Fractal curveA fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length. A famous example is the boundary of the Mandelbrot set. Fractal curves and fractal patterns are widespread, in nature, found in such places as broccoli, snowflakes, feet of geckos, frost crystals, and lightning bolts.
Problem solvingProblem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles.
Walls of ConstantinopleThe Walls of Constantinople (Τείχη της Κωνσταντινουπόλεως) are a series of defensive stone walls that have surrounded and protected the city of Constantinople (today Istanbul in Turkey) since its founding as the new capital of the Roman Empire by Constantine the Great. With numerous additions and modifications during their history, they were the last great fortification system of antiquity, and one of the most complex and elaborate systems ever built.
Stone AgeThe Stone Age was a broad prehistoric period during which stone was widely used to make stone tools with an edge, a point, or a percussion surface. The period lasted for roughly 3.4 million years and ended between 4,000 BC and 2,000 BC, with the advent of metalworking. Though some simple metalworking of malleable metals, particularly the use of gold and copper for purposes of ornamentation, was known in the Stone Age, it is the melting and smelting of copper that marks the end of the Stone Age.
GemstoneA gemstone (also called a fine gem, jewel, precious stone, semiprecious stone, or simply gem) is a piece of mineral crystal which, in cut and polished form, is used to make jewelry or other adornments. However, certain rocks (such as lapis lazuli, opal, and obsidian) and occasionally organic materials that are not minerals (such as amber, jet, and pearl) are also used for jewelry and are therefore often considered to be gemstones as well.
Spectral theory of ordinary differential equationsIn mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation, Hermann Weyl generalized the classical Sturm–Liouville theory on a finite closed interval to second order differential operators with singularities at the endpoints of the interval, possibly semi-infinite or infinite.
Surface triangulationTriangulation of a surface means a net of triangles, which covers a given surface partly or totally, or the procedure of generating the points and triangles of such a net of triangles. This article describes the generation of a net of triangles. In literature there are contributions which deal with the optimization of a given net. Surface triangulations are important for visualizing surfaces and the application of finite element methods.
Benoit MandelbrotBenoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.
PathfindingPathfinding or pathing is the plotting, by a computer application, of the shortest route between two points. It is a more practical variant on solving mazes. This field of research is based heavily on Dijkstra's algorithm for finding the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph theory, which examines how to identify the path that best meets some criteria (shortest, cheapest, fastest, etc) between two points in a large network.
AshlarAshlar (ˈæʃlər) is finely dressed (cut, worked) stone, either an individual stone that has been worked until squared, or a structure built from such stones. Ashlar is the finest stone masonry unit, generally rectangular cuboid, mentioned by Vitruvius as opus isodomum, or less frequently trapezoidal. Precisely cut "on all faces adjacent to those of other stones", ashlar is capable of very thin joints between blocks, and the visible face of the stone may be quarry-faced or feature a variety of treatments: tooled, smoothly polished or rendered with another material for decorative effect.
