Saturday, June 20, 2015
Shapes
How to Create a Tessellation
How
to Create a Tessellation
What to do:
1.
Begin by
creating a “template” using at least 1 of the nibbling methods. Be sure to
label all the pieces.
2.
Once the
template has been created, place your template at any of the four corners of
your graph paper and trace your first figure. The squares on the graph paper
should align with the original square you started with, and therefore your
template may hang off the edge of the paper.
3.
Once your
figure has been traced slide it or reflect it and trace your next figure
(whether you reflect for slide it depends on the nibbling technique you used)
4.
Continue
step 3 until the entire page is covered. All your figures on the paper should
fit together so that it looks like a puzzle. Figures at the edge will only be
partial images
5.
Once you
have the page covered in your tessellation, begin to add color in the figure.
6.
Be creative
and have fun with the project!
Creating Your Template:
Method 1- The nibbling technique for geometric transformations:
1.
Begin with a
square and design from one corner of the square to an adjacent corner. (Do not
draw diagonally). Do not stop halfway across!
2.
Cut on the
design line, being sure to have 2 pieces when done -the nibble and the rest of
the sheet. There should be no other pieces lying around. This is very
important! No trimming allowed.
3.
Slide the
nibble across the sheet to the opposite side and tape the straight edges
together. (Do not attach it to an adjacent edge. Do not flip the nibble around.
Do not overlap the edges when taping.) The corners of the piece and the nibble
should match perfectly.
4.
Repeat the
procedure for the other sides
Method 2- The Rotating and nibbling technique for
geometric transformations:
1.
Begin with a
rectangle and design from one corner of the rectangle to an adjacent corner.
(Do not draw diagonally). Do not stop halfway across!
2.
Cut on the
design line, being sure to have 2 pieces when done -the nibble and the rest of
the sheet. There should be no other pieces lying around. This is very
important! No trimming allowed.
3.
Instead of
sliding the nibble, rotate the nibble at its end point to an adjacent side of
their square (not an opposite side). Mark your point of rotation and tape the
straight edges together. (Do not overlap the edges when taping.) The corners of
the piece and the nibble should match perfectly.
4.
Repeat the
procedure for the other sides
Creating a Tessellation Using Reflections:
1.
Select any
figure you want to use as your pattern (can use a figure from the nibbling methods
or a combination of both).
2.
Then reflect
or “flip” the figure repeatedly vertically (over the y-axis).
3.
Once you
have a row of “flips”, take that row and reflect it horizontally (over the
x-axis)
4.
Continue
Steps 2 and 3 until your paper is covered.
http://www.fuhsd.net/view/3198.pdf
Tessellation Worksheet
Name:
Tessellation Worksheet
1.
List
3 different objects in the world around you that have tessellating patterns.
2.
Try
drawing each of these patterns
3.
How
many types of regular tessellations are there? List them.
4.
How
many semi-regular tessellations are there? List them.
Tessellation Treasure Map
Name:
Tessellation Treasure Map
Directions:
Ahoy matey! Captain
Tessellation is guarding his treasure. He will only surrender to the most fearsome
scallywag that sails the sea. Captain Tessellation
claims that no pirate be fierce enough to complete this treasure map. Are you?
Fill out each event and you may be the pirate who wins his booty. Good luck
matey!
Event 1: Answer
the following questions
1. What three rules
must a regular tessellation follow?
Event 2: Take a screen shot (or print out and paste to this
worksheet) the regular polygons that can be tessellated. Show more than just a
few repeated shapes. Make it clear that you discovered the regular polygons
that can be tessellated.
Event 3: Answer
the following questions
1. What is a
tessellation?
2. Another word for tessellation is
3. What is a regular
tessellation? Give an example.
Event 4: Answer
the following questions
1. How many
semi-regular tessellations are there? List them by their correct classification
(i.e. 4.8.8).
2. Explain why this image won't be a semi-regular
tessellation?
3. Explain why this image won't be a semi-regular tessellation?
3. Explain why this image won't be a semi-regular tessellation?
Event 5: Name each of the semi-regular tessellations (i.e. 4.8.8)
Event 6: Take
a screen shot (or print out and paste to this worksheet) at least two
tessellations you made in Tessellation Town.
Event 7: Answer
the following questions
1.
What is the
difference between Alhambra style tessellation and Escher style tessellation?
2.
Were all of the Alhambra tessellation
“true” tessellations? Explain why or why not.
3.
Who did the tilling/tessellations
in the Alhambra?
4.
Where is the Alhambra located?
Event 8: How
did M.C. Escher impact the “tessellation world”? Give examples.
Event 9: Using
the formula (360/n) prove whether or not these shapes can be tessellated. Show
all mathematical work.
1.
Triangle = 60°
2.
Square = 90°
3.
Pentagon = 108°
4.
Hexagon = 120°
Unlock The Code:
Ahoy there buccaneer! Looks
like you are almost done with your treasure hunt. Unlock this secret code and
you will be the first scallywag to find out where Captain Tessellations
treasure is located. But remembarrrr Captain Tessellation be guarding his
precious treasure and he will let no pirate pass unless they have the completed
treasure map and the three keys.
Directions:
Unlock the secret code at the
bottom of this page. Answer the following multiple-choice questions. Each
question corresponds to a blank space in the riddle below. The first question
corresponds with the first space. The second question corresponds with the second
blank space, and so on. Place the letter to your answer in the corresponding
space to unlock Captain Tessellation’s secret message.
1. M.C Escher was
born in
A. 1959
B. 1856
C. 1898
D. 2009
2. A tessellation is
J. a type of shape
K. a mathematical equation
L. a repeated pattern with no gaps or overlaps
M. none of the above
3. How many
semi-regular tessellations are there?
A. 8
B. 29
C. 5
D. 15
4. Which regular
polygon tessellates?
P. Triangle
Q. Square
R. Hexagon
S. All of the above
5. Which of the
following is NOT a semi-regular
tessellation?
R. 3.3.3.3.6
S. 4.8.4
T. 3.3.3.4.4
U. 4.8.8
6. Each vertices of
a tessellation is exactly
R. 360°
S. 90°
T. 180°
U. 270°
7. What famous 14th century palace is renowned
for its incorporation of intricate tessellated patterns?
M. Windsor Castle
N. Castle Frankenstein
O. The Alhambra
P. none of the above
8. What is a polygon?
O. any two-dimensional,
closed shape with three straight sides or more
P. any two-dimensional,
closed shape with four straight sides or more
Q. any two-dimensional,
closed shape with exactly four straight sides
R. any three- dimensional, closed
shape with three straight sides or more
9. Which of the following would NOT be an example
of a Tessellation?
L. a honeycomb
M. a rack of billiard balls
N. a grid
O. all of these are examples of tessellations
If the treasure is what you
seek to find then you must also keep in mind. Without the map and the three
keys Captain Tessellation will tell you to leave. Make sure that you have it
all. If you try to trick him then you will fall. You’ll walk the plank you’ll
lose your head so don’t think you can trick him instead. But if you have
completed all of the tasks then this is what Captain Tessellation asks, “Come
visit my home it is pretty cool. You can find me located at your school. If you
be lying get ready to meet your doom. If your not then look inside your ."
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