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Reference.org
Height function
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<p>A height function is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> that quantifies the complexity of mathematical objects. In <a href="/facts/Diophantine_geometry/H2x4wzUE">Diophantine geometry</a>, height functions quantify the size of solutions to <a href="/facts/Diophantine_equations/mYaHp7oX">Diophantine equations</a> and are typically functions from a set of points on <a href="/facts/Algebraic_variety/Vk7f97vn">algebraic varieties</a> (or a set of algebraic varieties) to the <a href="/facts/Real_numbers/R02gw5Pb">real numbers</a>. </p><p>For instance, the <i>classical</i> or <i>naive height</i> over the <a href="/facts/Rational_number/VJQmyY05">rational numbers</a> is typically defined to be the maximum of the numerators and denominators of the coordinates (e.g. 7 for the coordinates (3/7, 1/2)), but in a <a href="/facts/Logarithmic_scale/CvIGK5TQ">logarithmic scale</a>. </p>