Math | ActionScript 2.0 Language Reference for Macromedia Flash 8

Object | +-Math public class Math extends Object

The Math class is a top-level class whose methods and properties you can use without using a constructor.

Use the methods and properties of this class to access and manipulate mathematical constants and functions. All the properties and methods of the Math class are static and must be called using the syntax Math.method(parameter) or Math.constant. In ActionScript, constants are defined with the maximum precision of double-precision IEEE-754 floating-point numbers.

Several Math class methods use the measure of an angle in radians as a parameter.You can use the following equation to calculate radian values before calling the method and then provide the calculated value as the parameter, or you can provide the entire right side of the equation (with the angle's measure in degrees in place of degrees) as the radian parameter.

To calculate a radian value, use the following formula:

radians = degrees * Math.PI/180

The following is an example of passing the equation as a parameter to calculate the sine of a 45° angle:

Math.sin(45 * Math.PI/180) is the same as Math.sin(.7854)

Availability: ActionScript 1.0; Flash Player 5 - In Flash Player 4, the methods and properties of the Math class are emulated using approximations and might not be as accurate as the non-emulated math functions that Flash Player 5 supports.

Property summary

Modifiers	Property	Description
`static`	`E:Number`	A mathematical constant for the base of natural logarithms, expressed as e.
`static`	`LN10:Number`	A mathematical constant for the natural logarithm of 10, expressed as loge10, with an approximate value of 2.302585092994046.
`static`	`LN2:Number`	A mathematical constant for the natural logarithm of 2, expressed as loge2, with an approximate value of 0.6931471805599453.
`static`	`LOG10E:Number`	A mathematical constant for the base-10 logarithm of the constant e (`Math.E`), expressed as log10e, with an approximate value of 0.4342944819032518.
`static`	`LOG2E:Number`	A mathematical constant for the base-2 logarithm of the constant e (`Math.E`), expressed as log2e, with an approximate value of 1.442695040888963387.
`static`	`PI:Number`	A mathematical constant for the ratio of the circumference of a circle to its diameter, expressed as pi, with a value of 3.141592653589793.
`static`	`SQRT1_2:Number`	A mathematical constant for the square root of one-half, with an approximate value of 0.7071067811865476.
`static`	`SQRT2:Number`	A mathematical constant for the square root of 2, with an approximate value of 1.4142135623730951.

Properties inherited from class Object


constructor (Object.constructor property),  __proto__ (Object.__proto__ property), prototype (Object.prototype property),  __resolve (Object.__resolve property)

Method summary

Modifiers	Signature	Description
`static`	`abs(x:Number) : Number`	Computes and returns an absolute value for the number specified by the parameter `x`.
`static`	`acos(x:Number) : Number`	Computes and returns the arc cosine of the number specified in the parameter `x`, in radians.
`static`	`asin(x:Number) : Number`	Computes and returns the arc sine for the number specified in the parameter `x`, in radians.
`static`	`atan(tangent:Number) : Number`	Computes and returns the value, in radians, of the angle whose tangent is specified in the parameter `tangent`.
`static`	`atan2(y:Number, x:Number) : Number`	Computes and returns the angle of the point `y`/`x` in radians, when measured counterclockwise from a circle's x axis (where 0,0 represents the center of the circle).
`static`	`ceil(x:Number) : Number`	Returns the ceiling of the specified number or expression.
`static`	`cos(x:Number) : Number`	Computes and returns the cosine of the specified angle in radians.
`static`	`exp(x:Number) : Number`	Returns the value of the base of the natural logarithm (e), to the power of the exponent specified in the parameter `x`.
`static`	`floor(x:Number) : Number`	Returns the floor of the number or expression specified in the parameter `x`.
`static`	`log(x:Number) : Number`	Returns the natural logarithm of parameter `x`.
`static`	`max(x:Number, y:Number) : Number`	Evaluates `x` and `y` and returns the larger value.
`static`	`min(x:Number, y:Number) : Number`	Evaluates `x` and `y` and returns the smaller value.
`static`	`pow(x:Number, y:Number) : Number`	Computes and returns `x` to the power of `y`.
`static`	`random() : Number`	Returns a pseudo-random number n, where 0 <= n < 1.
`static`	`round(x:Number) : Number`	Rounds the value of the parameter `x` up or down to the nearest integer and returns the value.
`static`	`sin(x:Number) : Number`	Computes and returns the sine of the specified angle in radians.
`static`	`sqrt(x:Number) : Number`	Computes and returns the square root of the specified number.
`static`	`tan(x:Number) : Number`	Computes and returns the tangent of the specified angle.

Methods inherited from class Object


addProperty (Object.addProperty method),  hasOwnProperty (Object.hasOwnProperty method), isPropertyEnumerable (Object.isPropertyEnumerable method),  isPrototypeOf (Object.isPrototypeOf method), registerClass (Object.registerClass  method), toString (Object.toString method), unwatch (Object.unwatch  method), valueOf (Object.valueOf method), watch (Object.watch method)

abs (Math.abs method)

public static abs(x:Number) : Number

Computes and returns an absolute value for the number specified by the parameter x.

Parameters

x :Number - A number.

Returns

Number - A number.

Example

The following example shows how Math.abs() returns the absolute value of a number and does not affect the value of the x parameter (called num in this example):

var num:Number = -12; var numAbsolute:Number = Math.abs(num); trace(num); // output: -12 trace(numAbsolute); // output: 12

acos (Math.acos method)

public static acos(x:Number) : Number

Computes and returns the arc cosine of the number specified in the parameter x, in radians.

Parameters

x :Number - A number from -1.0 to 1.0.

Returns

Number - A number; the arc cosine of the parameter x.

Example

The following example displays the arc cosine for several values.

trace(Math.acos(-1)); // output: 3.14159265358979 trace(Math.acos(0)); // output: 1.5707963267949 trace(Math.acos(1)); // output: 0

See also

asin (Math.asin method), atan (Math.atan method), atan2 (Math.atan2 method), cos (Math.cos method), sin (Math.sin method), tan (Math.tan method)

asin (Math.asin method)

public static asin(x:Number) : Number

Computes and returns the arc sine for the number specified in the parameter x, in radians.

Parameters

x :Number - A number from -1.0 to 1.0.

Returns

Number - A number between negative pi divided by 2 and positive pi divided by 2.

Example

The following example displays the arc sine for several values.

trace(Math.asin(-1)); // output: -1.5707963267949 trace(Math.asin(0)); // output: 0 trace(Math.asin(1)); // output: 1.5707963267949

See also

acos (Math.acos method), atan (Math.atan method), atan2 (Math.atan2 method), cos (Math.cos method), sin (Math.sin method), tan (Math.tan method)

atan (Math.atan method)

public static atan(tangent:Number) : Number

Computes and returns the value, in radians, of the angle whose tangent is specified in the parameter tangent. The return value is between negative pi divided by 2 and positive pi divided by 2.

Parameters

tangent :Number - A number that represents the tangent of an angle.

Returns

Number - A number between negative pi divided by 2 and positive pi divided by 2.

Example

The following example displays the angle value for several tangents.

trace(Math.atan(-1)); // output: -0.785398163397448 trace(Math.atan(0)); // output: 0 trace(Math.atan(1)); // output: 0.785398163397448

See also

acos (Math.acos method), asin (Math.asin method), atan2 (Math.atan2 method), cos (Math.cos method), sin (Math.sin method), tan (Math.tan method)

atan2 (Math.atan2 method)

public static atan2(y:Number, x:Number) : Number

Computes and returns the angle of the point y/x in radians, when measured counterclockwise from a circle's x axis (where 0,0 represents the center of the circle). The return value is between positive pi and negative pi.

Parameters

y :Number - A number specifying the y coordinate of the point.

x :Number - A number specifying the x coordinate of the point.

Returns

Number - A number.

Example

The following example returns the angle, in radians, of the point specified by the coordinates (0, 10), such that x = 0 and y = 10. Note that the first parameter to atan2 is always the y coordinate.

TRace(Math.atan2(10, 0)); // output: 1.5707963267949

See also

acos (Math.acos method), asin (Math.asin method), atan (Math.atan method), cos (Math.cos method), sin (Math.sin method), tan (Math.tan method)

ceil (Math.ceil method)

public static ceil(x:Number) : Number

Returns the ceiling of the specified number or expression. The ceiling of a number is the closest integer that is greater than or equal to the number.

Parameters

x :Number - A number or expression.

Returns

Number - An integer that is both closest to, and greater than or equal to, parameter x.

Example

The following code returns a value of 13:

Math.ceil(12.5);

See also

floor (Math.floor method), round (Math.round method)

cos (Math.cos method)

public static cos(x:Number) : Number

Computes and returns the cosine of the specified angle in radians. To calculate a radian, see the description of the Math class entry.

Parameters

x :Number - A number that represents an angle measured in radians.

Returns

Number - A number from -1.0 to 1.0.

Example

The following example displays the cosine for several different angles.

trace (Math.cos(0)); // 0 degree angle. Output: 1 trace (Math.cos(Math.PI/2)); // 90 degree angle. Output: 6.12303176911189e-   17 trace (Math.cos(Math.PI)); // 180 degree angle. Output: -1 trace (Math.cos(Math.PI*2)); // 360 degree angle. Output: 1

Note: The cosine of a 90 degree angle is zero, but because of the inherent inaccuracy of decimal calculations using binary numbers, Flash Player will report a number extremely close to, but not exactly equal to, zero.

See also

acos (Math.acos method), asin (Math.asin method), atan (Math.atan method), atan2 (Math.atan2 method), sin (Math.sin method), tan (Math.tan method)

E (Math.E property)

public static E : Number

A mathematical constant for the base of natural logarithms, expressed as e. The approximate value of e is 2.71828182845905.

Example

This example shows how Math.E is used to compute continuously compounded interest for a simple case of 100 percent interest over a one-year period.

var principal:Number = 100; var simpleInterest:Number = 100; var continuouslyCompoundedInterest:Number = (100 * Math.E) - principal; trace ("Beginning principal: $" + principal); trace ("Simple interest after one year: $" + simpleInterest); trace ("Continuously compounded interest after one year: $" +   continuouslyCompoundedInterest); // Output: Beginning principal: $100 Simple interest after one year: $100 Continuously compounded interest after one year: $171.828182845905

exp (Math.exp method)

public static exp(x:Number) : Number

Returns the value of the base of the natural logarithm (e), to the power of the exponent specified in the parameter x. The constant Math.E can provide the value of e.

Parameters

x :Number - The exponent; a number or expression.

Returns

Number - A number.

Example

The following example displays the logarithm for two number values.

trace(Math.exp(1)); // output: 2.71828182845905 trace(Math.exp(2)); // output: 7.38905609893065

See also

E (Math.E property)

floor (Math.floor method)

public static floor(x:Number) : Number

Returns the floor of the number or expression specified in the parameter x. The floor is the closest integer that is less than or equal to the specified number or expression.

Parameters

x :Number - A number or expression.

Returns

Number - The integer that is both closest to, and less than or equal to, parameter x.

Example

The following code returns a value of 12:

Math.floor(12.5);

The following code returns a value of -7:

Math.floor(-6.5);

LN10 (Math.LN10 property)

public static LN10 : Number

A mathematical constant for the natural logarithm of 10, expressed as loge10, with an approximate value of 2.302585092994046.

Example

This example traces the value of Math.LN10.

trace(Math.LN10); // output: 2.30258509299405

LN2 (Math.LN2 property)

public static LN2 : Number

A mathematical constant for the natural logarithm of 2, expressed as loge2, with an approximate value of 0.6931471805599453.

log (Math.log method)

public static log(x:Number) : Number

Returns the natural logarithm of parameter x.

Parameters

x :Number - A number or expression with a value greater than 0.

Returns

Number - The natural logarithm of parameter x.

Example

The following example displays the logarithm for three numerical values.

trace(Math.log(0)); // output: -Infinity trace(Math.log(1)); // output: 0 trace(Math.log(2)); // output: 0.693147180559945 trace(Math.log(Math.E)); // output: 1

LOG10E (Math.LOG10E property)

public static LOG10E : Number

A mathematical constant for the base-10 logarithm of the constant e (Math.E), expressed as log10e, with an approximate value of 0.4342944819032518.

The Math.log() method computes the natural logarithm of a number. Multiply the result of Math.log() by Math.LOG10E obtain the base-10 logarithm.

Example

This example shows how to obtain the base-10 logarithm of a number:

trace(Math.log(1000) * Math.LOG10E); // Output: 3

LOG2E (Math.LOG2E property)

public static LOG2E : Number

A mathematical constant for the base-2 logarithm of the constant e (Math.E), expressed as log2e, with an approximate value of 1.442695040888963387.

The Math.log method computes the natural logarithm of a number. Multiply the result of Math.log() by Math.LOG2E obtain the base-2 logarithm.

Example

This example shows how to obtain the base-2 logarithm of a number:

trace(Math.log(16) * Math.LOG2E); // Output: 4

max (Math.max method)

public static max(x:Number, y:Number) : Number

Evaluates x and y and returns the larger value.

Parameters

x :Number - A number or expression.

y :Number - A number or expression.

Returns

Number - A number.

Example

The following example displays Thu Dec 30 00:00:00 GMT-0700 2004, which is the larger of the evaluated expressions.

var date1:Date = new Date(2004, 11, 25); var date2:Date = new Date(2004, 11, 30); var maxDate:Number = Math.max(date1.getTime(), date2.getTime()); trace(new Date(maxDate).toString());

See also

min (Math.min method), Date

min (Math.min method)

public static min(x:Number, y:Number) : Number

Evaluates x and y and returns the smaller value.

Parameters

x :Number - A number or expression.

y :Number - A number or expression.

Returns

Number - A number.

Example

The following example displays Sat Dec 25 00:00:00 GMT-0700 2004, which is the smaller of the evaluated expressions.

var date1:Date = new Date(2004, 11, 25); var date2:Date = new Date(2004, 11, 30); var minDate:Number = Math.min(date1.getTime(), date2.getTime()); trace(new Date(minDate).toString());

See also

max (Math.max method)

PI (Math.PI property)

public static PI : Number

A mathematical constant for the ratio of the circumference of a circle to its diameter, expressed as pi, with a value of 3.141592653589793.

Example

The following example draws a circle using the mathematical constant pi and the Drawing API.

drawCircle(this, 100, 100, 50); // function drawCircle(mc:MovieClip, x:Number, y:Number, r:Number):Void {   mc.lineStyle(2, 0xFF0000, 100);   mc.moveTo(x+r, y);   mc.curveTo(r+x, Math.tan(Math.PI/8)*r+y, Math.sin(Math.PI/4)*r+x,   Math.sin(Math.PI/4)*r+y);   mc.curveTo(Math.tan(Math.PI/8)*r+x, r+y, x, r+y);   mc.curveTo(-Math.tan(Math.PI/8)*r+x, r+y, -Math.sin(Math.PI/4)*r+x,   Math.sin(Math.PI/4)*r+y);   mc.curveTo(-r+x, Math.tan(Math.PI/8)*r+y, -r+x, y);   mc.curveTo(-r+x, -Math.tan(Math.PI/8)*r+y, -Math.sin(Math.PI/4)*r+x, -   Math.sin(Math.PI/4)*r+y);   mc.curveTo(-Math.tan(Math.PI/8)*r+x, -r+y, x, -r+y);   mc.curveTo(Math.tan(Math.PI/8)*r+x, -r+y, Math.sin(Math.PI/4)*r+x, -   Math.sin(Math.PI/4)*r+y);   mc.curveTo(r+x, -Math.tan(Math.PI/8)*r+y, r+x, y); }

pow (Math.pow method)

public static pow(x:Number, y:Number) : Number

Computes and returns x to the power of y.

Parameters

x :Number - A number to be raised to a power.

y :Number - A number specifying a power the parameter x is raised to.

Returns

Number - A number.

Example

The following example uses Math.pow and Math.sqrt to calculate the length of a line.

this.createEmptyMovieClip("canvas_mc", this.getNextHighestDepth()); var mouseListener:Object = new Object(); mouseListener.onMouseDown = function() {   this.origX = _xmouse;   this.origY = _ymouse; }; mouseListener.onMouseUp = function() {   this.newX = _xmouse;   this.newY = _ymouse;   var minY = Math.min(this.origY, this.newY);   var nextDepth:Number = canvas_mc.getNextHighestDepth();   var line_mc:MovieClip =   canvas_mc.createEmptyMovieClip("line"+nextDepth+"_mc", nextDepth);   line_mc.moveTo(this.origX, this.origY);   line_mc.lineStyle(2, 0x000000, 100);   line_mc.lineTo(this.newX, this.newY);   var hypLen:Number = Math.sqrt(Math.pow(line_mc._width,   2)+Math.pow(line_mc._height, 2));   line_mc.createTextField("length"+nextDepth+"_txt",   canvas_mc.getNextHighestDepth(), this.origX, this.origY-22, 100, 22);   line_mc['length'+nextDepth+'_txt'].text = Math.round(hypLen) +" pixels"; }; Mouse.addListener(mouseListener);

The MovieClip.getNextHighestDepth() method used in this example requires Flash Player 7 or later. If your SWF file includes a version 2 component, use the version 2 components DepthManager class instead of the MovieClip.getNextHighestDepth() method.

random (Math.random method)

public static random() : Number

Returns a pseudo-random number n, where 0 <= n < 1. The number returned is a pseudo-random number because it is not generated by a truly random natural phenomenon such as radioactive decay.

Returns

Number - A number.

Example

The following example outputs 100 random integers between 4 and 11 (inclusively):

function randRange(min:Number, max:Number):Number {   var randomNum:Number = Math.floor(Math.random() * (max - min + 1)) + min;   return randomNum; } for (var i = 0; i < 100; i++) {   var n:Number = randRange(4, 11)   trace(n); }

round (Math.round method)

public static round(x:Number) : Number

Rounds the value of the parameter x up or down to the nearest integer and returns the value. If parameter x is equidistant from its two nearest integers (that is, the number ends in .5), the value is rounded up to the next higher integer.

Parameters

x :Number - A number.

Returns

Number - A number; an integer.

Example

The following example returns a random number between two specified integers.

function randRange(min:Number, max:Number):Number {   var randomNum:Number = Math.round(Math.random() * (max-min+1) + (min-   .5));   return randomNum; } for (var i = 0; i<25; i++) {   trace(randRange(4, 11)); }

See also

ceil (Math.ceil method), floor (Math.floor method)

sin (Math.sin method)

public static sin(x:Number) : Number

Computes and returns the sine of the specified angle in radians. To calculate a radian, see the description of the Math class entry.

Parameters

x :Number - A number that represents an angle measured in radians.

Returns

Number - A number; the sine of the specified angle (between -1.0 and 1.0).

Example

The following example draws a circle using the mathematical constant pi, the sine of an angle, and the Drawing API.

drawCircle(this, 100, 100, 50); // function drawCircle(mc:MovieClip, x:Number, y:Number, r:Number):Void {   mc.lineStyle(2, 0xFF0000, 100);   mc.moveTo(x+r, y);   mc.curveTo(r+x, Math.tan(Math.PI/8)*r+y, Math.sin(Math.PI/4)*r+x,   Math.sin(Math.PI/4)*r+y);   mc.curveTo(Math.tan(Math.PI/8)*r+x, r+y, x, r+y);   mc.curveTo(-Math.tan(Math.PI/8)*r+x, r+y, -Math.sin(Math.PI/4)*r+x,   Math.sin(Math.PI/4)*r+y);   mc.curveTo(-r+x, Math.tan(Math.PI/8)*r+y, -r+x, y);   mc.curveTo(-r+x, -Math.tan(Math.PI/8)*r+y, -Math.sin(Math.PI/4)*r+x, -   Math.sin(Math.PI/4)*r+y);   mc.curveTo(-Math.tan(Math.PI/8)*r+x, -r+y, x, -r+y);   mc.curveTo(Math.tan(Math.PI/8)*r+x, -r+y, Math.sin(Math.PI/4)*r+x, -   Math.sin(Math.PI/4)*r+y);   mc.curveTo(r+x, -Math.tan(Math.PI/8)*r+y, r+x, y); }

See also

acos (Math.acos method), asin (Math.asin method), atan (Math.atan method), atan2 (Math.atan2 method), cos (Math.cos method), tan (Math.tan method)

sqrt (Math.sqrt method)

public static sqrt(x:Number) : Number

Computes and returns the square root of the specified number.

Parameters

x :Number - A number or expression greater than or equal to 0.

Returns

Number - A number if parameter x is greater than or equal to zero; NaN (not a number) otherwise.

Example

The following example uses Math.pow and Math.sqrt to calculate the length of a line.

this.createEmptyMovieClip("canvas_mc", this.getNextHighestDepth()); var mouseListener:Object = new Object(); mouseListener.onMouseDown = function() {   this.origX = _xmouse;   this.origY = _ymouse; }; mouseListener.onMouseUp = function() {   this.newX = _xmouse;   this.newY = _ymouse;   var minY = Math.min(this.origY, this.newY);   var nextDepth:Number = canvas_mc.getNextHighestDepth();   var line_mc:MovieClip = canvas_mc.createEmptyMovieClip("line"+nextDepth+"_mc", nextDepth);   line_mc.moveTo(this.origX, this.origY);   line_mc.lineStyle(2, 0x000000, 100);   line_mc.lineTo(this.newX, this.newY);   var hypLen:Number = Math.sqrt(Math.pow(line_mc._width,   2)+Math.pow(line_mc._height, 2));   line_mc.createTextField("length"+nextDepth+"_txt",   canvas_mc.getNextHighestDepth(), this.origX, this.origY-22, 100, 22);   line_mc['length'+nextDepth+'_txt'].text = Math.round(hypLen) +" pixels"; }; Mouse.addListener(mouseListener);

SQRT1_2 (Math.SQRT1_2 property)

public static SQRT1_2 : Number

A mathematical constant for the square root of one-half, with an approximate value of 0.7071067811865476.

Example

This example traces the value of Math.SQRT1_2.

trace(Math.SQRT1_2); // Output: 0.707106781186548

SQRT2 (Math.SQRT2 property)

public static SQRT2 : Number

A mathematical constant for the square root of 2, with an approximate value of 1.4142135623730951.

Example

This example traces the value of Math.SQRT2.

trace(Math.SQRT2); // Output: 1.4142135623731

tan (Math.tan method)

public static tan(x:Number) : Number

Computes and returns the tangent of the specified angle. To calculate a radian, use the information outlined in the introduction to the Math class.

Parameters

x :Number - A number that represents an angle measured in radians.

Returns

Number - A number; tangent of parameter x.

Example

The following example draws a circle using the mathematical constant pi, the tangent of an angle, and the Drawing API.

drawCircle(this, 100, 100, 50); // function drawCircle(mc:MovieClip, x:Number, y:Number, r:Number):Void {   mc.lineStyle(2, 0xFF0000, 100);   mc.moveTo(x+r, y);   mc.curveTo(r+x, Math.tan(Math.PI/8)*r+y, Math.sin(Math.PI/4)*r+x,   Math.sin(Math.PI/4)*r+y);   mc.curveTo(Math.tan(Math.PI/8)*r+x, r+y, x, r+y);   mc.curveTo(-Math.tan(Math.PI/8)*r+x, r+y, -Math.sin(Math.PI/4)*r+x,   Math.sin(Math.PI/4)*r+y);   mc.curveTo(-r+x, Math.tan(Math.PI/8)*r+y, -r+x, y);   mc.curveTo(-r+x, -Math.tan(Math.PI/8)*r+y, -Math.sin(Math.PI/4)*r+x, -   Math.sin(Math.PI/4)*r+y);   mc.curveTo(-Math.tan(Math.PI/8)*r+x, -r+y, x, -r+y);   mc.curveTo(Math.tan(Math.PI/8)*r+x, -r+y, Math.sin(Math.PI/4)*r+x, -   Math.sin(Math.PI/4)*r+y);   mc.curveTo(r+x, -Math.tan(Math.PI/8)*r+y, r+x, y); }

See also

acos (Math.acos method), asin (Math.asin method), atan (Math.atan method), atan2 (Math.atan2 method), cos (Math.cos method), sin (Math.sin method)