Tag Archives: Descartes

Geometry and Algebra

April 30, 2026 – 5:45 pm

Photo: Appearing the same size are the Eiffel Tower in the distance and a model in the foreground, standing on the railing of a window that overlooks other buildings

From a flat on the rue Saint-Jacques, Paris
Thursday, June 4, 2015

What René Descartes says here does not make a lot of sense to me:

it is far better never to contemplate investigating the truth about any matter than to do so without a method. For it is quite certain that such haphazard studies and obscure reflections blur the natural light and blind our intelligence.

Continue reading →

By David Pierce | Posted in Euclid, Mathematics | Also tagged , | Comments (0)

A Five Line Locus

November 13, 2024 – 6:46 pm

In high school, if not sooner, one learns theorems established more than two millenia ago by Euclid and Archimedes. I am thinking of the theorems expressed today by the equations

𝐶 = 2π𝑟,
𝐴 = π𝑟²

for the circumference and area of a circle whose radius is 𝑟, and

𝐴 = 4π𝑟²,
𝑉 = (4/3)π𝑟³

for the surface area and volume of a sphere whose radius is 𝑟. Continue reading →

By David Pierce | Posted in Mathematics | Also tagged , , | Comments (3)