NCTM 2012 Presentation 2

Geometry Resources for the TI-Nspire

NCTM 2012WWW.MEDIA4MATH.COM

http://www.media4math.com/

Geometry Resources for the TN-Nspire

Media4Math includes a variety of free and premium resources, including short video tutorials on the Nspire, Math in the News, and other tutorials.



In this presentation we will focus on our DVD Library, Geometry Applications.



Volume 1

1. Points and Lines

2. Angles and Planes

3. Triangles

4. Quadrilaterals

5. Polygons

Volume 2

6. Circles

7. 3D Geometry

8. Area and Volume

9. Coordinate Geometry

10. Transformations



Geometry Applications: Circles visits ancient Rome.



We look at the architecture of the Roman Coliseum.



The Coliseum was not circular, but elliptical.



Of the surveying tools at the time, the main one was the Groma.



The Groma was ideal for constructing circular structures, since it was simple to define the locus of points from the center.



The Romans built lots of circular structures. So why did they choose the more challenging elliptical shape for the Coliseum?



Rather than a center, the ellipse has the two foci and variable lengths for L1 and L2, even though their sum is constant.



You can easily construct an ellipse using push pins, string, and a pencil.



But translating this into the language of surveying and construction is not straightforward and introduces a great deal of error.



Because of the condition of the Coliseum, it’s not known exactly how it was built.



One theory involves using circles and piecewise arcs to construct the elliptical shape. We’ll use the Nspire to show how this is done.



Create a Graph Window. We’ll be using the Geometry Tools within this environment.



Turn on the background grid, which will make it easier to construct the circles.



Construct a circle of radius 6. Use the background grid as your guide.



Construct a line from (0, – 6) to (2, 0). Extend the line past the circle.



Find the midpoint of the segment between (0, –6) and (2, 0).



Construct a line from the midpoint to (4, 0). Extend this line past the circle.



Construct a second circle centered at (4, 0) of radius 2.



Construct an intersection point where the small circle and the second line intersect.



Construct another circle centered at the midpoint and intersecting the small circle. Notice that these two circles have the same tangent at that point.



Construct an intersection point where the third circle and the first line intersect.



Construct a circle centered at (0, 6) and intersecting the third circle. These two circles also share a tangent at that point.



Notice that the three arcs from the three circles form a seamless elliptical arc.



Here are the three arcs pieced together, forming a seamless elliptical arc. But this was all constructed with circles.



You can now see how this elliptical arc—constructed solely from circles—can be used to construct the Coliseum.



You can also turn this into a hands-on activity.



Using a compass, ruler, paper, and pencil, you can sketch out the pattern for constructing the elliptical outline.


Geometry Resources for the TI-Nspire

NCTM 2012WWW.MEDIA4MATH.COM


Education

NCTM 2012 Presentation 2