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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.

Installation

npm install @stdlib/assert-is-square-triangular-number

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.