Investigation: Geometry stories

Introduction

The measurement and geometry concepts that we use today have come from many diverse cultures, have changed over time, and still look different in different cultures. However, we often have many of the same concepts, but represented in different ways in different cultures.

 

Objective

Research and explore a geometric concept or measurement system to tell a story about how it came about and how it is used in a specific culture. Explain how the geometric concept or measurement system is relevant in a current context.

 

Materials

• Device with internet access or library access

 

Activity 1

As a class, create a list of geometric concepts or measurement systems that you have seen in the past. This could be in math class or in your own experiences. Here is a list to get you started:

• Customary system of measurement for a particular country or culture
• Cultural art with geometric shapes
• Buildings or structures that contain geometric shapes
• Imperial and/or metric and/or other measurement systems
• Any theorem or principle such as:
  • The side-length relationship for right triangles
  • Cavalieri's principle
  • \pi=\frac{\text{Circumference}}{\text{Diameter}}
• Scale models
• Symmetry

 

Activity 2

In a group of two or three do the following: 

1. Choose a geometric concept or measurement system that you will research. This could be a concept from the list from Activity 1, or one that you came up with as a group. If you came up with it as a group, ask your teacher to check it before going to the next step.
2. Create a 3 - 5 minute presentation telling the story of the number concept of your choice. Things that could be included are:
   • In present day, what this concept looks like in different cultures
   • Across one or more cultures, how the concept was initially developed compared to what it looks like in present day - who was it named after versus who first used it
   • A timeline
   • Any underlying assumptions that we might make about the concept
   • How the concept can be used in different contexts - present and past
   • Images of what the notation has looked like
   • What you want to learn more about
   • Sources for your information - if not from personal experience

 

 

Here is an example on the geometric concept of inscribed angles in a circle.

Example on inscribed angles

This geometric concept in its explicit form dates back to around 300 BCE where it can be seen in Euclid's Elements (Book 3, Proposition 20). Like many concepts they were likely used in other cultures and contexts prior to this, but this is one of the first written records we have of it. The inscribed angles theorem goes something along the lines of: 

The central angle subtended by any arc is twice any of the inscribed angles on that arc. 

From this theorem, we can show many other properties of arcs, chords, secants, tangents, and inscribed polygons in circles. 

This is what it looked like in Euclid's Elements (translated): "In a circle the angle at the center is double the angle at the circumference when the angles have the same circumference as base."

We can see many inscribed angles with the same measure in dreamcatchers. We can use this applet to explore the different patterns we can make. 

Sources: 

• Euclid, ., Heath, T. L., & Densmore, D. (2002). Euclid's Elements: All thirteen books complete in one volume : the Thomas L. Heath translation. Santa Fe, N.M: Green Lion Press.