Mathematical Constants HelixQL provides built-in mathematical constants PI and E for use in calculations. These constants are provided as functions that return their respective values with high precision.
Available Constants PI - Pi Constant PI() // Returns π ≈ 3.14159265358979323846
Returns the mathematical constant π (pi), the ratio of a circle’s circumference to its diameter.
E - Euler’s Number E() // Returns e ≈ 2.71828182845904523536
Returns the mathematical constant e (Euler’s number), the base of natural logarithms.
When using the SDKs or curling the endpoint, the query name must match what is defined in the queries.hx file exactly.
Example 1: Circle calculations with PI Calculate circle properties using the PI constant:
QUERY CalculateCircleProperties() => circles <- N::Circle ::{ radius, circumference: MUL(MUL(2.0, PI()), _::{radius}), area: MUL(PI(), POW(_::{radius}, 2.0)) } RETURN circles QUERY CreateCircle(radius: F64) => circle <- AddN<Circle>({ radius: radius }) RETURN circle
Here’s how to run the query using the SDKs or curl
Python
Rust
Go
TypeScript
Curl
from helix.client import Client client = Client( local = True , port = 6969 ) # Create circles with different radii radii = [ 1.0 , 5.0 , 10.0 , 15.0 , 20.0 ] for radius in radii: client.query( "CreateCircle" , { "radius" : radius}) result = client.query( "CalculateCircleProperties" , {}) print ( "Circle properties:" , result)
Example 2: Exponential growth with E Model exponential growth and decay using Euler’s number:
QUERY CalculateExponentialGrowth(time: F64, rate: F64) => populations <- N::Population ::{ initial_size, time_elapsed: time, final_size: MUL(_::{initial_size}, POW(E(), MUL(rate, time))) } RETURN populations QUERY CreatePopulation(initial_size: F64) => population <- AddN<Population>({ initial_size: initial_size }) RETURN population
Here’s how to run the query using the SDKs or curl
Python
Rust
Go
TypeScript
Curl
from helix.client import Client client = Client( local = True , port = 6969 ) # Create populations with different initial sizes initial_sizes = [ 100.0 , 500.0 , 1000.0 , 5000.0 ] for size in initial_sizes: client.query( "CreatePopulation" , { "initial_size" : size}) # Calculate growth after 10 time units with 5% growth rate result = client.query( "CalculateExponentialGrowth" , { "time" : 10.0 , "rate" : 0.05 }) print ( "Population growth:" , result)
Common Use Cases Degree-Radian Conversion Use PI for converting between degrees and radians:
// Degrees to radians radians = MUL(degrees, DIV(PI(), 180.0)) // Radians to degrees degrees = MUL(radians, DIV(180.0, PI()))
Circular Motion Calculate properties of circular motion:
QUERY CalculateAngularVelocity() => objects <- N::RotatingObject ::{ rpm, angular_velocity: MUL(MUL(2.0, PI()), DIV(_::{rpm}, 60.0)) } RETURN objects
Compound Interest Use E for continuous compound interest calculations:
QUERY CalculateCompoundInterest(principal: F64, rate: F64, time: F64) => amount <- MUL(principal, POW(E(), MUL(rate, time))) RETURN amount
Natural Decay Model radioactive decay or other natural decay processes:
QUERY CalculateDecay() => samples <- N::Sample ::{ initial_amount, half_life, time_elapsed, remaining: MUL( _::{initial_amount}, POW(E(), MUL(DIV(LN(0.5), _::{half_life}), _::{time_elapsed})) ) } RETURN samples
Constants are particularly useful when combined with trigonometric functions (SIN, COS, TAN) and exponential functions (EXP, LN).
Precision Both PI() and E() return high-precision values suitable for scientific and engineering calculations:
PI() returns π to approximately 20 decimal places
E() returns e to approximately 20 decimal places
The constants are implemented as functions rather than literals to maintain consistency with HelixQL’s function-based syntax.
Constants are often used in complex mathematical formulas:
// Gaussian distribution QUERY CalculateGaussian(x: F64, mean: F64, std_dev: F64) => coefficient <- DIV(1.0, MUL(std_dev, SQRT(MUL(2.0, PI())))) exponent <- DIV(POW(SUB(x, mean), 2.0), MUL(2.0, POW(std_dev, 2.0))) probability <- MUL(coefficient, POW(E(), MUL(-1.0, exponent))) RETURN probability // Euler's formula: e^(iθ) = cos(θ) + i*sin(θ) QUERY EulerFormula(theta: F64) => result <- N::ComplexNumber ::{ real: COS(theta), imaginary: SIN(theta), magnitude: POW(E(), 0.0) // Always 1 for pure imaginary exponent } RETURN result
Trigonometric Functions SIN, COS, TAN, ASIN, ACOS, ATAN, ATAN2
Unary Math Functions SQRT, ABS, LN, LOG10, EXP, CEIL, FLOOR, ROUND
Arithmetic Functions ADD, SUB, MUL, DIV, POW, MOD
Math Overview Overview of all math functions
