Cleaning the Floor Using a Robot: Intro to Random Numbers
Posed with a paradigmatic engineering problem, students consider and explore mathematical algorithms and/or geometric concepts to devise possible solutions. The problem: How should a robotic vacuum move in order to best clean a floor of unknown shape and dimensions? They grapple with what could be a complex problem by brainstorming ideas, presenting the best idea for a solution and analyzing all presented solutions, and then are introduced to an elegant solution. Rather than elaborately calculating the most efficient route and keeping track of which tiles the robot has visited, a random number generator determines which direction the robot will take when it hits a barrier. Students are able to visually confirm how an unfamiliar programming concept (a random number generator) can make for a simple and efficient program that causes an EV3 robot (that is suitably equipped) to clean a bare floor. Then students think of other uses for random numbers.
A Roomba® (iRobot) vacuum cleaner.Copyright 2006 Larry D. Moore, Wikimedia Commons http://commons.wikimedia.org/wiki/File:Roomba_original.jpg
Many problems faced in engineering can only be solved by the use of complex mathematics or specific mathematical algorithms. A random number generator is one example algorithm that is commonly used in computer programs for many purposes, from character actions in games to encrypting Internet communications. It can also be used for modeling real physical systems, which inherently contain some noise or randomness, such as weather forecasting. In addition, engineers must design products so that random or unpredictable processes from the surrounding environment have minimal impact on safety and reliability.
After this activity, students should be able to:
- Provide examples of how engineers approach problem solving using their knowledge of mathematics.
- Describe how the concept of random numbers can be used to solve real-world problems.