Mathematics Projects in the Greater Vancouver Regional Science Fair

PIMS initiated the inclusion of a Mathematical Sciences exhibit category within the existing Science Fairs, which are organized and administered by the Science Fair Foundation of British Columbia. PIMS is committed to informing and involving mathematics teachers, giving presentations and workshops to groups of students, helping and providing assistance to students that have undertaken mathematics projects, judging the projects, and supplying the monetary awards.

At the Greater Vancouver Regional Science Fair (GVRSF) for 2000, there were 25 projects exhibited within the Mathematical Sciences category. These consisted of 13 junior projects (grades 7 and 8), 7 intermediate (grades 9 and 10), and 5 senior (grades 11 and 12). University-Hill Elementary, Point Grey Mini School, and Killarney Secondary School were quite highly represented. Other participating schools were Windermere Secondary, Vancouver Technical, York Hose School, Magee Secondary, Our Lady of Perpetual Help School, Albion Elementary, and Gladstone Secondary. Projects were judged as gold, silver or bronze based on a point system. Among the senior level projects, 2 won silver and 3 won bronze designations: In Magic Squares (silver), a project by Hanson Ng from Windermere, the algebraic properties of odd magic squares when treated as matrices were investigated. Hanson discovered and proved that the product of two magic-square matrices is always a symmetric matrix. The Real Mathematics (silver), presented by Frank Chu and Harold Kwok from Killarney, was a study of the movement of a 3D object using the three axial rotations of its center of mass combined with its translation. The students created a computer program for graphic display of a spinning cube using the underlying mathematics of transformations. For the purpose of a more realistic display they delved into yet another area of mathematics, projective geometry. Connecting the points of the object to the ``eye'' and then calculating where these connecting lines meet the projective plane, the students achieved an impressive ``dancing'' cube on the computer screen. The three bronze projects were Luck or Chance, a calculation of the odds of winning the 649 Lottery, BC49, and Blackjack, Applications of the Derivative: Newton's Method, a study of the Newton's iterative method for numerical approximation of the roots of a function, and The Old Calculator, a comprehensive look at the history and use of the abacus.

One gold, two silver and two bronze medals were awarded at the intermediate level: The gold project, Code CAE, by Vanja Alispahic and David Robertson from Point Grey Mini School, was a study of cryptography and the invention of a genuine encryption method using a time scheme that changed the code with each second. To increase the difficulty of breaking into ciphers, the students successfully implemented other ideas like having the encoded version be independent of the surrounding letters in the original version and not mapping one original to one encoded letter. Beyond the Bars (silver), by Adrian Pau and Scott MacEachern from Point Grey Mini School, was a project exploring an alternative to the standard UPC barcode by incorporating the Morse code for coding letters and numbers. Unraveling the Mathematics of Knots (silver), by Stefanie Leung and Tiffany Yeung from York House School, was a study of the mathematics of knots. The students displayed knots according to their classification and demonstrated simplifications of knots using Reidemeister moves to determine the minimal crossing number invariant. The two bronze projects were Barcode researching, a study of the working theory and the decoding procedure of the UPC barcode and Vitruvian Proportions, a statistics project that tried to determine whether and to what extent the proportions of the human body, given by the Roman architect Vitrivius and depicted by Leonardo's Proportions of Man drawing, actually hold.

At the junior level, 2 projects won gold, 4 silver, 1 bronze, and 1 honourable mention: Polygon PI (gold), by Max Thompson from U-Hill Elementary, was a project that used the squeezing method to find the approximation of PI. Max used the idea of increasing the number of sides of the inscribed and the circumscribed regular polygons and calculating their perimeters to approximate Pi. Using elementary algebra and geometry, he devised the formula that, using the side-length of a regular polygon, calculates the side-length of a regular polygon with twice as many sides. He also displayed charts of how quickly these estimates approach Pi as the number of sides of the polygons increases. Pythagorean Proofs over the Centuries (gold), by Lara Siroti\'c from OLPH, was a study of various proofs of the Theorem. Lara constructed the dissection puzzles to display how each of the studied proofs works. She also constructed them using the dynamic geometry software and displayed their animations. Several applications of the theorem were also presented. Calculating the Number of Squares within the Square Grid (silver), by Mahmoud Bazargan from U-Hill Elementary, was a project to determine the total number of squares inside a general square grid without counting them. Fermat's Last Laugh (silver), by Monica Ray from Gladstone Secondary, was a project that displayed a great interest and careful study of the history of this famous theorem. Monica used two cubes made out of cent-cubes and challenged the audience to make a single cube out of them. Then she explained the history of the 350-year quest for the answer to the Fermat's Last Theorem. Combinations of numbers and letters (silver), by Tiffany Lu from U-Hill Elementary, was a project that studied how many total combinations for BC car license plates and Canada ZIP codes are there with and without letter/number repetitions. Perfect Picks (silver), by Ben Cline from Point Grey Mini School, was a project that explored how one can find an optimum strategy for selecting stocks using Game Theory. The bronze project Where Do You Get Information employed statistics to extract information about library services from a survey conducted in several schools.