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.