global variables - an alternate approach

For starters the emphasis is on 'global' variables common to muliple
translation units

Coding standard states that global variables should be defined as
static variables' within a class at public scope. One instance of
this class should exist and the recommendation is to use the singleton
design patten. IOW:

//common_data_b.h
# ifndef COMMON_DATA_B_H
# define COMMON_DATA_B_H

#include <iostream>
class common_data_b {
public :
   static int const a = 5 ;
   static const double pi ;
   static
   common_data_b& intance() {
     static common_data_b cd_b;
     return cd_b;
   }
};
#endif

//common_data_b.cpp
const double common_data_b::pi = 3.141;

OK!! But what's the difference if I did:

//common_data_a.h
# ifndef COMMON_DATA_A_H
# define COMMON_DATA_A_H

#include <iostream>
class common_data_a {
public :
   static int const a = 5;
   static const double pi ;
};
///common_data_a.cpp
const double common_data_a::pi = 3.141 ;

#endif

//later foo.h
class foo {
public :
   void do_work_a() { std::cout << common_data_a::pi << std::endl; }
   void do_work_b() { std::cout << common_data_b::intance().pi <<
std::endl; }
};
//bar.h etc

int main()
{
    foo f;
    f.do_work_a() ;
    f.do_work_b() ;
    std::cin.get();
}

I'm not seeing the value added surrounding the singleton design
pattern. In my view the common_data_a (alternate) approach suffices.
Am I wrong?

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