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The Randić index of a graph is defined as half the sum of the matrix elements of its Randić matrix. While the index was introduced to model the branching of the carbon-atom ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

The so-called reaching algorithm can solve the shortest path problem (i.e., the problem of finding the graph geodesic between two given nodes) on an m-edge graph in O(m) ...

A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram. The word rhomb is sometimes used ...

The rule which determines the orientation of the cross product u×v. The right-hand rule states that the orientation of the vectors' cross product is determined by placing u ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

The second Morley triangle is made by rotating line BC toward vertex A about vertex B by angle (B+2pi)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 ...

Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

A fractal which can be written as a Lindenmayer system with initial string "YF", string rewriting rules "X" -> "YF+XF+Y", "Y" -> "XF-YF-X", and angle 60 degrees.