WEBQUEST

1. WEBQUEST By: Rachel Barry, Allison Grotz, Jacqueline Jachymiak, & Sasha Fajerstein

2. Euclid You are going to be exploring Euclid and his elements through an exciting Webquest! You’re job is to complete each task and record the data. Good luck and have fun!

3. Who was Euclid? Euclid is one of the world's most famous mathematicians. It is believed that he was born around 365 BC in Alexandria, Egypt and died around 300 BC. Euclid is also referred to as the father of geometry. His work Elements is the most successful textbook in the history of mathematics. The content discussed in his 13 books within the Elements is the basis for what you know as Euclidean geometry.

4. Who was Euclid? After reading the article about Euclid, pretend that you have traveled back in time and you have the chance to have a mathematical discussion with Euclid himself! Please write a one page style interview with Euclid If you were given the chance to talk to Euclid, what questions would you ask him? Please include: Where and when he was born Where he studied Information relating to his life/family Three contributions he made to mathematics Resources: http://www.mathopenref.com/euclid.html http://www.gap-system.org/~history/Biographies/Euclid.html http://en.wikipedia.org/wiki/Euclid

5. The Elements The Elements is a text written by Euclid containing 13 books that led to the formation of geometry in a school setting. For centuries it was used as a school textbook around the world. It influenced the world of mathematics for over 2000 years! So let’s get started exploring more about The Elements!

6. Congratulations! You have just been hired as the new Journalist at the Euclidean Daily newspaper! You have inside information that there is something wrong with Euclid’s first 4 definitions, in Euclid’s first book, in terms of the Euclidean geometry we use today. It is up to you to write an article addressing these topics: Rewrite the first 4 definitions so that they apply to modern Euclidean Geometry Convince readers why Euclid is wrong in his first 4 definitions Resources: http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html http://www.gap-ystem.org/~history/HistTopics/Euclid_definitions.html

7. Euclids 22ndDefintion This is how Euclid defines different types of quadrilaterals: “Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.”

8. Different Types of Quadrilaterals Now that you have read how Euclid defines different types of quadrilaterals, it is your turn to explore quadrilaterals on your own. Click on the following applet: http://www.mathsisfun.com/geometry/quadrilaterals-interactive.html 1.) First select “parallelogram” and drag around the vertices. Observe how the figure changes. 2.) Click on “angles” and “diagonals” and see how they are affected when you drag around the vertices. 3.) Repeat these steps for square, rectangle, rhombus, trapezoid, and kite.

9. What did you discover? In your personal math journal, please reflect on what you discovered while using the quadrilateral applet. Please reflect on the following ideas: 1.) What properties do the rhombus, square, and rectangle share? 2.) For each type of quadrilateral you manipulated, how were the angles affected when you moved around the vertices? The diagonals? 3.) What was the most interesting thing you discovered that you did not know before exploring this quadrilateral applet? Additional Resources to explore: http://teacherweb.com/ON/Mayfield/RBesworth/properties_of_quad.pdf http://hpms.hpisd.org/LinkClick.aspx?fileticket=%2FzWbP6h77As%3D&tabid=2124

10. Comparing Circumference and Diameter of a Circle Now, we’re going to explore the concept of Pi and discover how pi came to be 3.14156… using Euclid. Go to the following website: http://www.mathopenref.com/circumference.html Drag the circle on the applet around to get any sized circle that you would like. Note that the distance around the circle is circumference. Record this number in your table under circumference. Note the distance across the circular object through the center (the diameter). Record this number in your table located on the next page, under diameter (for the same circle you used in when you recorded circumference). Calculate the circumference divided by the distance. Record this number in your table under Repeat steps 1-4 for five different sized circles.

11. Approximating the Value of Pi

12. You’re Done! Now you all know a little more about who Euclid was and his “Elements.” There are plenty of definitions, propositions, etc. that we did not discuss that Euclid wrote in the “Elements,” so feel free to explore them on your own! (Additional resources have been provided on the next slide.)

13. Additional Resources How to write a Journal Entry http://www.wikihow.com/Write-a-Journal-Entry How to write a Newspaper Article http://newspaper-journalism.suite101.com/article.cfm/how_to_write_a_newspaper_articleHow to conduct an interview How to write an Interview Short-Essay http://www.essaytown.com/writing/write-interview-essay