npm package: @stdlib/assert-is-square-triangular-number
Description: Test if a value is a square triangular number.
Author: The Stdlib Authors
Latest version: 0.2.3

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# isSquareTriangularNumber

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> Test if a value is a [square triangular number][square-triangular-number].

<section class="intro">

A **square triangular number** is an integer value which is both a [square number][@stdlib/assert/is-square-number] and a [triangular number][@stdlib/assert/is-triangular-number].

[Triangular numbers][@stdlib/assert/is-triangular-number] can be computed using the following formula

<!-- <equation class="equation" label="eq:triangular_number" align="center" raw="T_n = \frac{n(n+1)}{2}" alt="Triangular number formula."> -->

<div class="equation" align="center" data-raw-text="T_n = \frac{n(n+1)}{2}" data-equation="eq:triangular_number">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b295a09a80f4fd0cc84682dcda0fe3e354394c0c/lib/node_modules/@stdlib/assert/is-square-triangular-number/docs/img/equation_triangular_number.svg" alt="Triangular number formula.">
    <br>
</div> -->

<!-- </equation> -->

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`

<!-- <equation class="equation" label="eq:triangular_root" align="center" raw="n = \frac{\sqrt{8x+1} - 1}{2}" alt="Triangular root formula."> -->

<!-- <div class="equation" align="center" data-raw-text="n = \frac{\sqrt{8x+1} - 1}{2}" data-equation="eq:triangular_root">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b295a09a80f4fd0cc84682dcda0fe3e354394c0c/lib/node_modules/@stdlib/assert/is-square-triangular-number/docs/img/equation_triangular_root.svg" alt="Triangular root formula.">
    <br>
</div>

<!-- </equation> -->

Accordingly, an integer `x` is a [triangular number][@stdlib/assert/is-triangular-number] **if and only** if `8x+1` is a [square number][@stdlib/assert/is-square-number].

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### isSquareTriangularNumber( value )

Tests if a `value` is a [square triangular number][square-triangular-number].

<!-- eslint-disable no-new-wrappers -->

```javascript
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][square-triangular-number].

<!-- eslint-disable no-new-wrappers -->

```javascript
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][square-triangular-number].

<!-- eslint-disable no-new-wrappers -->

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

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

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

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Return values are not reliable for numbers greater than `1125899906842624`.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint-disable no-new-wrappers -->

<!-- eslint no-undef: "error" -->

```javascript
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
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/assert-is-integer`][@stdlib/assert/is-integer]</span><span class="delimiter">: </span><span class="description">test if a value is a number having an integer value.</span>
-   <span class="package-name">[`@stdlib/assert-is-number`][@stdlib/assert/is-number]</span><span class="delimiter">: </span><span class="description">test if a value is a number.</span>
-   <span class="package-name">[`@stdlib/assert-is-square-number`][@stdlib/assert/is-square-number]</span><span class="delimiter">: </span><span class="description">test if a value is a square number.</span>
-   <span class="package-name">[`@stdlib/assert-is-triangular-number`][@stdlib/assert/is-triangular-number]</span><span class="delimiter">: </span><span class="description">test if a value is a triangular number.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/assert-is-square-triangular-number/main/LICENSE

[square-triangular-number]: https://en.wikipedia.org/wiki/Square_triangular_number

<!-- <related-links> -->

[@stdlib/assert/is-integer]: https://www.npmjs.com/package/@stdlib/assert-is-integer

[@stdlib/assert/is-number]: https://www.npmjs.com/package/@stdlib/assert-is-number

[@stdlib/assert/is-square-number]: https://www.npmjs.com/package/@stdlib/assert-is-square-number

[@stdlib/assert/is-triangular-number]: https://www.npmjs.com/package/@stdlib/assert-is-triangular-number

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</section>

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