His argument shows that there are infinitely many solutions to Euler’s equation.
In conclusion, although there has been some success in the last fifty years in
limiting the number of rational points on varieties, there are still almost no methods
for finding such points. It is to be hoped that a proof of the Birch and Swinnerton
Dyer conjecture will give some insight concerning this general problem.
References
If a compact threedimensional manifold M3 has the property that every
simple closed curve within the manifold can be deformed continuously to a point,
does it follow that M3 is homeomorphic to the sphere S3?
coset space SO(3)/I60 where SO(3)
is the group of all rotations of Euclidean 3space and where I60 is the subgroup consisting of the 60
rotations that carry a standard icosahedron to itself. The fundamental group 1(M3), consisting
of all homotopy classes of loops from a point to itself within M3, is a perfect group of order 120.
Brightning Principle
Actually,natural light can be divided into single corresponding light wave of red,orange,yellow,green,blue,black and violet whthin 380760nm.But it is not necessary to have so many kinds of lingt with different waves to synthetize white light.On TV screen,only three colours of loght are needed to synthetize white light ln fact,only two kinds of proper light waves which are intercomplementary colors can also synthetize white light suchas blue and yellow,red and blue grenn.When illuminated,materials(fabric,plastics,etc)can absorb blue light,reflect yellow light,and therefore we see yellow not white light.Fluorescent brightener can absorb ultraviolet light and send out white and blue light ,and so blue light and original yellow light are complementary colors consequently,we see white light.This is the brightening pringciple of fluorescent brightenenr.
