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Tom Swift

The Integral

There are islands in the Cartesian Sea.

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Tom Swift
Sep 22, 2025
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This article is part of the mathematics sequence of the Tom Swift Academy.

Unlike the Tangent Problem and the study of rates of change, the calculation of area was an exercise well known to the ancients. Much of Greek mathematics was devoted to laws regarding angles, planes, triangles and quadrilaterals; the bread and butter of the geometry lessons of your schooldays. Yet in the Hellenistic era, Archimedes dared to approximate the area of a circle, by succesively calculating the areas of polygons with increasing numbers of sides in his volume The Measurement of a Circle. He ventured further with similar methods to calculate the area of the parabola. In doing so, he filled curved shapes with an unholy pile of squares and triangles.

As with other portions of the Calculus, integration would not be fully formed until the Faustian era; the Age of Discovery.

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