Parabolic art, coordinate system and spirals.

At the end of the Kamehameha Technology conference a few of us discussed my presentation on incorporating art into the math classroom.

One of the people realized the foundation of the piece of parabolic art to the left is the x-y coordinate system. 

It would be so easy to write directions up using coordinates to describe the placement of the lines running from the x axis to the y axis.

Each line would have two coordinates associated with it, a beginning and an end.  In addition, all the coordinates would contain a zero for one of the coordinates since the lines begin and end on the axis.  Admittedly, students would need to use graph paper for it, either actual paper or digital paper.

This gives students the opportunity to practice their graphing skills, remembering how to read coordinates, and produce a piece of art.  If you would rather not use the x and y axis as the starting point, you could just as easily translate or move it 5 units left and 3 units down so the center is at (-5,-3) instead of (0.0).  This way you are introducing transformation into the design and practice.

In addition, it wouldn't be that hard to include the shrink and stretch so one axis is twice the length of the other.  This would mean you might use 1/2 inch distance on the stretched axis and 1/4 inch on the shrunk axis.  You could also have students rotate the figure to add another element of transformations to the activity.

So one activity can be used to have students practice using the coordinate plane and play with transformations to create art work.  These ideas came out of a short discussion among three math geeks who were thinking of ways to make the art as part of the actual lesson.

Another topic we discussed was starting incorporating a Pythagorean Spiral in a geometry class by having students use compasses to draw the perpendicular line to create the 90 degree angle. 

In addition, the leg of the next triangle can be found using a compass or protractor depending on the skill required.   Students can also calculate the hypotenuse for each triangle in the spiral. 

It would be possible to include a short lesson on the Nautalis and the mathematics involved in it.  It shows a connection between real life and mathematics which is something students really need.

Again the above ideas came after my presentation from other math teachers who are taking the basics and adjusting them to meet the needs of their class. 

Math teachers rock.

Let me know what you think, I'd love to hear.