Hyperbolic Geometry and the Poincare Disk model formed the basis of a presentation “Enrichment Activities on the Poincare Disk” delivered by Bermuda College Mathematics professor Dr. Ali Arouzi recently at the 20th International Conference on Technology in Collegiate Mathematics in Chicago.
The Poincare Disk model offers several advantages for students to enhance their understanding of the hyperbolic plane through the study of hyperbolic geometry.
His presentation advocated how, through the use of technology, resources and activities could be integrated to encourage students to experiment for themselves.
Dr. Arouzi uses the model during his classes in a range of activities from materials covered in his algebra classes to more advanced topics that require differential and integral calculus.
“I find it most appropriate for those students with various mathematical training,” he said.
Mathematicians typically use hyperbolic geometry to study the curvature of the universe, and on the network flow on the internet. The two most widely used java applet technologies accessed by students are “Geogebra” and “NonEuclid”, which are free.
Dr. Arouzi said the feedback to the presentation was ‘good’. His audience consisted primarily of mathematicians with expertise in differential geometry and technology integration in the classroom, such as MAPLE or Mathematica.
The keynote addresses were delivered by Dr. Maria Anderson from Westminster College and Dr. Eric Mazur, from Harvard University.
Dr. Anderson has been writing and developing curricula for mathematic. She is also known for building iPad games for teaching algebra. Dr. Mazur is a Professor of Applied Physics at Harvard, and a prominent physicist known for his work in nanophotonics.