Quadrature (mathematics)

In mathematics, quadrature is an old word for finding areas. It is also used for finding integrals. The word comes from the Latin quadratus, meaning "square." This is because, for Ancient Greek mathematicians, finding an area meant making a square of the same size. This is why we sometimes use the word squaring today.

One well-known example is the quadrature of the circle, or squaring the circle. This was a famous problem that could not be solved with the tools the Ancient Greeks had. Later, in the 1600s, integral calculus gave a general way to find areas. After that, the word quadrature started meaning the finding of any integral.

Even today, quadrature is used in numerical analysis. It helps tell apart finding integrals from solving differential equations or differential systems. This way, scientists and mathematicians can solve hard problems by breaking them into smaller parts that can be measured as areas.

History

Greek mathematicians tried to find the area of shapes by drawing a square the same size. This is why they called it quadrature. They could find the area of some curved shapes like the lune of Hippocrates and the parabola, but not all shapes, like a circle, using just a compass and straightedge.

Later, mathematicians used new ways to find areas. For example, Archimedes found that the area of a sphere’s surface is four times the area of its biggest circle. These ideas helped create integral calculus, which is a way to calculate areas today.