isSquareTriangularNumber

Test if a value is a square triangular number.

A square triangular number is an integer value which is both a square number and a triangular number.

Triangular numbers can be computed using the following formula

$$T_n = \frac{n(n+1)}{2}$$

for n >= 0.

By analogy with the square root of x, one can define the positive triangular root of x such that T_n = x

$$n = \frac{\sqrt{8x+1} - 1}{2}$$

Accordingly, an integer x is a triangular number if and only if 8x+1 is a square number.

Usage

var isSquareTriangularNumber = require( '@stdlib/assert/is-square-triangular-number' );

isSquareTriangularNumber( value )

Tests if a value is a square triangular number.

var Number = require( '@stdlib/number/ctor' );

var bool = isSquareTriangularNumber( 36.0 );
// returns true

bool = isSquareTriangularNumber( new Number( 36.0 ) );
// returns true

bool = isSquareTriangularNumber( 3.14 );
// returns false

bool = isSquareTriangularNumber( -5.0 );
// returns false

bool = isSquareTriangularNumber( NaN );
// returns false

bool = isSquareTriangularNumber( null );
// returns false

isSquareTriangularNumber.isPrimitive( value )

Tests if a value is a primitive square triangular number.

var Number = require( '@stdlib/number/ctor' );

var bool = isSquareTriangularNumber.isPrimitive( 36.0 );
// returns true

bool = isSquareTriangularNumber.isPrimitive( new Number( 36.0 ) );
// returns false

isSquareTriangularNumber.isObject( value )

Tests if a value is a Number object having a value which is a square triangular number.

var Number = require( '@stdlib/number/ctor' );

var bool = isSquareTriangularNumber.isObject( 36.0 );
// returns false

bool = isSquareTriangularNumber.isObject( new Number( 36.0 ) );
// returns true

Notes

• Return values are not reliable for numbers greater than 1125899906842624.

Examples

var Number = require( '@stdlib/number/ctor' );
var isSquareTriangularNumber = require( '@stdlib/assert/is-square-triangular-number' );

var bool = isSquareTriangularNumber( 36.0 );
// returns true

bool = isSquareTriangularNumber( new Number( 36.0 ) );
// returns true

bool = isSquareTriangularNumber( 0.0 );
// returns true

bool = isSquareTriangularNumber( 1.0 );
// returns true

bool = isSquareTriangularNumber( 3.14 );
// returns false

bool = isSquareTriangularNumber( -5.0 );
// returns false

bool = isSquareTriangularNumber( NaN );
// returns false

bool = isSquareTriangularNumber( '0.5' );
// returns false

bool = isSquareTriangularNumber( null );
// returns false

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See Also

• @stdlib/assert/is-integer: test if a value is a number having an integer value.
• @stdlib/assert/is-number: test if a value is a number.
• @stdlib/assert/is-square-number: test if a value is a square number.
• @stdlib/assert/is-triangular-number: test if a value is a triangular number.