Geometry Racing
Liz Murphy Keith Thackery Bruce Urban
Class: Geometry
Materials: Paper, pencil, calculator, ruler, compass.
Goal: To apply geometric ideas of circumference, radius, and length to design a six-lane, 1000
meter running track.
Time Required: At least two class periods.
Background: Students will need a working knowledge of the concepts of circumference and the
relationship to the radius of a circle.
Setting: Coach Larry Lardbottom, by means of candy sales, has raised enough money to
construct a new running track. The track will be a new six-lane, 1000m type. The coach is a fine
motivator of athletes but doesn't have a clue in mathematical calculations.
Problem: Your task is to determine the lengths of the straightaways and the widths of each of
the six lanes. You will need to also identify the location of the staggers so as to make the track
fair to all runners no matter in which lane they start. The only restriction that you have is the
radius of each semicircular end must be 50 meters.
Sample Solution:
Assumptions: 1. The width of each lane is 1 meter.
2. The distance traveled by each runner will always be 1000 meters.
3. Measurement will be from the inside of each lane.
Solution: Using a lane width of 1 meter, compute the circumference of a circle with a radius of
50 meters:
....
C1 = 50 * 2π = 100π
C2 = (50 + 1)*2π = 102π
C3 = (50 + 2)*2π = 104π
C6 = (50 + 5)*2π = 110π
Funded in part by the National Science Foundation and Indiana University 1995
Next, compute total distance (S = straightaway distance):
.....
T1 = 2*S + 100π
T2 = 2*S + 102π
T6 = 2*S + 110π
Since each runner must travel 1000 meters, let G = length of stagger.
T1 + G = T2
2S + 100π + G = 2S + 102π
G = 2π
Evaluation:
Assumptions 20 points
Calculations 20 points
Report 10 points
Total
50 points
Extensions: You may want to change the following to make the problem more challenging:
1)
2)
3)
4)
5)
The number of lanes.
The width of the lanes.
The diameter of the semicircular ends.
The shape of the track.
Calculate the distance of each lane.
Teacher Notes: The following questions may or may not be given to assist the students
understanding of this problem:
1)
2)
3)
Is there a relationship between the radius and the positioning of the staggers?
How does the width of the lane affect the positioning of the staggers?
How does the length of each straightaway affect positioning of the staggers?
Funded in part by the National Science Foundation and Indiana University 1995