**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.