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In mathematics, the gluing axiom is introduced to define what a sheaf on a topological space must satisfy, given that it is a presheaf, which is by definition a contravariant functor
Animation of the missing square puzzle, showing the two arrangements of the pieces and the "missing" square Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid.
Let ,,, be as in the above example. But this time let denote the scheme obtained by gluing , along the isomorphism given by . [3] So, geometrically, is obtained by identifying two parallel lines except the origin; i.e., it is an affine line with the doubled origin.
The glue is regulated by the FDA. Adhesives used on foods are covered under a regulatory subsection called "Indirect Food Additives: Adhesives and Components of Coatings." It outlines with great ...
In topology, the pasting or gluing lemma, and sometimes the gluing rule, is an important result which says that two continuous functions can be "glued together" to create another continuous function.
Examples mentioned by Gardner include separating the red squares from the black squares of a checkerboard with one cut, and "an old paper-cutting stunt, of unknown origin" in which one cut splits a piece of paper into both a Latin cross and a set of smaller pieces that can be rearranged to spell the word "hell". Foreshadowing work on the ...
In January 2002, she folded a 4,000-foot-long (1,200 m) piece of toilet paper twelve times in the same direction, debunking a long-standing myth that paper cannot be folded in half more than eight times. [21] [22] The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete ...
Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is ...