EMAT 6700 Project
Geometric Aspects of the Structure and Design
of Commercial and Residential Field Irrigation 


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Preface

Welcome to the EMAT 6700 Project on Irrigation and its relevance to mathematics, and more specifically, geometry. Below is the information initially presented when this project was being driven under the original MATH 7200 course. As mentioned on my web page, the EMAT 6700 project will delve into the MATH 7200 project more deaply, not only from a mathematics standpoint, but from a mathematics education one as well. To find out more about the proposed changes and/or additions to this already-established link, go now to the EMAT 6700 Project Proposal Page. Otherwise, take a look below at what I discovered last year on this topic in the MATH 7200 course.

Introduction

About a year ago, a friend of mine was flying over the Midwest when he noticed below him a large farm. The farm had several crops growing at the same time. He noticed that the crops were divided up into squares but that the whole square was not being used (or so it seemed from up above). Instead, it looked like the farmer had laid out his crops in a "circular fashion", perhaps because it was more efficient to water the crops this way.

The circular crops were inside the square land areas. I choose not to use the word "inscribed" because sometimes there was more than one crop inside the square land area like the examples below:

However, these two circles are not considered "inscribed" by definition (i.e. that the circle is touching, or is tangent, to all four sides of the square).

In laying out the crops this way, it certainly raised many farming questions worth investigating. Some of these questions appear below:

• What might have been the farmer's reasoning for setting up his crops in this fashion?
• How could have the farmer constructed these large circles so precisely?
• If given two circles inside a square, what is the best way to maximize the total space inside the square to irrigate?
• What are the advantages/disadvantages to having more than one crop within the same square field?

As it turns out, the goal of any farmer is to get the most yield out of his/her fields as possible regardless of the shape of the field in which their crop(s) grow. Most likely what my friend saw was the circular shape of a type of irrigation system in use.

There are several factors as to why a farmer would lay his/her crops out in a certain fashion. Some of the main factors may include but are not limited to: topography, type and amount of crop, economic situations, and/or climate conditions. However this project will focus more on irrigation system designs, their geometric implications and how the geometry can be reconstructed, through Geometers Sketchpad, to discuss farming issues such as land area maximization and water usage and efficiency.

Below, you will find several links in the order which they are meant to be viewed. You will find several pictures or links to pictures, constructions or links to constructions, throughout the project. In order to successfully link to the constructions, you will need a copy of the Key Curriculum Press Geometers Sketchpad. You should be able to easily follow your way through the project by linking onto the next section at the bottom of each page. Good luck and I hope you enjoy! To give me feedback, please feel free to email me.

Thanks,

Kevin J. Mylod
M.Ed. candidate, Mathematics, 2001

In researching irrigation systems, I found that there were designs specific to commercial crop farm irrigation and to residential (lawn and garden) irrigation. In each case several geological, economical and topographical factors came into play when deciding the proper irrigation system.

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