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The Menger sponge is a fractal which is the three-dimensional analog of the Sierpiński carpet. The nth iteration of the Menger sponge is implemented in the Wolfram Language ...

The metric dimension beta(G) (Tillquist et al. 2021) or dim(G) (Tomescu and Javid 2007, Ali et al. 2016) of a graph G is the smallest number of nodes required to identify all ...

The middle layer graph of order n is the graph whose vertex set consists of all bitstrings of length 2n+1 that have exactly n or n+1 entries equal to 1, with an edge between ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

A sequence of positive integers 1<=a_1<a_2<a_3<... (1) is a nonaveraging sequence if it contains no three terms which are in an arithmetic progression, i.e., terms such that ...

A word is said to be overlapfree if it has no subwords of the form xyxyx. A squarefree word is overlapfree, and an overlapfree word is cubefree. The numbers t(n) of binary ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

The Sierpiński carpet is the fractal illustrated above which may be constructed analogously to the Sierpiński sieve, but using squares instead of triangles. It can be ...

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

A median A_1M_1 of a triangle DeltaA_1A_2A_3 is the Cevian from one of its vertices A_1 to the midpoint M_1 of the opposite side. The three medians of any triangle are ...