Loci

August 2008. Article ID 2842

Mathematical Brooding over an Egg

André Heck

AMSTEL Institute

Universiteit van Amsterdam

Author Information

André Heck is project manager at the Faculty of Science of the Universiteit van Amsterdam, The Netherlands. His research area is the application of information technology to mathematics and science education. You may contact him by e-mail, or visit his personal home page for more information about his projects and research interests.

Abstract

Algebra and geometry can be brought to life with dynamic geometry software that allows the use of digital images. I will illustrate this statement by discussing how mathematical techniques, digital images, and dynamic geometry software can be used to analyze a real-world situation originating from poultry science. The topic is the mathematical modeling of the shape of an egg, where the underlying question is: "What is the volume and surface area of a hen's egg?". Although the practical investigation is meant for students at pre-university level or at undergraduate level, I will not present a model lesson on mathematical egg shapes. I will only discuss various modeling approaches using algebraic, geometric, and regression techniques, which are also applicable in similar investigative work, and I will discuss how dynamic geometry software, and GeoGebra in particular, can be applied as a modeling tool.

Technologies Used in This Article

Keywords

Contents

  1. Introduction
  2. Measuring is no piece of cake
  3. The egg as a surface of revolution
  4. A geometric approach
  5. Computing with ellipses and eggs
  6. An algebraic approach
  7. The egg curve as a regression curve
  8. Easy data collection in GeoGebra and regression analysis
  9. A potpourri of mathematical egg curves
  10. Dynamic use of digital images in GeoGebra
  11. Bringing mathematics to life via digital images and vice versa
  12. References