Welcome to the Academy!








Introduction
Today the Xenos children, Helen and Alexandar, invite you to attend class with them at the Academy. You decide that it might be fun to meet more friendly Grecians your age and see what they are learning. Soon, you and the Xenos children are seated in Arithmeticbackpack class and you learn about these new ideas that have recently been discovered in Greece and labeled "Geometry." You soon learn that Ancient Greece is not only important to today's society because of its advancements in democracy, but this country and period of time also helped come up with the basic principles of what we know today as geometry!




     
     


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You will learn...




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What you learn...
Much of what we know today in geometry, stems all the way back to Ancient Greece. There were many Greek figures who discovered the basic principles. In turn, our knowledge has become much more advanced in geometry. The Greeks should be specially credited for building their mathematic concepts from information they learned from even earlier ancient civilizations.

The following are some of the most important Ancient Grecians in geometry: Pythagoras, Euclid, Archimedes, Appollonius, Leno of Elea, Thales of Miletus, Plato, Aristotle, Eratosthenes, Heron of Alexandria, and Hyaptia.

The following links will help you learn more about these influential figures:


What is significant is that because of these pioneers in geometry, a large portion of what you learn in math class today is due to their actions! Who would have thought people who lived so far away and such a long time ago could affect you so much?



Tessellations
Now, your Greek teacher gives you a lesson about tessellations.


What is a tessellation anyway?
A tessellation is a tiling of an area where repetitions of the same shape or shapes completely cover an area without gaps or overlapping.
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If you think for a moment, there are many of examples of tessellations that we see each day. You can think of a carefully crafted quilt with its many connected patches, a tiled floor or wall, and even bees are impacted by tessellations as they store honey in hexagonal (6 sided shape) cells made of wax called honeycombs. The picture to the right is an example of Greek tiling.


http://www2.spsu.edu/math/tile/historical/greek/index.htm               


Click on the following to see over a hundred uses of tessellations:
http://www.geocities.com/williamwchow/escher/nesting.htm








For your task, you are to use a polygon to create a tessellation pattern on a page of your journal.

Step 1
Chose one of these regular polygons: parallelogram, square, hexagon, or equilateral triangle.  Click on the following to see an example of these polygons: http://www.mathleague.com/help/geometry/polygons.htm
Step 2
Next, trace it repeatedly, leaving no spaces and covering the entire surface of the paper.
Step 3
Then, color each shape, either randomly or in some form of a colored pattern.
Step 4
Before you begin, click on the following link to get some practice making a tessellation ... remember that no white should be showing or shapes overlapping. You can even experiment by using 2 or 3 regular polygons to form a solid tessellation pattern. http://ejad.best.vwh.net/java/patterns/patterns_j.shtml
Step 5
Finally, write 3 things you learned about tessellations and geometry in general in your journal in addition to the pattern you created.


Remember that you can check out the evaluation page to see how you will be evaluated.


If you have time, click on the following to do an additional activity on tessellations! Extension




Index
Introduction
Process
Task
Resources
Teacher
Conclusion
Evaluation