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Animation depicting the process of completing the square. (Details, animated GIF version)In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1]
the kernel is the space of solutions to the homogeneous equation f(v) = 0, and its dimension is the number of degrees of freedom in the space of solutions, if it is not empty; the co-kernel is the space of constraints that the solutions must satisfy, and its dimension is the maximal number of independent constraints.
More precisely, if Z is a subspace of Y and g : Z → Y is the inclusion map we can "glue" Y to another space X along Z using an "attaching map" f : Z → X. The result is the adjunction space , which is just the pushout of f and g. More generally, all identification spaces may be regarded as pushouts in this way.
Negative Space; Representational; A symmetrical pattern block design created by eight year olds. The EDC Teacher's Guide continues: "Many children start by making abstract designs — both symmetrical and asymmetrical. As play continues these designs may become more and more elegant and complex, or they become simple as the child refines his ...
Sam Loyd's chessboard paradox demonstrates two rearrangements of an 8×8 square. In the "larger" rearrangement (the 5×13 rectangle in the image to the right), the gaps between the figures have a combined unit square more area than their square gaps counterparts, creating an illusion that the figures there take up more space than those in the ...
A Canadian woman was arrested after trying to smuggle over 20 pounds of methamphetamine through a New Zealand airport, authorities said. The illicit drugs were disguised as Christmas presents, New ...
Sean “Diddy” Combs has been accused in a new lawsuit of dangling a woman from the 17th-floor balcony of an apartment during an altercation.
There are various equivalent ways to define the determinant of a square matrix A, i.e. one with the same number of rows and columns: the determinant can be defined via the Leibniz formula, an explicit formula involving sums of products of certain entries of the matrix. The determinant can also be characterized as the unique function depending ...
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