<p><strong>Noun</strong></p><ul><li>a group or set of four persons or things</li><li>four gathered sheets folded in two for binding together (Bookbinding)</li><li>an expression of the form <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mi>i</mi><mo>+</mo><mi>c</mi><mi>j</mi><mo>+</mo><mi>d</mi><mi>k</mi></mrow><annotation encoding="application/x-tex">a + bi + cj + dk</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6667em; vertical-align: -0.0833em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.2222em;"></span></span><span class="base"><span class="strut" style="height: 0.7778em; vertical-align: -0.0833em;"></span><span class="mord mathnormal">bi</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.2222em;"></span></span><span class="base"><span class="strut" style="height: 0.854em; vertical-align: -0.1944em;"></span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right: 0.05724em;">j</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.2222em;"></span></span><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right: 0.03148em;">k</span></span></span></span> in Mathematics, where <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo separator="true">,</mo><mi>b</mi><mo separator="true">,</mo><mi>c</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">a, b, c,</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.8889em; vertical-align: -0.1944em;"></span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right: 0.1667em;"></span><span class="mord mathnormal">b</span><span class="mpunct">,</span><span class="mspace" style="margin-right: 0.1667em;"></span><span class="mord mathnormal">c</span><span class="mpunct">,</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span> are real numbers</li><li>a quantity or operator expressed as the sum of a real number and three complex numbers, equivalent to the quotient of two vectors</li><li>the field of quaternions is not commutative under multiplication</li></ul>