Keywords: Archimedes Parabola.png 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 geometric series is 4/3 Paràbola d'Arquimedes http //en wikipedia org/wiki/Image Archimedes_Parabola png 00 08 10 August 2007 Jim belk en wikipedia Jim belk Archimedes_Parabola svg original upload log page en wikipedia Archimedes_Parabola png 2007-08-10 00 08 Jim belk 500×437× 19218 bytes <nowiki>Archimedian 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 </nowiki> Geometric series Quadrature of the Parabola |