Keywords: Archimedes Parabola.svg validSVG en Archimedean decomposition of a parabolic segment into infinitely many triangles Each green triangle is 1/8 of the area of the blue triangle each yellow triangle is 1/8 the area of a green triangle and so forth Assuming the blue triangle has area 1 the total area under the parabola is <math>1 \ +\ \frac 2 8 \ +\ \frac 4 64 \ +\ \cdots</math> <math> 1 \ +\ \frac 1 4 \ +\ \frac 1 16 \ +\ \cdots</math> The sum of this en geometric series is 4/3 en File Archimedes_Parabola png en User Jim belk uploader date /2009-02-03 svg version of the image from en Quadrature of the Parabola |