : i==14? '2S': ele[i]);}))
.enter().append("text").attr("class","ele")
.style("fill-opacity",0).text(function(d){return d}).style("text-anchor","middle")
.attr("x",function(d,i){ return x(i)}).attr("y",200)
.filter(function(d,i){ return i==0||i==2||i==4||i==8||i==10||i==12||i==14;})
.transition().delay(function(d,i){return (i+1)*500;}).duration(500)
.attr("y",240).style("fill-opacity",1);
},duration);
duration+=5000;
setTimeout(function(){
d3.select("#row3").selectAll(".ele").transition().duration(500)
.attr("y",240).style("fill-opacity",1);
},duration);
duration+=3000;
setTimeout(function(){
d3.select("svg").append("g").attr("id","row4").selectAll(".ele")
.data([''+(+ele[12])+'('+(+ele[12]+1)+')','=','2S'])
.enter().append("text").attr("class","ele")
.attr("x",function(d,i){ return i==0 ? 580: x(12+i);}).attr("y",300)
.style("text-anchor","middle").text(function(d){return d;});
},duration);
duration+=3000;
setTimeout(function(){
d3.select("svg").append("g").attr("id","row5").selectAll(".ele")
.data([''+(+ele[12])+'('+(+ele[12]+1)+')/2','=','S'])
.enter().append("text").attr("class","ele")
.attr("x",function(d,i){ return i==0 ? 570: x(12+i);}).attr("y",360)
.style("text-anchor","middle").text(function(d){return d;});
},duration);
duration+=3000;
setTimeout(function(){
d3.select("svg").append("text").attr("x",0).attr("y",420).text("So");
d3.select("svg").append("g").attr("id","row6").selectAll(".ele")
.data(ele.map(function(d,i){ return i!=14? d : ''+(+ele[12])+'('+(+ele[12]+1)+')/2';}))
.enter().append("text").attr("class","ele")
.attr("x",function(d,i){ return i==14? x(i)+50: x(i);}).attr("y",420)
.style("text-anchor","middle").text(function(d){return d;});
},duration);
</script>
</body>
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