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Maria Regina CollegeBoys’ Junior Lyceum
MATHEMATICS PROJECT COMPETITION
MATHEMATICS PROJECT COMPETITION
This is open to all students who are in forms 3 and 4 during the scholastic year 2009 − 2010.
The competition is open to teams of two students.
All participants will be awarded a school- based certificate of participation.
The best five entries will be chosen to represent the school in the national competition and will each receive a prize.
These five will be awarded a national certificate of participation.
Furthermore, the first three placed teams in the national competition will receive a prize.
A statistics project
A number of charts (not more than three)
A Power Point presentation
Mathematical models
Participants would need to produce one of the following:
On any one of the themes below:
The Story of NumbersSymmetry Archimedes Magic Squares Newton The Golden RatioFibonacci Numbers
Women Mathematicians The Story of Pi (π)FractalsCircles Conic Sections TrianglesTessellations (Tiling) Polygons
Prime Numbers Quadrilaterals Pythagorean Triples Mathematics in the Press Pascal’s Triangle The Theorem of Pythagoras Graphs
Examples of Mathematical Models
Straw Geometrical Models
Conic Sections model
Fractal Tree model
Quilt of Symmetries
The Story of Numbers
Babylonian (3100 B.C.)
ANCIENT EGYPT
ANCIENT EGYPT
MAYAN (c. 2000 BC to 250 AD)
ROMAN
INDIAN 100AD
SYMMETRY
In nature
Carpet Design
Rotational Symmetry
Archimedes
Magic Squares
NEWTON (1642 – 1727)
The Golden Ratio
Fibonacci Numbers
1,1,2,3,5,8,13,21,34,55,89,144,…
Women Mathematicians
Hypatia of Alexandria
350AD
She wrote a commentary on the 13th volume of the famous Greek mathematics text book, 'Arithimetica'.
Women Mathematicians
Sophie Germain(1776)
Initially, she worked on number theories and gave many an interesting theorems on prime numbers. Many such numbers are now called as "Sophie Germain primes".
The Story of Pi (∏)
∏=
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989…
FRACTALS
Fractals are, simply put, repetitions of an object or pattern at different scales. This concept and the math behind it have become studied more recently due to the availability of computer generated images. Fractals are beautiful to observe when created by computers, but are also readily observable in nature.
Snowflake
Serpinsky Triangle
Star fractal
H Fractal
Fractals in Nature
A fractal that models the surface of a mountain
Circles
Circle crops
Circles in nature
Conic sections
Gravitational orbits
The orbits of some of the planets (e.g., Venus) are ellipses of such small eccentricity that they are essentially circles, and we can put artificial satellites into orbit around the Earth with circular orbits if we choose.
The orbits of the planets generally are ellipses. Some comets have parabolic orbits; this means that
they pass the Sun once and then leave the Solar System, never to return.
The gravitational interaction between two passing stars generally results in hyperbolic trajectories for the two stars.
ORBITS
Plotting parabolas
Drawing an Ellipse using string and thumb tacks
Triangles
The Bermuda Triangle
Musical Instrument
Delta wings
Greek Delta
TESSELLATIONS
Two shape tessellation
3 D Tessellation
Tessellations in Art
Old Maltese Floor Tiles
Polygons
Sum of Interior angles
Polygon Frameworks
Prime Numbers
Prime Factors of 1050
Quadrilaterals
Cyclic quadrilaterals
Forming a Parallelogram
Mathematics in the Press
Electoral Results
Sports results
Cartoon 1
Cartoon 2
What ?
Pascal’s triangle
The Theorem of Pythagoras
Symmetrical Pythagorean Fractal
Graphs
Bar Chart
Line graph
Pie chart
Travel Graph
Pythagorean triples
( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17) ( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)
Proposals are to be made to your Mathematics teacher by Monday 30th November 09.
Completed projects are to be handed in not later than Monday 18th January 2010.
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