# Erich's Top 10 Scientific Formulas
# Chemical formula for water
> H[2] * O
# Einstein's conversion of mass to energy
> ein := E = m*c^2;

                                         2
                           ein := E = m c

> solve(ein, c);

                              1/2         1/2
                         (m E)       (m E)
                         --------, - --------
                            m           m

# Pythagorean theorem for right angle
> pyth := a^2 + b^2 = c^2;

                                  2    2    2
                         pyth := a  + b  = c

> subs({a = 3, b = 4, c = 5} , pyth);

                               25 = 25

> plots[display](plots[polygonplot]([[0,0], [0,3], [4,0]],
> color=brown),scaling = constrained);

# Solution of quadratic
> solve(a*x^2 + b*x + c = 0 , x);

                     2         1/2             2         1/2
              -b + (b  - 4 a c)         -b - (b  - 4 a c)
          1/2 --------------------, 1/2 --------------------
                       a                         a

# Four building blocks of DNA with their matchings
> (A-T)/(C-G)
# Law of gravitation
> grav := F = gamma * (m[1] * m[2])/r^2;

                                 gamma m[1] m[2]
                     grav := F = ---------------
                                        2
                                       r

# Fundamental theorem of calculus
> F := diff(f(x),x);

                                  d
                             F := -- f(x)
                                  dx

> int(F, x=a..b);
> 

                             f(b) - f(a)

# Ohm's law
> ohm := V = R*I;

                            ohm := V = I R

# Radioactive decay of uranium
> U[92]^238#  --> Th[90]^234 + He[2]^4
# Compound interest
> P[n] := P[0] * (1 + r/k) ^ (k*n);

                                           (k n)
                     P[n] := P[0] (1 + r/k)

> limit(P[n], k=infinity);

                            exp(r n) P[0]