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The prime spiral, also known as Ulam's spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes indicated in some way along the ...

The decimal expansion of a number is its representation in base-10 (i.e., in the decimal system). In this system, each "decimal place" consists of a digit 0-9 arranged such ...

An out-shuffle, also known as a perfect shuffle (Golomb 1961), is a riffle shuffle in which the top half of the deck is placed in the right hand, and cards are then ...

A riffle shuffle, also called the Faro shuffle, is a shuffle in which a deck of 2n cards is divided into two halves. The top half of the deck is placed in the left hand, and ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of a ...

In any triangle, if one of the sides is extended, the exterior angle is greater than both the interior and opposite angles.

The angle bisector of an angle in a triangle divides the opposite side in the same ratio as the sides adjacent to the angle.

In a cochain complex of modules ...->C^(i-1)->^(d^(i-1))C^i->^(d^i)C^(i+1)->..., the module B^i of i-coboundaries is the image of d^(i-1). It is a submodule of C^i and is ...

A partition p is said to contain another partition q if the Ferrers diagram of p contains the Ferrers diagram of q. For example, {3,3,2} (left figure) contains both {3,3,1} ...