Why are automobile logos so symmetrical?
DUE: November 30, 2015
Why aren’t all of them?
Or are they?
Name: ________________________________
Elmont Memorial High School
-
Date: ______________ Period: ____
Geometry – 9A
Consider the three types of symmetry studied in class.
Line symmetry: occurs in a figure when the figure is its own image
under a reflection in a line.
Point symmetry: occurs when the figure is its own image under a
reflection through a point.
Rotational symmetry: occurs in a figure if the figure is its own image
under a rotation about a fixed center point of θ degrees,
0° < θ < 360°
Your assignment is to find FOUR automobile logos that meet the following
criteria:
1) Out of the four logos, 1 is required to have NO symmetry. For example,
the Ford logo above may appear to have symmetry since its shape is an
oval. However, the word “Ford” disqualifies it since the word has no
symmetry.
2) The remaining 3 logos must include the three types of symmetry in some
way. For example, the Pontiac logo above has line symmetry.
3) Of the 3 remaining logos, if two of them have rotational symmetry, you
must have two different angles of rotation. For example, the Chevrolet
logo above has point and rotational symmetry (180°). So far, the three
logos on this assignment sheet have covered the three types of
symmetries. Since one more image is required to complete the
assignment, if the fourth image contains rotational symmetry, it cannot
be one that has rotational symmetry of 180° since it was already
accounted for in the Chevrolet logo.
4) Of the 3 logos that ARE symmetric, you must identify all the types of
symmetry that are contained in that logo.
5) You are NOT to use the three logo examples on this assignment sheet.
Sample assignment on the back…
Name: Mrs. Mojocoa
EMHS
Image
OTHER IMAGE
Date: Any
Period: Any
Geometry – 9A
Line
Symmetry? If
so, how many
lines of
symmetry?
Point
symmetry?
Rotational
symmetry?
What is the
smallest angle
of rotation?
No
No
No
No
Yes
Yes, 180°
Yes
No
No
?
? (If it had
rotational
symmetry, it
could not be
180° since it
has been
accounted for
above)
?
Each section is worth 15 points. There are four images and a written portion.
The written portion is worth 40 points. Maximum score is 100.
This assignment will count as a TEST grade.
A FIVE-POINT deduction will occur for every calendar day that the
assignment is late. After a week, the grade received will be a zero.
Name: ________________________________
Elmont Memorial High School
Date: ______________ Period: ____
Geometry – 9A
Why are automobile logos so symmetrical?
Why aren’t all of them?
Or are they?
Image
[15 points]
[15 points]
[15 points]
[15 points]
Line
Symmetry? If
so, how many
lines of
symmetry?
Point
symmetry?
Rotational
symmetry?
What is the
smallest
angle of
rotation?
Answer the following questions: [1 – 5 are each worth 5 points]
1) How did this assignment affect your knowledge of symmetry?
2) What was the most difficult part of the assignment? How did you
overcome this difficulty?
3) How did this assignment affect the way you see car logos now?
4) Notice that although the Ford logo fails to have symmetry because of the
word inside the oval, it still “looks” symmetrical. Why do you think
automobile companies care so much about making their logos appear
symmetrical?
5) Was any part of your non-symmetrical logo symmetrical? Explain.
(For instance, the Ford logo in the sample assignment was selected as the logo that failed to
have symmetry because the letters were not symmetrical. However, what is symmetrical about
the logo is its outer shape, i.e., the oval.)
6) [15 points]
On a separate sheet of paper, create your own logo. You can use a computer to
design it or simply draw it. Include color if appropriate. If it has no symmetry,
explain why you chose to create a logo with no symmetry. If it does have
symmetry, identify the type(s) of symmetry.