Everybody knows how frustrating it is to sit at a red light. Worse, a light that stays red too long can cause cars to back up, leading to gridlock. It's the traffic engineer's job to time things so that cars do not have to wait too long.
On this site, you are the traffic engineer. Through a computer simulation, you control the timings of the lights at six intersections. Each road has two lanes, one in each direction. You have measured the traffic densities and you know that traffic behavior follows a particular mathematical model (the model is described onsite).
- decide whether traffic lights are even feasible;
- find what happens when a long light of cars is waiting at a red light and the light turns green;
- find the best light timings for three specific situations.
You are invited to try your hand at exploring mathematics in action in this real life situation. The competition was held in 1996 by the Univ. of Toronto Mathematics Network.
All about the abacus, a calculator whose earliest known use was c. 500 B.C. in China. The abacus was used by the Japanese beginning around 1600 A.D., and excavations have revealed an Aztec abacus, c. 900-1000 A.D., "where the counters were made from kernels of maize threaded through a strong that attached to a wooden frame."
- Construction and anatomy, abacus basics - Proper finger technique - A Java applet representing the number 87,654,321 - Instructions for addition and subtraction - The Abacus vs. the Electric Calculator - The Japanese, Chinese, and Aztec abacus, compared - Resources: purchase an abacus or build one out of LEGO - Abacus Museum
A mailing list from B. Clay. Each Monday an email message is sent to more than 4000 subscribers, with an exercise that illustrates how to do mental math computations faster than with a calculator. Learn to square numbers made up of 9's; multiply a 2-digit number by 594 or 693; or divide a repeating 6-digit number by 7, 11, and 13, then subtract 101... and many more.
More than 90 of these mental tricks have been archived by the Math Forum: