Activity I: Industrial Design: The Geometry of Bicycle Designs (Grade Level 35)
The Geometry of Bicycle Designs 
Using Symmetry to Create Corporate Logos 
Patterns and Weaving 
Career Connections 
More Math Concepts
Standards:
Standard 4: Measurement (Attributes, Units, Techniques, and Tools of Measurement)
Objectives:
 Investigate how triangles can be used to design bicycles
 Measure lengths and angles used to make different bicycle frames
 Make conjectures about angle sizes and type of bicycles
Note to teachers:
Have students perform measurements in groups. Discuss the variation in answers and the meaning of precision. Also, discuss the usefulness of measuring twice to check for accuracy. Suggest averaging group measurements to obtain accuracy.
* These standards have been adopted and are based on the information from Principals and
Standards for School Mathematics: Discussion Draft, October l998, National Council of Teachers of Mathematics.
Activity I
The diagram below identifies
the various parts of a bicycle: the frame size, chain stay, seat angle,
head angle, and back angle. On the pages that follow, measure the different
parts for bicycles that have been designed for different purposes (racing,
riding on trials, and performing tricks). You can measure the parts on
the pictures provided on each page. If you have a real bike available,
make the measurements on it as well.
A.
Road Bike or Racing Bike (Cannondale^{tm} Saeco Team Replica)
The bicycle below
is known as a road bike, used for riding on paved surfaces and for long
distance races. The line diagram at the side is made of two triangles
and describes the geometry of the frame for this road bike.
1. Use a ruler and
a protractor to measure the lengths and angles that make up the bicycle
frame. You should measure the frame size and the chain stay on the picture
of the bicycle. The angles can be measured on the line diagram to the
right.
Frame Size 

Chain Stay 

Seat Angle 

Head Angle 

Back Angle 

2. Find the ratio
of the frame size to the chain stay (the frame Size divided by the length
of the chain stay):
B.
Mountain Bike or Trail Bike (Cannondale^{tm} F700)
The next bicycle
is known as a mountain bike. It is designed for offroad use, for riding
and climbing on trails, through woods, over puddles and streams. A line
diagram is next to the bicycle to show its frame design clearly.
1. Use a ruler and
a protractor to measure the lengths and angles that make up the bicycle
frame. You should measure the frame size and the chain stay on the picture
of the bicycle. The angles can be measured on the line diagram to the
right.
Frame Size 

Chain Stay 

Seat Angle 

Head Angle 

Back Angle 

2. Find the ratio
of the frame size to the chain stay.
C.
BMX Bike (Huffy^{tm} BMX)
The bicycle below
is called a BMX. It is designed for doing tricks on special tracks with
ramps and quarterpipes. BMX bikes are designed for picking up speed
quickly and doing spins, wheelies, and jumps.
1. Use a ruler and
a protractor to measure the lengths and angles that make up the bicycle
frame. You should measure the frame size and the chain stay on the picture
of the bicycle. The angles can be measured on the line diagram to the
right.
Frame Size 

Chain Stay 

Seat Angle 

Head Angle 

Back Angle 

2. Find the ratio
of the frame size to the chain stay:
D.
Questions about all three bikes.
Use the information
from your tables and the ratios that you calculated for the Road, Mountain,
and BMX bikes to respond to the following:
1. Explain the differences
in the frame sizes, the chain stays, and the three ratios you found.
Are they very different for each bike? Why?
2. Explain why the
back angle is different on each bike. Why is it designed that way? Did
you find any differences in the seat angle or the head angle? Explain.
3. The last bike
is a fullsuspension mountain bike with a new style design to allow for
a spring that absorbs shock for the back wheel (Cannondale^{tm}
Super V800). Notice the familiar geometry involving triangles can no
longer be found in this new design. Bicycle designers are now using much
more complicated polygons and shapes.
a. Explain any special
features you notice about this new style bicycle.
b. Why do you think
these designs now being used?
