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  2. Algebra tile - Wikipedia

    en.wikipedia.org/wiki/Algebra_tile

    Once the sides of the rectangle are represented by the algebra tiles, one would then try to figure out which algebra tiles would fill in the rectangle. For instance, if one had x×x, the only algebra tile that would complete the rectangle would be x 2, which is the answer.

  3. Lists of uniform tilings on the sphere, plane, and hyperbolic ...

    en.wikipedia.org/wiki/Lists_of_uniform_tilings...

    In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r.

  4. Difference of two squares - Wikipedia

    en.wikipedia.org/wiki/Difference_of_two_squares

    This follows from the left side of the equation being equal to zero, requiring the right side to equal zero as well, and so the vector sum of a + b (the long diagonal of the rhombus) dotted with the vector difference a - b (the short diagonal of the rhombus) must equal zero, which indicates the diagonals are perpendicular.

  5. Zero-divisor graph - Wikipedia

    en.wikipedia.org/wiki/Zero-divisor_graph

    In mathematics, and more specifically in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements of the ring as its vertices , and pairs of elements whose product is zero as its edges .

  6. Orthonormality - Wikipedia

    en.wikipedia.org/wiki/Orthonormality

    What does a pair of orthonormal vectors in 2-D Euclidean space look like? Let u = (x 1, y 1) and v = (x 2, y 2). Consider the restrictions on x 1, x 2, y 1, y 2 required to make u and v form an orthonormal pair. From the orthogonality restriction, u • v = 0. From the unit length restriction on u, ||u|| = 1. From the unit length restriction on ...

  7. Zero object (algebra) - Wikipedia

    en.wikipedia.org/wiki/Zero_object_(algebra)

    Over a commutative ring, a trivial algebra is simultaneously a zero module. The trivial ring is an example of a rng of square zero. A trivial algebra is an example of a zero algebra. The zero-dimensional vector space is an especially ubiquitous example of a zero object, a vector space over a field with an empty basis. It therefore has dimension ...