Category: Math

var xp:Number = 0;
var yp:Number = 0;
var t:Number = 0;
var a:Number = 200;
x = stage.stageWidth / 2;
y = stage.stageHeight / 2;

graphics.lineStyle(0,0x000000);
addEventListener(Event.ENTER_FRAME, onRun);
function onRun(evt:Event):void {
	xp = a * Math.cos(t) - (a * Math.pow(Math.sin(t),2))/Math.sqrt(2);
	yp = a * Math.cos(t) * Math.sin(t);
	if (t == 0){
	  graphics.moveTo(xp, yp);
	}else{
	  graphics.lineTo(xp, yp);
	}
	t += 0.05;
}

While surfing mathworld I stumbled upon the equation for something called the Fish Curve. This snippet will draw something like this:

var xp:Number = 0;
var yp:Number = 0;
var t:Number = 0;
var r:Number = 200;
x = stage.stageWidth / 2;
y = stage.stageHeight / 2;

graphics.lineStyle(0,0x000000);
addEventListener(Event.ENTER_FRAME, onRun);
function onRun(evt:Event):void {
	r = 200 * Math.cos(t / 10);
	xp = r * Math.pow(Math.cos(t), 3);
	yp = r * Math.pow(Math.sin(t), 3);
	if (t == 0){
	  graphics.moveTo(xp, yp);
	}else{
	  graphics.lineTo(xp, yp);
	}
	t += 0.1;
}

While browsing mathworld I decided to do a variation on this curve . The above snippet will draw something like this:

// print some floats as fractions
printFraction(0.5);
printFraction(0.75);
printFraction(0.48);

// try something a little more complex
var float:Number = 0.98765432;
trace("na more complex example:");
printFraction(float);
var frac:Array = asFraction(float);
trace("double check it:");
trace(frac[0] + "/" + frac[1] +" = " + frac[0] / frac[1]);

/* outputs:
0.5 = 1/2
0.75 = 3/4
0.48 = 12/25

a more complex example:
0.98765432 = 12345679/12500000
double check it:
12345679/12500000 = 0.98765432
*/


function printFraction(n:Number):void{
	var frac:Array = asFraction(n);
	trace(n + " = " + frac[0] + "/" + frac[1]);
}

// takes any value less than one and returns an array 
// with the numerator at index 0 and the denominator at index 1
function asFraction(num:Number):Array{
    var decimalPlaces:int = num.toString().split(".")[1].length;
	var denom:Number = Math.pow(10, decimalPlaces);
	return reduceFraction(num * denom, denom);
}

// divide the numerator and denominator by the GCF
function reduceFraction(numerator:int, denominator:Number):Array{
	// divide by the greatest common factor
	var divisor:int = gcf(numerator, denominator);
	if (divisor){
		numerator /= divisor;
		denominator /= divisor;
	}
	return [numerator, denominator];
}
					
// get the greatest common factor of two integers
function gcf(a:int, b:int):int{
	var remainder:int;
	var factor:Number = 0;
	var maxIter:int = 100;
	var i:int = 0;
	while (1){
		if (b > a){
		   var swap:int = a;
		   a = b;
		   b = swap;
		}
		remainder = a % b;
		a = b;
		b = remainder
		if (remainder == 0){
			factor = a;
			break;
		}else if (remainder==1){
			break;
		}else if (i > maxIter){
			trace("failed to calculate gcf");
			break;
		}
		i++;
	}
	return factor;
}

This snippet contains a few functions for calculating fractions based on float values. Writing this brought back some memories from grade school math.