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∡A_2MA_3=∡A_2A_1A_3+∡P_2P_1P_3, where ∡ is a directed angle.

A fractal based on iterating the map F(x)=ax+(2(1-a)x^2)/(1+x^2) (1) according to x_(n+1) = by_n+F(x_n) (2) x_(y+1) = -x_n+F(x_(n+1)). (3) The plots above show 10^4 ...

An image of an object obtained by reflecting it in a mirror so that the signs of one of its coordinates are reversed.

Two objects form a mirror pair if one can be translated and rotated in such a way that the two objects together possess mirror symmetry, i.e., one is the mirror image of the ...

A version of nim-like games in which the player taking the last piece is the loser. For most impartial games, this form is much harder to analyze, but it requires only a ...

The statistical index P_M=(sump_nq_a)/(sump_0q_a), where p_n is the price per unit in period n and q_n is the quantity produced in period n.

A quartic surface named after its resemblance to the liturgical headdress worn by bishops and given by the equation 4x^2(x^2+y^2+z^2)-y^2(1-y^2-z^2)=0.

A mixed fraction is an improper fraction p/q>1 written in the form n+r/s. In common usage such as cooking recipes, n+r/s is often written as n r/s (e.g., 1 1/2), much to the ...

A mixed graph in which both directed and undirected edges may exist. If only directed edges exist, the graph is called a directed graph. If only undirected edges exist, it is ...

A partial derivative of second or greater order with respect to two or more different variables, for example f_(xy)=(partial^2f)/(partialxpartialy). If the mixed partial ...