 
Summary: 22 Centuries Measuring Area
Miguel Abreu
IST  Technical University of Lisbon and Portuguese Mathematical Society
Schola Europaea, Brussels, February 2012
Introduction and Goals
Based on a Klein Vignette written in collaboration with Ana
Cannas da Silva for the Mathematics Klein Project in
Portuguese, a brazilian initiative with portuguese cooperation,
within the Klein Project of the International Mathematical Union
(IMU) and International Commission on Mathematical
Instruction (ICMI).
Give a symplectic explanation for the formula
Volume B2n
(R) =
nR2n
n!
= (2)n
·
(R2/2)n
n!
