192 lines
4.7 KiB
Markdown
192 lines
4.7 KiB
Markdown
<!--
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@license Apache-2.0
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Copyright (c) 2020 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# isTriangularNumber
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> Test if a value is a [triangular number][triangular-number].
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<section class="intro">
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[Triangular numbers][triangular-number] can be computed using the following formula
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<!-- <equation class="equation" label="eq:triangular_number" align="center" raw="T_n = \frac{n(n+1)}{2}" alt="Triangular number formula."> -->
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<div class="equation" align="center" data-raw-text="T_n = \frac{n(n+1)}{2}" data-equation="eq:triangular_number">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0e41839343d292d7f99581a15ee8086b1e1dea68/lib/node_modules/@stdlib/assert/is-triangular-number/docs/img/equation_triangular_number.svg" alt="Triangular number formula.">
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<br>
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</div>
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<!-- </equation> -->
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for `n >= 0`.
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By analogy with the square root of `x`, one can define the positive triangular root of `x` such that `T_n = x`
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<!-- <equation class="equation" label="eq:triangular_root" align="center" raw="n = \frac{\sqrt{8x+1} - 1}{2}" alt="Triangular root formula."> -->
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<div class="equation" align="center" data-raw-text="n = \frac{\sqrt{8x+1} - 1}{2}" data-equation="eq:triangular_root">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0e41839343d292d7f99581a15ee8086b1e1dea68/lib/node_modules/@stdlib/assert/is-triangular-number/docs/img/equation_triangular_root.svg" alt="Triangular root formula.">
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<br>
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</div>
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<!-- </equation> -->
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Accordingly, an integer `x` is a [triangular number][triangular-number] **if and only** if `8x+1` is a [square number][@stdlib/assert/is-square-number].
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var isTriangularNumber = require( '@stdlib/assert/is-triangular-number' );
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```
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#### isTriangularNumber( value )
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Tests if a `value` is a [triangular number][triangular-number].
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<!-- eslint-disable no-new-wrappers -->
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```javascript
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var Number = require( '@stdlib/number/ctor' );
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var bool = isTriangularNumber( 36.0 );
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// returns true
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bool = isTriangularNumber( new Number( 36.0 ) );
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// returns true
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bool = isTriangularNumber( 3.14 );
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// returns false
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bool = isTriangularNumber( -5.0 );
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// returns false
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bool = isTriangularNumber( NaN );
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// returns false
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bool = isTriangularNumber( null );
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// returns false
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```
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#### isTriangularNumber.isPrimitive( value )
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Tests if a `value` is a primitive [triangular number][triangular-number].
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<!-- eslint-disable no-new-wrappers -->
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```javascript
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var Number = require( '@stdlib/number/ctor' );
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var bool = isTriangularNumber.isPrimitive( 36.0 );
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// returns true
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bool = isTriangularNumber.isPrimitive( new Number( 36.0 ) );
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// returns false
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```
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#### isTriangularNumber.isObject( value )
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Tests if a `value` is a `Number` object having a value which is a [triangular number][triangular-number].
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<!-- eslint-disable no-new-wrappers -->
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```javascript
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var Number = require( '@stdlib/number/ctor' );
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var bool = isTriangularNumber.isObject( 36.0 );
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// returns false
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bool = isTriangularNumber.isObject( new Number( 36.0 ) );
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// returns true
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Return values are not reliable for numbers greater than `1125899906842624`.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint-disable no-new-wrappers -->
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<!-- eslint no-undef: "error" -->
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```javascript
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var Number = require( '@stdlib/number/ctor' );
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var isTriangularNumber = require( '@stdlib/assert/is-triangular-number' );
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var bool = isTriangularNumber( 36.0 );
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// returns true
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bool = isTriangularNumber( new Number( 36.0 ) );
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// returns true
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bool = isTriangularNumber( 0.0 );
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// returns true
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bool = isTriangularNumber( 1.0 );
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// returns true
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bool = isTriangularNumber( 3.14 );
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// returns false
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bool = isTriangularNumber( -5.0 );
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// returns false
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bool = isTriangularNumber( NaN );
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// returns false
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bool = isTriangularNumber( '0.5' );
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// returns false
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bool = isTriangularNumber( null );
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// returns false
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[triangular-number]: https://en.wikipedia.org/wiki/Triangular_number
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[@stdlib/assert/is-square-number]: https://www.npmjs.com/package/@stdlib/assert/tree/main/is-square-number
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</section>
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<!-- /.links -->
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