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Let X_1,X_2 subset P^2 be cubic plane curves meeting in nine points p_1, ..., p_9. If X subset P^2 is any cubic containing p_1, ..., p_8, then X contains p_9 as well. It is ...

The substitution of x=w-p/(3w) (1) into the standard form cubic equation x^3+px=q. (2) The result reduces the cubic to the equation w^3-(p^3)/(27w^3)-q=0, (3) which is easily ...

Let O be an order of an imaginary quadratic field. The class equation of O is the equation H_O=0, where H_O is the extension field minimal polynomial of j(O) over Q, with ...

A figurate number which is equal to the cubic number n^3. The first few are 1, 8, 27, 64, ... (OEIS A000578).

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

A pivotal isocubic is an isocubic on the lines connecting pairs of isoconjugates that pass through a fixed point P (the pivot point). Pivotal isocubics intersect the ...

Cubic symmetric graphs are sometimes called Foster graphs and denoted F_(nnn)X, where nnn is the vertex count and X is a letter A, B, C, ... indicating the particular such ...

In 1850, Bravais demonstrated that crystals were comprised of 14 different types of unit cells: simple cubic, body-centered cubic, face-centered cubic; simple tetragonal, ...