Spider Math

Patricia Winkler
DeBakey High School for Health Professions
Houston, TX  77021
email:  pwinkler@houstonisd.org

Previous Lesson (taught by Rosamaria Ynfante) will cover:

  1. Wandering Spider vs. Web Builders
  2. Types of Web-builders
  3. Where do these spiders live?
  4. other biological information about the spiders

This lesson will cover:

  1. Geometric Aspects of different types of webs
  2. Discuss specifically the Orb spiders' webs
  3. Create a spider web using string and cardboard/paper

Purpose

The purpose of this lesson is to discuss the presence of geometry in the world around us. This will help the students realize that geometry has been a discovery not an invention.

Terminology

radius of the web	consecutive radii of the web
spiral of the web	logarithmic spiral
chord of the web	equiangular spiral
corresponding angles	catenary curve
geometric progression

Procedures

  1. Review the different shapes of webs which spiders make.
  2. Take a closer look at an orb spider and its web.
  3. Look at an example of an orb spider's web.
  4. Discuss the terminology looking at the sample web.
    • 2 spiral-like curves
    • Radii from the center
    • Chords connecting 2 consecutive radii
      • How are these chords related?
    • Discuss the basic properties which make the spiral logarithmic
      • The angles formed by tangents drawn at the points where the spiral intersects the radii are congruent. That makes the spiral equiangular.
      • The chords which form the spiral form a geometric progression. the sprial increass at a geomtric rate.
    • The spiral-like web is very strong and flexible and is build with minimal materials by the spider.
  5. Ask students:
    • How would you begin to construct a web like this if you were a spider? Does the spider construct it randomly or is there a pattern?
    • Allow students time to consider their answers and then share a few.
  6. How does the orb spider really do it?
      The spider initially sits up a triangular from its web. The puter sprial forms the main part of the snare. It is spun from the outer edge toward the center with sticky silk.
  7. Internet Resources:

Geometric Art

  • Have the students create a spider web using string art techniques.