Google Voyager Stories: Quadrilaterals

In this exploration, we will investigate quadrilaterals by looking at different architectural sites. We start with Stonehenge to look at post and lintel construction, then we visit Frank Lloyd Wright's Fallingwater house in Pennsylvania. Each structure is an application of the geometric principles behind quadrilaterals. There is a companion Google Earth exploration found at this link (best viewed in Chrome).

To see the complete collection of Google Earth Voyager Stories from Media4Math, go to this link.

1. Introduction to Quadrilaterals: Stonehenge

To start this lesson, watch this video about Stonehenge, which is an example of post and lintel construction. This is also an example of a basic quadrilateral form used in many architectural structures.

 

2. The Geometry of Frank Lloyd Wright's Fallingwater

Watch this video clip to learn about Fallingwater, its architect, Frank Lloyd Wright, and how it uses rectangular shapes.This segment introduces the concept of rectangles.

In addition the following concepts are introduced:

  • Maximum area
  • Using two congruent triangles to construct a quadrilateral
  • Using two right triangles to construct a rectangle
  • Properties of rectangles

 

3. Constructing a Quadrilateral with the TI-Nspire

In this video construct a quadrilateral using the TI-Nspire graphing calculator. All keystrokes are clearly shown for constructing this type of triangle.

The following geometric concepts are introduced:

  • Parallel and perpendicular sides
  • Side length
  • Parallelograms
  • Formula for the area of any quadrilateral
  • Formula for the area of a rectangle
  • Maximumum area of a quadrilateral

 

4. Properties of Rectangles

In this video learn about the geometric properties of rectangles and why they are used by architects for the interiors of buildings. This video is a continuation of the geometric construction using the TI-Nspire (see previous section).

The rigidity of triangles is contrasted with the flexibility of quadrilaterals. All triangles with the same side lengths are congruent. This isn't necessarily the case with quadrilaterals.

The following geometric concepts are discussed:

  • Parallel sides
  • Square corners
  • Congruent right triangles
  • How rectangles relate to other quadrilateral forms

 

5. Center of Gravity

In this video learn about the center of gravity for a rectangular shape and how Frank LLoyd Wright used this property to build the large balcony for Fallingwater. This video presents the engineering concepts behind building such a balcony.

The following geometric concepts are discussed:

  • Cantilevers
  • Center of gravity
  • Midpoints of rectangular sides

 

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6. Using the TI-Nspire to Find Center of Gravity

In this video learn how to find the center of gravity of a quadrilateral using the TI-Nspire. All keystrokes are clearly shown. Then manipulate the quadrilateral to see what impact that has on the center of gravity.

 

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7. Cantilevers and Torque

In this video learn how the location of the center of gravity affects the weight of a cantilever balcony. Arranging a rectangular balcony in different ways creates a different torque on the cantilever. Then see how Frank Lloyd Wright used reinforced concrete to overcome some of the engineering challenges imposed by the cantilever and center of gravity.

8. Conclusion

In this video, we summarize how important quadrilaterals are to architects and why they are so prevalent in the buildings in which we live, work, and learn.