Articles — CODEE Agent-Based Fabric Modeling Using Differential Equations by Joseph Rusinko, Hannah Swan published November 25, 2012 We use an agent-based modeling software, NetLogo, to simulate fabric drape by applying a modified mass spring system. This model provides an application of harmonic motion to textiles and fashion, fields not typically discussed in the undergraduate differential equations classroom.
21 GIFs That Explain Mathematical Concepts “Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.” Danica McKellar As we usher in the start of a new school year, it’s time to hit the ground running in your classes! Logic Problem Solver Problem Description This is a program that can help solve many logic problems commonly found in puzzle magazines and books. Here is a simple example: Look-and-say sequence The lines show the growth of the numbers of digits in the look-and-say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic scale) tend to straight lines whose slopes coincide with Conway's constant. In mathematics, the look-and-say sequence is the sequence of integers beginning as follows:
Math and Music – Equations and Ratios Previously in the “math and music” lesson we derived equations for expressing intervals as functions of relative frequencies. This week we’re going to define conventions for interval sizes and then derive three variables where we can determine the composition of any frequency ratio. Guess what – all intervals can be described as different combinations of the octave, perfect fifth and major third – the first three overtones. In the last lesson we talked about the frequency ratios of common intervals. The standard convention is that interval ratios are greater than 1 and less than 2. A ratio of 2:1 is an octave, so it makes sense that all the other intervals are defined to be smaller than an octave.
Game Theory Explains How Cooperation Evolved When the manuscript crossed his desk, Joshua Plotkin, a theoretical biologist at the University of Pennsylvania, was immediately intrigued. The physicist Freeman Dyson and the computer scientist William Press, both highly accomplished in their fields, had found a new solution to a famous, decades-old game theory scenario called the prisoner’s dilemma, in which players must decide whether to cheat or cooperate with a partner. The prisoner’s dilemma has long been used to help explain how cooperation might endure in nature. After all, natural selection is ruled by the survival of the fittest, so one might expect that selfish strategies benefiting the individual would be most likely to persist.
Substitution Cipher A substitution cipher is a pretty basic type of code. You replace every letter with a drawing, color, picture, number, symbol, or another type of letter. This means, if you have your first "E" encoded as a square, all of your other "E"s in the message will also be squares. This tool has been created specifically to allow for as much flexibility as possible. You'll see what I mean when you start playing with it. The "Dancing Men" images are based on the Sherlock Holmes story of The Dancing Men.
Manifold The surface of the Earth requires (at least) two charts to include every point. Here the globe is decomposed into charts around the North and South Poles. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. Manifolds may have additional features. Aristotle was right about mathematics after all — Ae... What is mathematics about? We know what biology is about; it’s about living things. Or more exactly, the living aspects of living things – the motion of a cat thrown out of a window is a matter for physics, but its physiology is a topic for biology. Oceanography is about oceans; sociology is about human behaviour in the mass long-term; and so on.
Detexify LaTeX handwritten symbol recognition Want a Mac app? Lucky you. The Mac app is finally stable enough. See how it works on Vimeo. Braess’ Paradox – or Why improving something can make it worse On Earth Day in 1990 they closed New York’s 42nd Street for the parade and in 1999 one of the three main traffic tunnels in South Korea’s capital city was shut down for maintenance. Bizarrely, despite both routes being heavily used for traffic, the result was not the predicted chaos and jams, instead the traffic flows improved in both cases. Inspired by their experience, Seoul’s city planners subsequently demolished a motorway leading into the heart of the city and experienced exactly the same strange result, with the added benefit of creating a 5-mile long, 1,000 acre park for the local inhabitants. It is counter-intuitive that you can improve commuters’ travel times by reducing route options: after all planners normally want to improve things by adding routes. This paradox was first explored by Dietric Braess in 1968[4,5] where he explored the maths behind how adding route choices to a network can sometimes make everyone’s travel time worse.