## RWA Basic Geometric Definitions

### Topic

The \begin{align*}4^{th}\end{align*} dimension

### Vocabulary

- point
- line
- plane

### Student Exploration

#### Can our brains see the \begin{align*}4^{th}\end{align*} dimension?

**Can our brains see the \begin{align*}4^{th}\end{align*} dimension?**

“For someone who's only known life in two dimensions, 3-D would be impossible to comprehend. And that, according to many researchers, is the reason we can't see the fourth dimension, or any other dimension beyond that” Go to the link to learn more...

http://science.howstuffworks.com/science-vs-myth/everyday-myths/see-the-fourth-dimension.htm

The \begin{align*}4^{th}\end{align*} dimension? http://sprott.physics.wisc.edu/pickover/fourth.html

http://www.mathopenref.com/plane.html

### Extension Investigation

- Discovery Dimensions Activity - Have students bring in photos, maps, magazine pictures to draw one. They will identify and label points, lines, planes along with representations he first, second and third dimensions in their 2-dimensional photo.
- What do hamburgers have to do with Geometry? Find out here - Have http://www.keycurriculum.com/products/supplementals/patty-paper-geometry Have students do a patty paper investigation of points, lines, and planes http://www.summitlearning.com/pdfs/DG202118.pdf
- Have a class discussion about what the fourth dimension might be. Next have groups of students research and report on theories about the fourth dimension.
- Have students watch Flatland as an introduction to the basic building blocks of geometry.

#### Layering (optional)

For more exploration of dimensions...

**Flatland: The movie**

“*Flatland: The movie* is based on one of the best mathematical tales ever written. Inhabiting a two-dimensional world populated by polygons and ruled by circular tyrants, a bright young hexagon, through sheer mathematical willpower, imagines a third dimension.” Read more at...

http://plus.maths.org/content/flatland-movie

**Official Movie Website**

http://www.flatlandthemovie.com/

**Flatlander Extension Activities**

http://www.geom.uiuc.edu/video/sos/materials/dimensions/

**The Shape of Space Movie**

“*The Shape of Space*, The Geometry Center's last production video, is based on Jeff Weeks' book, *The Shape of Space*. The 11-minute video and supplementary classroom materials are appropriate for middle school and high school mathematics students: More information at http://www.geom.uiuc.edu/video/sos/

**The Shape of Space Movie on You Tube**

### Resources Cited

http://www.mathopenref.com/plane.html

http://www.geom.uiuc.edu/video/sos/

http://www.youtube.com/watch?v=Uzd484Mvm2k

http://plus.maths.org/content/flatland-movie

http://www.flatlandthemovie.com/

http://www.geom.uiuc.edu/video/sos/materials/dimensions/

http://science.howstuffworks.com/science-vs-myth/everyday-myths/see-the-fourth-dimension.htm

http://www.summitlearning.com/pdfs/DG202118.pdf

http://www.keycurriculum.com/products/supplementals/patty-paper-geometry