https://aphinum.com/tags/calculus/ Recent content in Calculus on Philosophy Structured Notes Hugo en-US Sat, 03 Jan 2026 22:51:43 +0000 https://aphinum.com/posts/a-mathematical-exploration-the-method-of-exhaustion-and-its-limitations/ Fri, 02 Jan 2026 19:52:27 +0000 https://aphinum.com/posts/a-mathematical-exploration-the-method-of-exhaustion-and-its-limitations/ <p><strong>A Mathematical Exploration: The Method of Exhaustion and its Limitations</strong></p> <p>The <strong>method of exhaustion</strong>, a precursor to calculus, is a mathematical technique used to find the area and perimeter of shapes by inscribing and circumscribing polygons with an increasing number of sides. This method, developed in ancient Greece, has been instrumental in solving various mathematical problems, including squaring the circle.</p> <p><strong>Context</strong></p> <p>In the Hellenistic period (323-31 BCE), mathematicians such as Archimedes and Eudoxus made significant contributions to mathematics, laying the foundation for later developments in calculus. The <strong>method of exhaustion</strong> was a key tool in their work, allowing them to approximate areas and perimeters of shapes with great precision.</p> https://aphinum.com/posts/a-precise-calculation-the-method-of-exhaustion-and-its-significance/ Fri, 02 Jan 2026 19:47:18 +0000 https://aphinum.com/posts/a-precise-calculation-the-method-of-exhaustion-and-its-significance/ <p><strong>A Precise Calculation: The Method of Exhaustion and Its Significance</strong></p> <p>The <strong>Method of Exhaustion</strong>, also known as the <strong>Method of Indivisibles</strong>, was a mathematical technique developed by Eudoxus and later refined by Archimedes. This method, an anticipation of integral calculus, allowed for precise calculations of areas and volumes of complex shapes.</p> <p><strong>Context</strong> In the 3rd century BCE, Greek mathematicians were grappling with the problem of finding exact measurements for curved figures. The <strong>Method of Exhaustion</strong> was a response to this challenge, drawing on earlier ideas from geometry and arithmetic. This method would later influence the development of calculus in the 17th century CE.</p> https://aphinum.com/posts/the-geometrical-theory-of-proportion-a-new-foundation-for-mathematics/ Fri, 02 Jan 2026 19:42:28 +0000 https://aphinum.com/posts/the-geometrical-theory-of-proportion-a-new-foundation-for-mathematics/ <p><strong>The Geometrical Theory of Proportion: A New Foundation for Mathematics</strong></p> <p><strong>Overview</strong> The discovery of irrationals by ancient Greek mathematicians led to significant advancements in mathematical thought, particularly in the development of a geometrical theory of proportion. This new approach, attributed to Eudoxus (ca. 408 - ca. 355 B.C.), revolutionized the field by introducing a more comprehensive and versatile framework for understanding ratios and proportions. The geometrical theory of proportion, as described in Euclid&rsquo;s works, has had a lasting impact on mathematics, laying the groundwork for later developments in calculus and analysis.</p>