Math

Constants

Icon	Name	Syntax	Inputs	Outputs
	Pi	Math.PI	none	double

Pi - is a mathematical constant which represents the ratio of circle's circumference to its diameter. The value is commonly used in trigonmetric functions and is one of the more prevalent constants used in parametric modeling. A rounded value for Pi is 3.14159.

Icon	Name	Syntax	Inputs	Outputs
	e	Math.E	none	double

e - The number e is a mathematical constant which is based on the natural logarithm. Like pi, e is an irrational number which is commonly used in mathematics. The number is fundamental to growth prediction, and shows itself often in the fields of biology and economics. A rounded value for e is 2.71828.

Icon	Name	Syntax	Inputs	Outputs
	phi	Math.GoldenRatio	none	double

φ: The Golden Ratio - Another irrational constant, the golden ratio defines that two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. This ratio appears often in geometry and biological systems, and is considered for a wide-range of applications ranging from the practical to the aesthetic. A rounded value for φ is 1.61804.

Arithmetic Operators

Operators are a set of components that use algebraic functions with two numeric input values, which result in one output value (addition, subtraction, multiplication, division, etc.).

You use the Math Operators to perform arithmetical actions on a set of numbers. These can be found under Operators>Actions.

Addition, Subtraction, Multiplication, Division - These four operators are commonplace. Let's look at a few other operators which dive deeper:

Name	Syntax	Inputs	Outputs
Add	+	var[]...[], var[]...[]	var[]...[]
Subtract	-	var[]...[], var[]...[]	var[]...[]
Multiply	*	var[]...[], var[]...[]	var[]...[]
Divide	/	var[]...[], var[]...[]	var[]...[]

Power - Exponentiation, or the power operator, involves two numbers: the base number (x) and the power (y). The power of x to the y is defined as x repeatedly multiplied by itself for a total of y times.

Icon	Name	Syntax	Inputs	Outputs
	Power	Math.Pow	number, power	var[]...[]

2 ^ 3 = 2 x 2 x 2 = 8

Square Root - The square root of x referes to the number z such that z^2=x. This operator is commonplace in a wide-range of geometric applications, most notably the Pythagorean Theorem.

Icon	Name	Syntax	Inputs	Outputs
	Square Root	Math.Sqrt	number	double

Sqrt(4) = 2

Absolute Value -The absolute value of a number refers to its non-negative value. This operator comes in handy when parametrically, especially when a calculation concerns itself with scalar values rather than vectors (ie speed vs. velocity).

Icon	Name	Syntax	Inputs	Outputs
	Absolute Value	Math.Abs	number	double

|-10| = 10 and |10| = 10

Modulo - The modulo operation refers to the remainder after a division.

Icon	Name	Syntax	Inputs	Outputs
	Modulo	%	var[]...[],var[]...[]	var[]...[]

11 % 6 = 5 (6 goes into 11 once, and has a remainder, or modulo, of 5)

While this may not seem like much, the modulo is a great tool for creating patterns. The image below demonstrates how quickly one can parse out even and odd numbers with pure operations:

Ceiling, Floor, Round - The ceiling, floor, and round operation refer to methods for reducing a decimal (or float) number to an integer.

Name	Syntax	Inputs	Outputs
Ceiling	Math.Ceiling	number	int
Floor	Math.Floor	number	int
Round	Math.Round	number	int

11/6 = 1.833

The floor represents the lower bound of the integer within the decimal range.

Floor(11/6) = Floor(1.833) = 1

The ceiling represents the upper bound.

Ceil(11/6) = Ceil(1.833) = 2

The round operations will 'round' to the closest number in the range.

Round(11/6) = Round(1.833) = 2

Functions

Remap Range -This is one of the most important functions in parametric modeling. The component maps a set of values in one domain into another domain, while maintaining the same distribution ratio.

Icon	Name	Syntax	Inputs	Outputs
	Remap Range	Math.RemapRange	numbers, newMin, newMax	var[]...[]

Average - Determines the average (mean) of a list of numbers.

Icon	Name	Syntax	Inputs	Outputs
	Average	Math.Average	numbers	double

Sum - Determines the sum of a list of numbers.

Icon	Name	Syntax	Inputs	Outputs
	Sum	Math.Sum	values	double

Random/RandomList -Create a random number or a random list of numbers.

Icon	Name	Syntax	Inputs	Outputs
	Random	Math.Random	seed	double
	Random List	Math.RandomList	amount	var[]...[]

Trigonometric Functions

In summary, trigonometric functions are functions of an angle, relating the angles of a triangle to the lengths of its sides. The input in Dynamo is degrees.

Name	Syntax	Ratio
sine	Math.Sin	opposite/hypotenuse
cosine	Math.Cos	adjacent/hypotenuse
tangent	Math.Tan	opposite/adjacent

Inverse Trigonometric Functions

Inverse trigonometric functions use a ratio as an input, with the resultant output being an angle. The output in Dynamo is degrees. These are less commonly used in modeling.

Icon	Name	Syntax	Formula
	arcsine	Math.Asin
	arccosine	Math.Acos
	arctangent	Math.Atan

Hyperbolic Functions

Even less common in trigonometry are the hyperbolic functions, which are analogs to the trigonometric functions. These functions have applications in physics, fluid dynamics, and complex analysis, but are outside of the scope of this primer.

Icon	Name	Syntax	Formula
	sinh	Math.Sinh
	cosh	Math.Cosh
	tanh	Math.Tanh

Math.RadiansToDegrees/Math.DegreesToRadians -Convert Radians to Degrees. This is a handy node for quickly converting angle units. Dynamo works in degrees by default for inputs and outputs.

Icon	Name	Syntax	Inputs	Outputs
	Radians To Degrees	Math.RadiansToDegrees	radians	degrees
	Degrees to Radians	Math.DegreesToRadians	degrees	radians

Formula

Icon	Name	Syntax	Inputs	Outputs
	Formula	Formula	Text box	objects, numbers,strings,lists...

Formula - All of the functions described above, and many more, can be defined explicitly in the formula node. This node is compatible with a range of expressions, as well as conditional statements and other equations.

For a similar node which expands this ability even further, check out the code block. The code block will be discussed in detail in a future section.

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