Benford's law. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of numbers that start with that digit. Frequency of first significant digit of physical constants plotted against Benford's law Benford's law, also called the first-digit law, is a phenomenological law about the frequency distribution of leading digits in many (but not all) real-life sets of numerical data. The law states that in many naturally occurring collections of numbers the small digits occur disproportionately often as leading significant digits.[1] For example, in sets which obey the law the number 1 would appear as the most significant digit about 30% of the time, while larger digits would occur in that position less frequently: 9 would appear less than 5% of the time.
The graph here shows Benford's law for base 10. Mathematical statement[edit] Example[edit] History[edit] Explanations[edit] Overview[edit] Multiplicative fluctuations[edit] with. Rod calculus. Rod calculus or rod calculation is the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were replaced by the more convenient and faster abacus.
Rod calculus played a key role in the development of Chinese mathematics to its height in Song Dynasty and Yuan Dynasty, culminating in the invention of polynomial equations of up to four unknowns in the work of Zhu Shijie. Japanese counting board with grids Hardware[edit] The basic equipment for carrying out rod calculus is a bundle of counting rods and a counting board. In 1971 Chinese archaeologists unearthed a bundle of well preserved animal bone counting rods stored in a silk pouch from a tomb in Qian Yang county in Shanxi province, dated back to the first half of Han dynasty(206 BC – 8AD).
Software[edit] Rod Numerals[edit] Displaying Numbers[edit] representation of the number 231 For numbers larger than 9, a decimal system is used. Displaying Zeroes[edit] 日. Matrix Reference Manual: Matrix Calculus. The Prime Puzzles & Problems Connection, by Carlos Rivera. Reaction Diffusion-Java. This applet displays a reaction-diffusion system. Begin exploring by using the "Preset" choice at the bottom - and the "Restart" button below it - to see some of the possible configurations. Configurable parameters include a number of manual colour-map controls (on the left) - and six main parameters of the reaction-diffusion system (on the right). Take care if using the other controls on the right.
They are usually very sensitive. The model is a cellular automaton, based on the von-Neumann neighbourhood. It is based on the Gray-Scott model, and was taken from John E. More details about the type of system used can be found at the [Xmorphia web site]. Toroidial boundary constraints are appled, so the images will tesselate seamlessly. Optionally, a bumpmap technique is employed to give the images a sense of depth. Geometric note Also, the "saturated" state in the automaton is often a chequer-board pattern. Math Humor.