Lesson 8: Working at a golf course
By: Tim Lehman
In this exercise, the students will become workers at a golf course for a day. Their mission is to determine how much fertilizer should be applied to each green. However, they will not be working at any golf course. They are at the Augusta National Course in Augusta, GA, home of the Masters Golf Tournament.
To begin their work, the students will first need to determine a method for finding the area of a golf green. Students can be given a copy of the green of Hole #1 or they can open the GSP sketch (version 4.0) here to investigate how to find its area.
Students can present their ideas to the class where the positive and negative points of each can be discussed. One method would be to put the green on a grid. Though this would accurate and is easy on GSP, it is not practical to carry out on a golf course. Another method would be to divide the green into figures with areas that could be found. Again, this method would be accurate and easy to complete on GSP but is more difficult to complete on the course. Some sort of marker (such as strings) would be needed to mark of the areas that had been measured to keep them from being measure more than once.
A method suggested for measuring greens given by Palmer Maples appears to works and is practical to carry out as well. He estimated the area by using the formula for a circle. After finding a point in the center of the green, measure the distance from this center to points equally spread around the boundary. These distances can then be averaged, the averages squared, and then this multiplied by pi to find the estimated area. If students do not determine a good method for finding the area, they can be given one such as the Maples' Method and then find out why it works.
Once students determine how to find the area of the greens, several possible exercises exist. Click here for information on greens management that can be used to locate possible problems to give the students. One would be for the students to determine how much nitrogen to apply to each green. Since 1981, Augusta National has had bentgrass on its greens. According to the Aggie Horticuluture website, bentgrass needs about 5 pounds of nitrogen a year per 1000 square feet (0.5 lbs a month from October to May and 0.25 lbs per month from June to September.)
Other investigations could include the amount of seeds, mulch, phosphorus, potassium, or water needed on the green. To find this information on bentgrass, click here. Wondering what all these things do to the grass? Click here for information on fertilizer.
In 1981, Augusta National Golf Course switched its greens from bentgrass to bermuda grass. What changes had to be made in the care of the green? How much more or less of the items found above would have been needed on the old greens? For infomation of bermuda grass, click here.
Click on each to the following for links to GSP 4.01 sketches with the the greens of:
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An Excel Spreadsheet could assist this problem. After taking 16 measurements evenly around the green, enter the measurements in the spreadsheet here to get an estimate of the area using the Maple's Method.
However, an obstacle exists in finding the scale of the greens. I have been unable to find this information. Thus, it will need to be estimated. If you know where this information could be found or have accurate estimates for the dimensions for the greens, please email me.
All information
about grass, fertilizer, and green management are from or links
to the Aggie Horticultire website that is the information server
of the Texas Horticulture Program from information from the Texas
A&M University System.
Link to the Aggie Horticulture Website
All diagrams of greens, golfing photographs, and information about the course were taken from the official site of the Masters.
Link to Masters Golf Tournament Website
More information on this problem
(as well as more solutions-one of which uses Heron's formula)
can be found in an article by W. Gary Martin and Joao Ponte, "Measuring
the Area of Golf Greens and Other Irregular Regions" from
the May, 1985, issue of Mathematics Teacher.
Palmer Maples article "Maples' Method
of Measuring Greens" can be found in the June, 1980, issue
of Golf Course Management.
The idea for this
page is from questions posed by Dr.
Jim Wilson on the homepage for his EMAT
6600 class.
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