Google Earth Voyager Story: Circular Structures, Part 2
In this exploration, we continue to explore circular structures and in the process learn even more about the geometry of circles. We return toPueblo Bonito in Chaco Canyon, New Mexico, to review basic concepts of circles. This network of circular kivas will reveal some interesting properties of circular structures. To see the Google Earth Voyager Story, go to this link.
To see the complete collection of Google Earth Voyager Stories from Media4Math, go to this link.
1. Introduction to Circles: Pueblo Bonito
To start this lesson, watch this video about Pueblo Bonito, which consists of a network of circular structures called kivas. One of the features of circular structures is the ability to observe the sky from any angle. Ever wonder why observatories are circular in shape? Watch how Pueblo Bonito is an ancient celestial observatory.
The following geometric concepts are introduced:
- Center
- Radius
- Diameter
- Chord
- Intercepted arc
2. The Geometry of the Roman Pantheon
Watch this video clip to learn about the Roman Pantheon and how it uses the properties of circles. The interior of the Pantheon is one large circular shape. Also the opening at the top, the Oculus, is also a circle. Light from the sun comes through the Oculus, and it is the only source of light for the Pantheon. As you look at the interior of the Pantheon, think of other buildings that you've seen that have a similar interior.
The following geometric concepts are introduced:
- Center
- Radius/radii
- Diameter
- Chord
- Inscribed Angle
- Intercepted Arc
- Central Angle
3. Constructing a Model of the Roman Pantheon with the TI-Nspire
In this video construct a simple model of the interior of the Roman Pantheon using the TI-Nspire graphing calculator. All keystrokes are clearly shown for constructing this shape. In this model the Oculus of the Pantheon is modeled by a single point. You'll also see the relationship between a central angle and an inscribed angle that define the same intercepted arc.
The following geometric concepts are introduced:
- Line
- Intersection point of a line and circle
- Intersecting chords
- Constructing an intercepted arc
- Constructing a central angle
- Constructing an inscribed angle
- Angle/angle measurement
4. The Significance of the Oculus
In this video continue we look at the significance of the Oculus and what its architecture would have communicated. The previous model from our geometric construction had the Oculus as a single point. In the next construction we model the oculus as a line segment through which a column of light, modeled by two parallel lines, shines into the Pantheon.
5. Constructing a Better Model of the Roman Pantheon with the TI-Nspire
In this video we continue to model of the Pantheon, with a more accurate rendition of the Oculus. A proportional line segment models the opening of the Oculus. A column of light is modeled using parallel lines. The measurement of the resulting intercepted arcs reveals more about the architecture of the Pantheon.
The following geometric concepts are introduced:
- Parallel lines
- Arc length
- Radians
- Scale drawing
- Converting radians to degrees
6. Coming Full Circle with the Pantheon
In this video we come full circle and see how the measurement of the intercepted arc from the previous construction relates to the four key dates when light shines through the main door of the Pantheon.
