Significance & Application

PIVOT! History & Background Explanation of Mathematics Significance & Application References

Why do We Care?

To some this idea of every two isometries is one singular isometry is enough to decide to care and show love to isometries. However, not everyone is a nerd the fascinating things to learn about different isometries are endless. Through translations, rotations, and reflections, a singular shape can end up anywhere else on the coordinate plane. While the two dimensional plane is fun to explore the different possibilities of isometries. The third dimension is where things come to life.
Try this applet of moving the couch up the stairs, just like in FRIENDS.

PIVOT Applet

The possibilites with three dimensional transformations are endless. Just like that previous video explained. Through the different transformations we gain matrix rules for them, which can lead to great leaps and bounds in graphic design, 3D printing, animation, etc.. The math behind these transformations full so much of our lives now, including movies and video games.
Referring back to our beloved sitcom characters we now have a deeper understanding of how isometries work and we are able to determine that there are multiple ways to get from point a to b. Using the Euclidean coordinate plane may simplify compared to the third dimension, but we can still use our knowledge of isometries to make our lives a little easier.