with at least one of                    A, B, C, D, E
not equal to zero.
This equation has 15 constants.                                 However,
it can                    be multiplied by                  
                    any non-zero constant
without changing              the curve;                                  thus by the choice
of an appropriate                  constant of multiplication,
any one           of the coefficients                                              can be set
          to 1,
                     leaving                                                only      ­             14 constants.                                      Therefore,       the space
of quartic curves can be
                          identified with the real
projective                         space
RP14 It also follows,                             from Cramer's   
      theorem
on algebraic curves,                                that there is exactly one
quartic curve                                 that passes                        through a set of
                 14
distinct points                                 in general
                                              position, since a quartic
has                               14 degrees of freedom.
One may                              also consider
            quartic curves over
other fields                        (or even rings),           for instance
                     the complex                numbers. In this way,                    one
gets
m                   Riemann                                         surfaces,
       which are
                                                     one-dimensional
objects over C,                             but are two-dimensional over R.
An example           is the Klein                        quartic.
                               Additionally,
one can loo                k at curves in the                 projective                
          plane,
                given by                                homogeneous polynomials.

Heartless yet merciful tis’,
A cracked one in my torn pocket to please;
Into number of pieces it keeps multiplying me,
Even in darkness with latent eyes it could still see.


Initially unscarred and unscathed my wrinkled reflection with an MRP,
Dusty ages have gathered now to wipe using tissue papers of poetry;
I’ve a rendezvous with myself in wee moments of us without any battery for free,
In rear view,
Oft window panes,
Rarely wash basin of restaurants and seldom empty glasses sketch me incomplete.


We have smiled together to burst into mockery,
Even like naïve cries for latter moist kohl teardrops murky;
A chaotic satire agonizes as it’s infidel loyalty betrays not the reality,
Although a cracked one yet it scans faces without any partiality.

Do you know that Riemann Hypothesis
still remains unsolved?
We are moving like a pendulum
between our families, jobs
and deep wishes to create.
Sharing hours and fleeting days
of our lives.

Curiosity about the next move, wit,
and silence when support is not enough.
Everyday rituals,
healer and side effects…
How good it is to say, “I’m still here!”
Keeping a morning cup of bitter coffee
with a strong will thanks to a lucky twist of fate.