The responses continue to the study by Dr. Andreescu and his colleagues. Geekdad, a blog of Wired Magazine, has the following article which contains contributions from Mary O’Keefe, mother of IMO team member Alison Miller. Mary hits themes that Richard Rusczyk stressed in his talk, particularly the importance of play and community.
I know that Alison got an enormous sense of belonging out of her first math Olympiad summer training camp experience, and it literally transformed her life. Melanie Wood was a staff member at Alison’s first camp and I think she deserves an enormous amount of credit for her leadership in transforming the culture there. Alison has tried to “pay that forward” by mentoring younger students and helping to create mathematical communities they could enjoy. For Alison and Melanie, I think coaching and mentoring has been even more fun and rewarding than competing.
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Alicia Prieto Langarica continued her tradition of actively engaging the students as they explored deep mathematical concepts. Ms. Langarica began with a discussion of the regular polyhedron and allowed the students to prove for themselves why there can be no more than 5. She then talked about these 5 Platonic Solids and gave some of the cultural context of these important objects.
From this basis, Ms. Langarica was able to describe the wide variety of non-regular polyhedron. As diverse as these objects are, they all have the common properties described by Euler. Ms. Langarica showed how the relationship between the number of vertices, faces and sides would be constant for all of these figures.
To involve the students more directly, the students built their own polyhedron and demonstrated their own diversity and talent. This break activity prepared them for listening to the more challenging portion of the lecture on Minimal Surfaces. Ms. Langarica described the very practical value of finding minimal surfaces to conserve cost or weight in construction projects. She then showed several beautiful examples of minimal surfaces.
By finding the surface normal of any point on a curved shape, Ms. Langarica showed how a minimal surface could be tested or created. To drive this point home, Ms. Langarica took the math circle outside with their polyhedron creations. By dipping these objects into soap bubbles she was able to beautifully demonstrate how minimal surfaces would form spontaneously as a result of the physical properties of the air and soap film.
Ms. Lanagrica has provided her slides from the lecture and answers to the problems. Members of the Metroplex Math Circle e-mail group can download these files from the group site. To join the e-mail group simply click below.
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