A Jubilant Connection: General Jubal Early's Troops and the Golden Ratio

Abstract

The golden ratio, one of the most beautiful numbers in all of mathematics, arises in some surprising places. At first glance, we might expect that a General checking his troops’ progress would be nothing more than a basic distance-rate-time problem. However, further exploration reveals a multi-faceted problem, one in which the ratio of rates (rather than the explicit rates) is critical to the solution, and one that lends itself to several methods of solution with increasing levels of precision and complexity. This problem is accessible on several levels: it can provide students in elementary courses with an in-depth exposure to proportional reasoning and modeling, as well as offer students in upper division courses the challenge of finding the generalized solution and several intriguing connections to the Golden Ratio.

Keywords:

• Proportional reasoning
• Golden Ratio
• problem-solving