46 posts on mathematics. All posts · RSS feed
Kaczmarz's algorithm is an iterative algorithm for solving a system of linear equations. In its simplest form, the equations are written in matrix form, and, starting with the initial guess for the solution, , the zero vector, successive approximations are generated by projecting onto the …
The Dottie number is the (real) root of the equation . As the only fixed point of the cosine function, it is the number that is converged to by the iterated function sequence i.e. it is the number returned if you mash the COS button …
The Cistercian numeral counting system used by the Cistercian monastic order in the late medieval period. The digits 1 – 9 are depicted as symbols arranged around a vertical stave. By placing these symbols reflected vertically and/or horizontally into each of four locations the decimal …
The shape with the minimum surface-to-volume ratio is the sphere. The code below plots this ratio for a variety of shapes as a function of a characteristic length: Rectangular box of length with square cross section of area The minimum value of is realised for …
A Babyonian spiral (OEIS A256111) is the figure formed by starting with a zero-vector at the origin and concatenating vectors such that each subsequent vector is the next one longer than the previous one that also lands on a position with integral Cartesian coordinates. That …
The Padovan sequence is a cousin of the more famous Fibonacci sequence defined by the initial values and the recurrence relation . That is, the next value is obtained not by summing the previous two values but by summing the two values before the last …
The Trapped Knight problem is a chess-based problem apparently invented by Neil Sloane and giving rise to a finite number sequence in his Online Encyclopedia of Integer Sequences (OEIS A316667). The squares of an infinite chess board are numbered in a spiral, as in this …
The Recamán sequence is a famous sequence invented by the Colombian mathematician, Bernardo Recamán Santos. It is defined by the following algorithm, starting at : if this number is positive and has not already appeared in the sequence; otherwise . It was covered in a …
This blog post was inspired by Holly Krieger's video for Numberphile. The Möbius function, , is related to the factorization of the positive integer through where is the number of prime factors of , is the number of distinct prime factors of , and is …
Loosely speaking, in the Gregorian calendar, Easter falls on the first Sunday following the first full Moon on or after 21 March. There are various algorithms (Computus) which can be used to calculate its date, and the cycle of dates repeats every 5.7 million years. …
