Since n = q /(2*pi), one can differentiate with respect to q, and the following differential equation can be used to calculate n Thus a numerical solution can determine the theta corresponding to this Ldesired value. The initial condition for the differential equation is Writing the above integral equation as an ordinary differential equation (using Polymath notation) givesĭ(L)/d(theta) =sqrt((x+y*theta)^2+y^2) (1)Įquation (1) can be used for a desired length *Ldesired” when the gap and x values are known.
Y = gap/(2π) where gap is known (gap = 4)ī = θ = 2π n (where n = turns) so n = θ /2 π The objective of the problem is to be able to design a spring system for a garage roller door to determine the number of turns for the door for the starting radius and the gap between spirals. Michael's Solution using Polymath Problem 1: Given L, Determine n
The problem is detailed in the article Roller Door Problem, which contains some solutions. This solution utilizes numerical analysis problem solving capabilities such as are available in the easy-to-use Polymath Software. University of Connecticut, Storrs, CT 06269-3222
#Polymath software software#
Michael worked on the roller door problem using Polymath Software and provided some more solutions.Įmeritus Professor of Chemical Engineering Roller Door Problem Solution with Numerical Methods The application of numerical methods can make math much easier and much more fun. Perhaps this is because I am a retired engineering professor and have been working in this area since about 1980. My feeling is that real world problems are solved with numerical methods, and thus students and their teachers should utilize these techniques while math is being taught. My approach to general problem solving is to use numerical methods that are easily available within Polymath Software. It's quite easy to set up problems and there are many example ones to get you going. I had a play with Polymath, and I feel it is an interesting tool for numerical solutions to various problems. There is some integration with Matlab, too.
#Polymath software plus#
Data analysis and Regression - up to 200 variables with up to 1000 data points for each, with capabilities for linear, multiple linear, and nonlinear regressions with extensive statistics plus polynomial and spline fitting with interpolation and graphing capabilitiesīeing numerical in approach, Polymath can export solutions to Excel for further analysis, or graphing.Differential Equations - up to 300 simultaneous ordinary differential and 300 additional explicit algebraic equations.Nonlinear Equations - up to 300 simultaneous nonlinear and 300 additional explicit algebraic equations.Linear Equations - up to 264 simultaneous equations.
#Polymath software professional#
According to the site, the professional version can cope with: Polymath uses numerical approaches for problem solving. I presented 3 different models for solving the problem, all of which gave pretty good results.Ī while later, I heard from Michael Cutlip, developer of Polymath Software. A reader needed a formula so he could easily work out the number of turns of a roller door for different height doors. Some time ago I wrote an article about a roller door problem.