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

<details> <summary> About stdlib... </summary> <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p> <p>The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.</p> <p>When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.</p> <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href="https://github.com/stdlib-js/stdlib">GitHub</a>, and please consider <a href="https://opencollective.com/stdlib">financially supporting stdlib</a>. We greatly appreciate your continued support!</p> </details> # isSquareTriangularNumber [![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]  > 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  <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> -->  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`   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>  <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].  ```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].  ```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].  ```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>  <section class="notes"> ## Notes - Return values are not reliable for numbers greater than `1125899906842624`. </section>  <section class="examples"> ## Examples   ```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>   <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>   <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 [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors]. </section>   <section class="links"> [npm-image]: http://img.shields.io/npm/v/@stdlib/assert-is-square-triangular-number.svg [npm-url]: https://npmjs.org/package/@stdlib/assert-is-square-triangular-number [test-image]: https://github.com/stdlib-js/assert-is-square-triangular-number/actions/workflows/test.yml/badge.svg?branch=v0.2.2 [test-url]: https://github.com/stdlib-js/assert-is-square-triangular-number/actions/workflows/test.yml?query=branch:v0.2.2 [coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/assert-is-square-triangular-number/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/assert-is-square-triangular-number?branch=main  [chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg [chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im [stdlib]: https://github.com/stdlib-js/stdlib [stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors [umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules [deno-url]: https://github.com/stdlib-js/assert-is-square-triangular-number/tree/deno [deno-readme]: https://github.com/stdlib-js/assert-is-square-triangular-number/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/assert-is-square-triangular-number/tree/umd [umd-readme]: https://github.com/stdlib-js/assert-is-square-triangular-number/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/assert-is-square-triangular-number/tree/esm [esm-readme]: https://github.com/stdlib-js/assert-is-square-triangular-number/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/assert-is-square-triangular-number/blob/main/branches.md [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  [@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  </section>