MATHEMAGIC 22: FIGURATE NUMBERS AND PI
Figurate numbers (on the left)
and the general formula
for the n-th p-gonal number G(n,p).
THEOREM
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented
as the sum of four square numbers.
The MAGIC Euler formula which gives a relation between the squares of the integer numbers and pi.
My (π,π)-property
Consider the area bounded by the curve with equation
y = 8 sin(x/2) and the x-axis in the interval [0, 2π].
Then the center of gravity of this area is the point Z(π,π).
You may find the proof (in Dutch) on
http://blogimages.bloggen.be/gnomon/attach/270651.pdf.
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