Mathematics Projects...

Making a 3D Snowflake

2010-06-01T09:40:00.004+05:30

Project Guidelines

2009-05-01T16:15:00.002+05:30

Publish at Scribd or explore others: Essays & Theses Business & Economics Business & Law Non-fiction project mathematics

Mathematical designs using A.P.

2008-12-04T14:03:00.004+05:30

Following students of class X I made beautiful mathematical designs using paper cutting and pasting. They used the concept of Arithmetic Progression (A.P.) while making each design.

Anchal Bajaj
Somya Chopra
Arpana
Anshul Narula
Aditya Wadhwa
Akansh Garg
Here is the slide show.

Scooby string art -2

2008-10-02T00:56:00.002+05:30

Cobra Stich

Scooby string art -1

2008-10-01T23:58:00.002+05:30

Square Stitch...

Icosahedron (using coffee cups)

2008-09-02T11:37:00.002+05:30

Project Making Icosahedron using paper plates

2008-09-02T09:16:00.002+05:30

This week we had fun and learning in our Mathematics Laboratory. Last week I posted an instructional video for making an Icosahedron using Paper plates and cups . Students of my class worked in groups and made amazing 3 dimensional structures.

This is the work done by group 1 of class XB.

Making an icosahedron

2008-08-17T10:01:00.003+05:30

This time I have to show you the unimaginable imagination capabilities of using creativity in making a 3 dimensional mathematical structure. I am so fond of doing things differently. This video is a true reflection of what I expect from my students to try and experiment. Mathematics is not so a phobia kind of a thing. This is something which somebody says when he/she is not ready to accept the truth and the truth is one must atleast try once.

Just watch it !!!

This is taken from Weekend Picnic projects. Here is the link for instructions of making an icosahedron.
Thanks for such an interesting resource.

Playing with match sticks

2008-07-22T10:19:00.001+05:30

Dear students ,
some of you are making a maths project on match sticks activities. Please use the following links, you will find useful information which will help you in collecting ideas.

Mathematics Project Idea

2008-06-03T18:43:00.001+05:30

Frequency of letters / words in a language

ObjectiveAnalysis of a language text, using graphical and pie chart techniques.

Description
1.Select any paragraph containing approximately 250 words fromany source. e.g. newspaper, magazine, textbook, etc.
2. Read every word and obtain a frequency table for each letter of thealphabet as follows
Letter Frequency
A
B
C
D
...
X
Y
Z
3. Note down the number of two-letter words, three-letter words, …. so onand obtain a frequency table as follows
Number of words Frequency
2 letters
3letters
4 letters
....
4. Select 10 different words from the text which have frequency greater than 1. Giveranks 1, 2, 3, …., 10 in decreasing order of their frequency. Obtain a table as follows
Word Frequency
on
it
......
5. Investigate the following
From table 1
a) What is the most frequently occurring letter?
b) What is the least frequently occurring letter?
c) Compare the frequency of vowels
d) Which vowel is most commonly used?
e) Which vowel has the least frequency?
f) Make a pie chart of the vowels a, e, i, o, u, and remaining letters. (The piechart will thus have 6 sectors.)
g) Compare the percentage of vowels with that of consonants in the given text.
From table 2
a) Compare the frequency of two letter words, three letter words, ….. and so on.
b) Make a pie chart. Note any interesting patterns.
From table 3
a) The relation between the frequency of a word to its rank.
b) Plot a graph between the frequency and reciprocal of word rank. What do youobserve? Do you see any interesting pattern?
c) Repeat the experiment by choosing text from any other language that you knowand see if any common pattern emerges.

Making e Snowflakes

2008-05-23T13:20:00.001+05:30

Dear students,
Some of you have choosen Paper folding and cutting as the strategy for making mathematics project. I was exploring some ideas of making paper snowflakes and I noticed the following link :

Making e snowflakes

Use this for making snowflakes and save images and upload them on the KHMS e Mathematics.It is very enjoyable and creative project.

Here is one example

Iris Folding Project

2008-02-25T20:54:00.001+05:30

This is a beautiful card made using iris folding technique.
Iris folding is a technique that originated in Holland. Color coordinated strips of folded paper are taped into place over a pattern, creating a spiralling design that resembles the iris of an eye or camera.
To learn more about it visit the following link.

About Iris Folding

free patterns

We are proud of such a creative student!!

Showing Models

2008-01-28T16:29:00.000+05:30

Today, it was an examination day for grade 10 D students. All of them brought their mathematics projects and models. Look the confidence and happiness on their face. They love mathematics!!

Here is the slide show.

BubbleShare: Share photos - Find great Clip Art Images.

Making Paper Snowflakes

2008-01-05T08:57:00.001+05:30

I have shared work done by students of class X F who worked on creating paper snowflakes on the Mathematics Projects blog .

Click on the following link to read about it.

Paper Snowflake Project.

Making Paper Snowflakes

2008-01-05T07:40:00.002+05:30

Snowflakes

Students created incredible ,highly creative paper snowflakes and explained mathematical concepts of symmetry and congruency of geometrical shapes involved.

Making of paper snowflakes utilises the concept/idea of paper folding and cutting which is Kirigami.

They used the following Web links ...

Making Paper Snowflakes
All information about Paper Snowflakes
Dave's Page instructions 6 identical points , 6 pointed pattern, 8 point pattern
Making interactive flakes

Making interactive flakes
Making 3D Snowflakes

Have a look at Paper Snoflakes created by following students.

All students enjoyed making snowflakes .

Podcasting Projects...

2007-12-10T15:37:00.000+05:30

Today, students of class IX A recorded their mathematics podcast projects. Their recorded projects are uploaded on http://mykhmsmathclass.mypodcast.com

The separate links are given below...

http://mykhmsmathclass.mypodcast.com/2007/12/Utility_of_maths_in_various_fields-63679.html By Harshvardhan, Nandan, Mukul, Anuj, Jatin and Madhur
http://mykhmsmathclass.mypodcast.com/2007/12/Application_of_mathematics_in_Indian_Governmenta_podcast_project-63666.html By Vijay, Puneet, Vineet, Rishabh,Paras and Vishal

Also, some of the students shared their experience on learning mathematics through mathematics activities and using math blog. Links of their podcast are given below.

Experimenting with Geoboard

2007-11-16T12:42:00.000+05:30

Historical background
Georg Pick (1859 - 1942) ,discovered a theorem ,which allows us to find the area of any polygon that is embedded on a lattice or grid. It is especially useful for concave polygons, for which the usual textbook area formulas do not work.

Some Important Terms
Lattice points : Points in the coordinate plane with integer coordinates.

Geoboard : Mathematical tool used to explore basic concepts in plane geometry such as perimeter, area or the characteristics of triangles and other polygons.

The nails fixed on the geoboard are called the lattice points.

What is Pick's theorem?
If the number of lattice points on the boundary of the polygon is ‘b’, and the number of lattice points inside the polygon is ‘i’, then the area ‘A’ of the polygon is given by Pick's Theorem:
A = i + b/2 −1.

Material Required
Physical Geoboard
few rubber bands

To make a Geoboard
Piece of wood
Some nails

Procedure

Making a Geoboard

http://mathematicsprojects.blogspot.com/2007/07/making-geoboard-and-exploring-geometry.html

Experimenting with Pick's theorem
Make any geometrical shape using a rubber band.

Count the number of lattice points which are inside the figure.

In this figure number of lattice points inside the polygon = 14.

Now,count the number of lattice points touching the rubber bands.

Value of ‘i’ = 14
Value of ‘b’ = 14
(in this case)

Using the formula calculate the area.

A=i + b/2 –1

=14 + 7 – 1

= 20 sq unit

On dividing this polygon into regular shapes and then calculating the areas using formulae results the same answer.

Get a dot paper from the link

http://mathforum.org/trscavo/geoboards/dotpaper.html

Java applet http://www.cut-the-knot.org/Curriculum/Geometry/Geoboard.shtml

Geometry in nature

2007-07-25T18:46:00.000+05:30

Dear students,
I came across this slide show while searching ,something related to geometry in nature. I liked it and sharing it with you. Look how the geometrical shapes are hidden in the nature.

This album is powered by BubbleShare - Add to my blog

Exploring a dodecahedron

2007-07-25T10:44:00.001+05:30

This Project is contributed by Kapil Khurana XF

Aim Exploring a dodecahedron

Material required

Procedure
Step 1. Take a blank sheet and draw the outline of a CD .

Step 2. Now find out the centre of the circle formed by drawing two chords and their perpendicular bisectors and draw one radius and produce it slightly out of the circle .

Step 3. Now taking the centre and with the help of a protector make an angle of 72 degree .

Step 4 . Repeat the process till the first radius and the last radius also make an angle of 72 degree .

Step 5 . Now put a CD over it and mark the meeting points of CD corners and these lines

Step 6 .Now join all five points on the CD obtained by the previous step
Step 7 . Now cut the CD along these lines
Step 8. Repeat all the previous steps to form 11 more polygons of CD and hence we have 12 CDs

Step 9 . Now paste the two sets CDs with the help of M seal in the following manner

Step 9 . Put the two sets over one another and paste them very carefully
Step 10. Cover all the boundaries with tape and then paint it with a permanent marker to give it a metallic look

A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. It has twenty (20) vertices and thirty (30) edges.

The Dodecahedron has been a source of metaphysical interest for at least 2000 years. Like a crystal or gem, its facets and symmetries compel our eyes and hearts to observe life more deeply. Some have believed that the Dodecahedron represents an idealized form of Divine thought, will, or idea. To contemplate this symbol was to engage in meditation upon the Divine. Today many people believe there is a lost knowledge residing in the past, slowly being rediscovered. It is known that figures like Pythagoras, Kepler, and Leonardo, among many, were educated in these Sacred Geometries, and held many beliefs about them and their role in the Universe .
This is a very creative work done by Kapil. He has utilised e-waste for making such a useful mathematical model.I would like to thank him on behalf of the members of Planet Infinity.

Math In nature

2007-07-23T18:25:00.000+05:30

I came across this photograph, and really liked it. It is showing the incredible beauty in nature and mathematics too. It is depicting the Fibonacci sequence.

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. It begins with the number 1, and each new term from there is the sum of the previous two.

Project on Sieves method.

2007-07-18T11:40:00.002+05:30

This album is powered by BubbleShare - Add to my blog

This project is contributed by Harmeet X F.

Project on magic square

2007-07-16T16:44:00.001+05:30

This album is powered by BubbleShare - Add to my blog
This project is contributed by Arushi Bansal X F.

Making a Fractal Card

2007-07-13T16:27:00.000+05:30

Q. What is a fractal ?

Ans. A fractal is a shape which is repeated many times at different intervals . They are similar to each other . In other words , if we magnify one portion of the fractal card then it will look like the whole fractal.

Fractals were introduced by IBM scientists Benoit Mandelbrot while studying geometrical figures like structure of coastline and lightening flashes .

Trees branching, rivers meandering, lightening zigzagging, insects whirring and birds wheeling in the sky...flames leaping, metal fracturing, earthquakes rendering…all trace fractal paths through space and time. Processes in lungs, bile duct system, bowel and kidney, in the neutral networks in the brain, in the placenta and the heart, in the ways we walk and talk, are full of fractals. Each of the topics contains examples of fractals in the arts, humanities, or social sciences.

AIM:
To create paper sculptures of fractal shapes by cutting and folding paper.

MATERIAL REQUIRED :
Geometry box , white ivory sheet , black pastel sheet , big ruler , scissors , cutter , fevicol , box board sheet .

Step 1: Take a rectangular white ivory sheet with dimensions 24x11 inches.

Step 2: Draw lines on both sides at a distance of ½ inches. Leave 1 inch as a border.

Step 3: Draw diagram of the design of fractal card we are willing to represent. Draw the lines darker than the previous ones.

Step 4: According to the diagram, cut the vertical lines. Use a cutter to cut the lines.

Step 5: Draw crease on horizontal lines according to the diagram. Use a scale and an empty refill of gel pen to draw creases.

Step 6: Fold along the creases properly. Wrinkles should not be there on the card.

Step 7: Similarly, complete other folds according to the diagram .

Step 8: Take a box board sheet. Cut to squares of 13 inches. Box board sheet should be very hard.

Step 9: Take a black pastel sheet. Cut a rectangle of dimensions of 26x13 inches.

Step 10: Paste the black rectangular sheet (26x13”) on the two square sheets (13”). Keep the two square sheets adjacent to one another, so that they are joined together through the black sheet. This becomes a folder.

Step 11: Paste the final fractal card on this folder.The final Fractal Card looks like…..This is really a beautiful fractal card.

Making a geoboard and exploring geometry

2007-07-13T16:23:00.001+05:30

Aim To make a geoboard and verify properties of geometrical shapes on it.

IntroductionA geoboard is a device often used to explore basic concepts in plane geometry such as perimeter, area or the characteristics of geometrical figures.It was invented and popularized by Egyptian mathematician Caleb Gattegno in the 1950's

Material Required

•A wooden board•A white chart paper•Fevicol•Sketch pen•Nails•Hammer•Rubber bands

Procedure

Step 1- Take a wooden board of size 12inches x 12inches

Step 2- Take a white sheet of paper and cover one side of the board with it.
Step 3-Now, with a sketch pen, draw 11 lines horizontally (parallel to length) and 11 lines vertically (parallel to breadth) leaving a gap of 1 inch between every line
After completing step 3, the board will look like this
Step 4-Now,hammer the nails on the points where vertical and horizontal lines intersect each other. Now the geoboard is ready.
ExperimentTake a rubber band and stretch it along 6 horizontal and 4 vertical nails, so as to form a rectangle of size 5in.x3in.Now calculate the number of squares(1inchx1inch), inside the rectangular figure. The number of squares inside the rectangular figure i.e. 15 is equal to area of that rectangle.ProofArea of rectangle= length x breadthArea of rectangle= 5 x 3 sq.inchesArea of the rectangle= 15 sq.inches
UtilityIt can be used to calculate areas of regular and irregular shapes.

Making Shapes using Tangram Pieces

2007-07-12T16:48:00.001+05:30

This project was made by Mansi of XB

BubbleShare: Share photos - Cheap Printer Ink

Mathematics Around

2007-07-12T12:01:00.001+05:30

Pictures clicked by Jigyasu X F

Musical Instruments and Mathematics

2007-07-10T11:14:00.001+05:30

Explore the various musical instruments in the music room and try to find out mathematics in them.Observe their shapes. Find out the reason of their unique shape.

Have fun.

Pascal Triangle Link

2007-07-09T11:16:00.001+05:30

Dear Students,
Use this link for your project on Pascal's triangle.
http://ptri1.tripod.com/

Making Platonic Solids

2007-07-09T10:44:00.001+05:30

This Project is contributed by Sahil XB

Aim:To make Platonic solids and verification of Euler's formula , F - E + V = 2
where , F represents number of faces , E represents the number of edges and V represents number of vertices .

Introduction
A platonic solid is a polyhedron all of whose faces are congruent regular polygons and where the same number of faces meet at every vertex.
Platonic solids are 3 – dimensional solids bounded by regular polygons which are equilateral triangle , square and regular Pentagon . They are only five in number , namely cube , Tetrahedron , Octahedron , Dodecahedron and Icosahedron .

There are 5 platonic solids
Why??

The Greeks recognized that there are only five platonic solids.

The key observation is that the interior angles of the polygons meeting at a vertex of a polyhedron add to less than 360 degrees. To see this note that if such polygons met in a plane, the interior angles of all the polygons meeting at a vertex would add to exactly 360 degrees.

About Leonard Euler...
Born April 15, 1707Basel, Switzerland
Died September 18 ,1783St Petersburg, Russia
Nationality Swiss
Field Mathematics and physics
Pre requisite Knowledge...

Knowledge of a regular polygon
and vertices , faces and edges of 3D solids
Material Required
Nets of Platonic solids ,a pair of scissors , transparent sheets (OHP sheets) ,a marker , cello tape , compass and a ruler.
What is a net of a solid?
A net is a form of skeleton-outline in 2-D which when folded results in a 3-D shape .
For example . A tetrahedron net a dodecahedron net
an icosahedron net

an octahedron net

a cube net

My observations

The interior angle of an equilateral triangle is 60 degrees. Thus on a regular polyhedron, only 3, 4, or 5 triangles can meet a vertex. If there were more than 6 their angles would add up to at least 360 degrees which they can't. Consider the possibilities:3 triangles meet at each vertex. This gives rise to a Tetrahedron .

The tetrahedron also has a beautiful and unique property ... all the four vertices are the same distance from each other! And it is the only Platonic Solid with no parallel faces.

Tetrahedron Facts
•It has 4 Faces
•Each face has 3 edges, and is actually an Equilateral Triangle
•It has 6 Edges
•It has 4 Vertices (corner points) and at each vertex 3 edges meet

cube Facts
•It has 6 Faces
•Each face has 3 edges, and is actually a Square
•It has 12 Edges
•It has 8 Vertices (corner points) and at each vertex 3 edges meet
Since the interior angle of a square is 90 degrees,therefore atmost 3 squares meet at a vertex.

A cube is called a hexahedron because it is a polyhedron that has 6 (hexa- means 6) faces.
Cubes make nice 6-sided dice, because they are regular in shape, and each face is the same size.

Octahedron Facts
•It has 8 Faces
•Each face has 3 edges, and is actually an Equilateral Triangle
•It has 12 Edges
•It has 6 Vertices (corner points) and at each vertex 4 edges meet
4 triangles meeting at a vertex,gives rise to an octahedron.

It is called an octahedron because it is a polyhedron that has 8 (octa-) faces, (like an octopus has 8 tentacles)

Icosahedron Facts
•It has 20 Faces
•Each face has 3 edges, and is actually an Equilateral Triangle
•It has 30 Edges
•It has 12 Vertices (corner points) and at each vertex 5 edges meet
5 triangles meeting at a vertex gives rise to an icosahedron.

It is called an icosahedron because it is a polyhedron that has 20 faces (from Greek icosa- meaning 20)

Dodecahedron Facts
•It has 12 Faces
•Each face has 5 edges, and is actually an Equilateral Triangle
•It has 30 Edges
•It has 20 Vertices (corner points) and at each vertex 3 edges meet
3 pentagons meeting at a vertex, gives rise to a dodecahedron.

It is called a dodecahedron because it is a polyhedron that has 12 faces (from Greek dodeca- meaning 12)

Experimentation with Platonic Solids.

Now I will verify the Euler’s formula .
* F - E + V = 2
where , F represents number of faces , E represents the number of edges and V represents number of vertices .
Firstly, take a solid e.g. an octahedron. Using a pin and thermocol balls , mark the vertices.

It is observed that there are 6 vertices.

Now, count the number of faces.Using a marker ,number them.
It is observed that there are 8 faces.

Now, count the number of edges.

It is observed that there are 12 edges.

Now ,In an octahedron V= 6

F= 8

E= 12

Therefore, V+F-E= 6+8-12 =2

Thus Euler's formula is verified.
Similarly the formula is verified for other solids also.

This is a creative project done by Sahil.He has made beautiful Platonic Solids and experimented on them.

Tangram My Way

2007-07-07T16:41:00.001+05:30

This work is contributed by Khilesh X F.
It was a wonderful experience for me working on such as interesting topic.I also taught my elder brother and sisters about tangram and how to play with it. I enjoyed working on this topic.
Firstly, On a square board I made the tangram lines according to the instructions given .
1. Draw a square ABCD of side 5 inches.
2. Joint BD
3. Mark mid point of BC as E and CD as F.
4. Joint EF.
5. Mark mid point of EF as G and BD as H.
6. Join AHG.
7. Mark mid point of DH as I and HB as J.
8. Join FI and GJ.
9. Cut all 7 pieces and make the figures.

Tangram is the oldest Chinese puzzle. It consists of seven pieces called tans.
5 right isosceles triangles( 2 small ,1 medium size ,2 large size )
1 square
1 parallelogram

Then I made various shapes and figures using the 7 shapes.

Geoboard is Fun!

2007-07-07T16:17:00.001+05:30

This project is contributed by Tushar Bansal X B

Aim To make a geoboard and verify properties of geometrical shapes on it.

Introduction
A geoboard is a device often used to explore basic concepts in plane geometry such as perimeter, area or the characteristics of geometrical figures.
It was invented and popularized by Egyptian mathematician Caleb Gattegno in the 1950's

Material Required
•A wooden board
•A white chart paper
•Fevicol
•Sketch pen
•Nails
•Hammer
•Rubber bands

Procedure
20th June 2007(starting date of project)
Step 1- Take a wooden board of size 12inches x 12inches

Step 2- Take a white sheet of paper and cover one side of the board with it

Step 3-Now, with a sketch pen, draw 11 lines horizontally (parallel to length) and 11 lines vertically (parallel to breadth) leaving a gap of 1 inch between every line

After completing step 3, the board will look like this

Step 4-Now,hammer the nails on the points where vertical and horizontal lines intersect each other.
Now the geoboard is ready.

Experiment
Take a rubber band and stretch it along 6 horizontal and 4 vertical nails, so as to form a rectangle of size 5in.x3in.Now calculate the number of squares(1inchx1inch), inside the rectangular figure.
The number of squares inside the rectangular figure i.e. 15 is equal to area of that rectangle.
Proof
Area of rectangle= length x breadth
Area of rectangle= 5 x 3 sq.inches
Area of the rectangle= 15 sq.inches

Utility
It can be used to calculate areas of regular and irregular shapes.

Its a very useful device to learn various geometrical results and verify them .

Good Job!

Students Sharing Experiences

2007-07-05T10:44:00.000+05:30

Dear students,
Today I thought of having your reviews about this new way of learning and doing mathematics. Please write about your experiences of your e-mathematics laboratory giving a reference of any incident/instance by which you have gained any knowledge. Post your experience in the comment box with your name ,class and section mentioned.

Thanks

Making Clinometer

2007-07-03T21:26:00.001+05:30

This Project is contributed by Mohammad Wasif X F

Introduction
WHAT IS TRIGONOMETRY?

THE WORD TRIGONOMETRY IS DERIVED FROM THE GREEK WORDS:
I)TRIGONO AND 2)METRON.THE WORD TRIGONON MEANS A TRIANGLE AND THE
WORD METRON MEANS A MEASURE.HENCE TRIGONOMETRY MEANS THE SCIENCE OF MEASURING TRIANGLES.
Line of sight:- is the line drawn from the eye of an observer to the point in the object viewed by the observer.
Angle of depression:-of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.
Angle of elevation:-of a point viewed is the angle formed by the line of sight with the horizontal when the point being viewed above the horizontal level.
A clinometer is an instrument that measures vertical slope, usually the angle between the ground or the observer and a tall object, such as a tree or building.

Aim :-TO MAKE A CLINOMETER
Material Required :
1-Protactor
2-Straw
3-Stone
4-Thread

Procedure
Step 1 Get a protractor with one straight edge (a 180 degree protractor).

Step 2
Tape a straw along the straight edge of the protractor.

Step 3.
Tie a string through the small hole on the straight edge that is directly across from the 0 degree mark on the protractor. This may also be labelled as 90 degrees. If your protractor does not have a small hole here, or if the hole is not situated correctly (this is a common problem with some cheap protractors), tape or glue the string to the protractor at this mark. Make sure the string dangles a few inches below the protractor.

Step 4
Attach a washer or fishing weight to the dangling end of the string.

Step 5
Sight the top of a tall object through the straw.

Step 6
Note the number where the string crosses. Subtract this number from 90 to determine the angle of elevation between your eye and the top of the object you are sighting

In the above case I measured the angle of elevation and observed that the angle is 36 degrees. According to the above rule I will have to subtract the measured angle with 90 degrees. So the angle of elevation is 90 degrees -36 degrees = 54 degrees.

Conclusion:
From the above discussion we have seen that we can easily find out the heights and distances without any actual measurement. We used only clinometers to measure the angle of elevation & angle of depression. with the help of trigonometric formulae's we can easily find out the height and distances.
Astronomers can easily find the distance of stars from earth with help of trigonometric formulae's.

Resources:

Planet infinity.
Mathematics Encyclopedia.

I would like to congratulate Mohammad on behalf of Planet Infinity for doing such a wonderful job.

Srinivasa Ramanujan

2007-07-01T13:01:00.001+05:30

Mathematician SRINIVASA RAMANUJAN AIYANGAR used to say ' An equation means nothing to me unless it express a thought of god' Ramanuja .

The Indian mathematician made substancial contribution to the analytical theory of numbers and worked on elliptic functions,continued fractions, and infinite series .S.R.Ramnujan is best known for his work in hypergeometry and continued fractions.
Ramanujan ,born into a poor family of brahmin at irode inon Dec.22,1887,attended school in nearby Kumbakonam. By the time he was 13 ,he could solve unaided every problem in Loney;s Trignometry,and at 14 he obtain the theorems for the sine and the coisine that had been anticipated by L.Eular .
In 1903 he came upon George Shoobridge Carr's Synopsis of Elimentary Results in Pure and Applied Mathematics.The book'its coverage reaching 1860,opened a whole new worldto him'and he set out to establish the 6,165 theorems in it for himself having no contact with other good books ,he had to do Original research for each solution. Trying to device them several new algebraic series.
In 1911 he started to publish some of his results.
In January 1913 Rmanujan sent some of his work to G.H.Hardy,Cayley lecture in mathematics at Cambridge . Hardy noticed that whereas Ramanujan had rediscovered , and gone gone for beyond,some of the latest conclusions of western mathematician,he was completely ignorant of western mathematician, he was completely ignorant of some of the most fundamental areas.In may the University of Madras gave Ramanujan a scholarship .
In 1914 Ramanujan went to Cambridge .The universities experience gave him considerable sophistication , but his mind , by this time somewhat hardened,generally continued continued to work according to the old pattern ,in which intutions play more important role than argument. In Hardy's opinion ,if Ramanujan's gift had been recognised early,he could have become one of the greatest mathematicians of all time. In hypergeometric series and continued fractions ,"he was unquestionably and intutions made him the greatast formalist of his day . But his passionate ,profolic,and in some ways profound work in the theory of numbers and his ways profound work in the theory of numbers and his ways profound work in the theory of numbers and his work in analysis were seriously marred by misdevelopment.
In 1918 Ramnujan was elected a fellow of the Royal Society and o fellow of Trinity College,Cambridge.
He died on April 26,1920.

Article contributed by Mansi X B

Making Icosihenagon

2007-06-30T13:32:00.001+05:30

This project is contributed by Pooja Kumar X B
Aim To make an ICOSIHENAGON (a 21-sided polygon)… with one long continuous piece of thread.

Material Required
1.Ply wood.
2.A long continuous thread or wool.
3.Nails and hammer.
4.Geometry box

Introduction
Icosihenagon is also known as icosikaihenagon and henicosagon. The adjective and noun icosikaihenagon means a plane figure with 21 straight sides.
An icosihenagon is created by a long continuous piece of thread. This project shows that maths can also be explained with the help of creativity. As in this project a continuous thread shows that an Icosihenagon has 21 sides.
Procedure

Step 1
Draw a large 21-point circle on a sheet as it helps in space the nails evenly in a circular shape on the design backing. So that it looks like…..

Step 2
Take a ply wood, lay the design template on it and press small nails through each of the 21 points forming one circular ring.

Step 3
After pressing the pegs through the 21 points carefully pull the paper off the board.
Step 4
Now, Take a thread and tie its one end around the top peg, then follow the following steps:
1.Skip 0 pegs, and
wrap thread around
the 1st peg.
2.Skip 1 peg, and wrap
thread around the 2nd
peg.
3.Skip 2 pegs, and wrap thread around the 3rd peg.
4.Skip 3 pegs, and wrap thread around the 4rt peg.
5.Skip 4 pegs, and wrap thread around the 5th peg.
6.Skip 5 pegs, and wrap thread around the 6th peg.
7.Skip 6 pegs, and wrap thread around the 7th peg .
8.Skip 7 pegs, and wrap thread around the 8th peg.
9.Skip 8 pegs, and wrap thread around the 9th peg.
10.Skip 9 pegs, and wrap thread around the 10th peg.

STEP5
After the first 10 steps, make a mark on the piece of paper.

STEP6
Now start the 10 steps over again from the previous 10th peg.
After the second set of 10 steps are complete, make a second mark on the piece of paper. Repeat the 10 steps 21 times.

The following is obtained after after completing set of 10 steps 18 times.

After completing set of 10 steps 21 times tie off the thread on the final peg. So that it looks like…..
STEP7
Remove the marks from the board.

And finally it looks like………

Resources taken from
http://www.mykhmsmathclass.blogspot.com/
http://www.google.com/

Working with thread is a great fun. Different types of polygons and patterns can be created by using a continuous piece of thread.

It is a great effort put by Pooja and her parents. I would like to thank them on behalf of Planet Infinity K.H.M.S.She has proved that mathematics is not a dull subject and there is a lot of scope of creativity in it.

Moving Sculpture & Geodesic Dome

2007-06-24T18:49:00.001+05:30

A moving sculpture and Geodesic dome

Try making a moving sculpture made from paper. I find this information interesting for making models in the mathematics laboratory.

http://sci-toys.com/scitoys/scitoys/mathematics/paper_ring.html

There is one more model making description on this URL which is called a Geodesic Dome.For more detail click on the above link.

Paper snowflakes

2007-06-20T19:03:00.002+05:30

How to make interesting,creative snowflakes?

http://highhopes.com/snowflakes.html

Sundial

2007-06-20T19:01:00.001+05:30

Know about Sundials

http://en.wikipedia.org/wiki/Sundial

How Sundials work?

http://liftoff.msfc.nasa.gov/Academy/Earth/Sundial/Sundial-how.html

Make Sundials.

http://www.sundials.co.uk/projects.htm#edial

Sundials on internet

http://www.sundials.co.uk/

Prime numbers Sieves method

2007-06-14T10:41:00.001+05:30

This project is contributed by Harshit Thakur X B

Title Prime Numbers Eratosthenes’ Sieve

Introduction
Eratosthenes(ehr-uh-TAHS-thuh-neez)
Eratosthenes was the librarian at Alexandria, Egypt in 200 B.C.
Eratosthenes was a Greek mathematician, astronomer, and geographer.
He invented a method for finding prime numbers that is still used today.
This method is called Eratosthenes’ Sieve.
A sieve has holes in it and is used to filter out the juice.

Eratosthenes’s sieve filters out numbers to find the prime numbers.

Some basic knowledge
Factor – a number that is multiplied by another to give a product.

7 x 8 = 56
7 and 8 are the factors of 56

Factor – a number that divides evenly into another.

56 ÷ 8 = 7
8 is a factor of 56.

Prime Number – a number that has only two factors, itself and 1.
7 is prime because the only numbers
that will divide into it evenly are 1 and 7.

Procedure
Step 1 On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.

Step 2 Cross out 1;it is not prime.

Step 3
Remember all numbers divisible by 2 are even numbers.

So leaving 2, cross all multiples of 2.

Step 4.
To find multiples of 3, add the digits of a number; see if you can divide this number evenly by 3; then the number is a multiple of 3.

e.g.
2 6 7
Total of digits = 15
3 divides evenly into 15
267 is a multiple of 3

So, leaving 3,cross all multiples of 3.

Step 5.
To find the multiples of 5 look for numbers that end with the digit 0 and 5.
e.g.
385 is a multiple of 5
& 890 is a multiple of 5
because the last digit
ends with 0 or 5.

So, leaving 5, cross all multiples of 5.

Step 6. Similarly, leaving 7 cross all multiples of 7.

Step 7 Leaving 11, cross all multiples of 11.

Step 8 All the numbers left are prime numbers.

Conclusion
The Prime Numbers from 1 to 100 are as follows:
2,3,5,7,11,13,17,19,
23,29,31,37,41,43,47,
53,59,61,67,71,73,
79,83,89,97

Quincunx Board

2007-06-13T18:53:00.001+05:30

This project is contributed by Sheetal Aggarwal X-B

Overview
The Quincunx Board, also called the Galton Board, was named after Sir Francis Galton. This structure consists of a triangular array of pegs. Small balls, according to the space left between consecutive pegs, are dropped onto the top peg. These balls bounce their way down and move either towards the right or left on hitting a peg. At the bottom, they are collected in small bins.

But it is interesting to note that if there is an equal chance of bouncing left or right, most of the balls tend to fall in the bins towards the middle. If the graph of the data is made, then the ‘bell-shaped’ curve of normal distribution can be seen.

Aim of the project
The aim of our project is to make a Quincunx board and visualize the curve of normal distribution. We will see what happens when we pass 100 balls through the quincunx board.

Material Required
To make a Quincunx Board, we require the following material
•Plywood
•Enamel Paints
•Nails and Hammer
•Cardboard and Covering paper
•Geometry box
•Marbles

Procedure
STEP 1: Firstly, take the piece of plywood and paint it.

STEP 2: After it dries, draw the lines and dots on which you want to fix the nails……

……so that it looks like this.

STEP 3: Fix nails into the board at the marked points. Then cut the plywood.

STEP 4: Paint numbers from 1 to 11 under the spaces between the nails in the bottom row.

STEP 5: Make a bin using cardboard and cover it. The bin should be big enough to keep the board in it.
Now it’s ready!

STEP 6: Drop 100 balls on top of the board and record how many balls fall through specific spaces. Then draw the graph of your observations.

On dropping 100 marbles through the Quincunx board, these were my observations-

Slot No..............No. of balls
1......................... 2
2.........................0
3.........................4
4.........................15
5.........................11
6.........................27
7.........................22
8.........................10
9.........................8
10......................1
11......................0
The graph appears to be like

This resembles to the graph of a normal curve.
We can get even better results by using more marbles.

We saw that most of the balls ended up in the middle bins. So, after performing this activity, we can conclude that in a quincunx board, if all the balls have an equal chance of bouncing left or right, a large proportion of them will fall in the center and we will be able to see a skewed version of the curve of normal distribution.

Extension
You can take a look at Pascal's Triangle. In fact, the Quincunx is just like Pascal's Triangle, with pegs instead of numbers. The number on each peg shows you how many different paths can be taken to get to that peg. Amazing but true.

References
I have picked up some of the information for my presentation from the following sites-

http://www.mathsisfun.com/
http://www.wikipedia.org/

This is a great effort by Sheetal and her Parents. I would like to thank them on behalf of all the members of Planet Infinity, K.H.M.S.

Sierpinski Tetrahedron

2007-06-04T16:54:00.001+05:30

Sierpinski tetrahedron project

Click on the given link to find the details
http://classes.yale.edu/fractals/Labs/SierpTetraLab/SierpTetraLab.html

Optical illusions

2007-05-28T23:13:00.002+05:30

Dear students,

You can make a project on optical illusions. Check out for the reasons behind each one of them. Some of the illusions are shown in the slide show.

Know About Mathematicians(1)

2007-05-28T23:09:00.002+05:30

Dear students,

You can collect information about the famous mathematicians and their contribution.

Mathematics around you

2007-05-22T19:01:00.001+05:30

Do you see some mathematics in these pictures?
Definitely yes.

Make a project on finding mathematics around you.
in the house...
in the garden...
in the market...
in the bank....
in the nature...
so on
I think its a great idea.It will not only add to your knowledge but also enhance your creativity .Click real photographs and make a beautiful project.You can make a slide show on http://www.slide.com/ and send it to me through E-mail.

All the Best

Project idea ''Mathematical Rangolis"

2007-05-16T19:17:00.001+05:30

Dear students,

This is a great idea for making a mathematics project.You can explore the Rangoli patterns and search for the mathematics hidden behind each pattern .It is not necessary that you work on the given patterns,however you may choose any of the patterns.Take atleast 10 patterns.

Keep on working

2007-05-12T22:24:00.000+05:30

Karmanye Va Dhika Raste, Ma Fhaleshu Kadhachana...
Keep doing your part of work
Don't expect the fruits for your work.
Don't remain idle.
Expect nothing in return for whatever you do.
He will be decidingthe results for your efforts.
The efforts should continue without thinking of their fruits as anything done for enjoyment enslaves us to desire.
Whatever one does with desire binds us to the cycle of birth and death." – Bhagavad Gita

Make an Icosihenagon

2007-05-12T21:51:00.002+05:30

Dear Students,
Creativity plays an important role in all the fields.You can choose this idea of making an icosihenagon for your math project.For knowing more about it, click on the following link.

http://www.mathcats.com/crafts/icosihenagon.html

Fun activity...

2007-05-10T10:35:00.000+05:30

Dear Students,

This is an activity to be done by all of you.
Find the day of the week on which you were born.

Click on the given link...

http://www.mathsisfun.com/games/dayofweek.html

So let me know the day...

First 10 students names will be posted in the Hall Of Fame.
Write your answer in the comment box in the following format

Name ...............
Class/Sec..............
D.O.B ...............
Day ...............

Have Fun!

Platonic Solids guidelines

2007-05-10T10:20:00.001+05:30

For making and exploring Platonic solids click on the given link.

http://www.mathsisfun.com/platonic_solids.html

8 Project Ideas

2007-05-09T22:20:00.001+05:30

1. Types of numbers

Discuss the different number types and explain the relationships between the types.· Explore the followingnatural numberswhole numbersintegersrational numbersirrational numbersetc.· Write the information about the origin of various types of numbers.· Explore the information about the history of numbers.Explorehttp://id.mind.net/~zona/mmts/miscellaneousMath/typesOfNumbers/typesOfNumbers.htmlMake a project on it.

2.Matchstick Games
Matchsticks games link
http://www.puzz.com/matchstickpuzzles.html
You can prepare a project on matchstick games .

3.Number Spirals
Know about number spiral and explore the beauty of hidden mathematics in it.http://www.numberspiral.com/index.html

4. Number Systems of the world
This is an interesting link which contain interesting information about the number systems of the world. Explore this site and make an interesting project.http://www.sf.airnet.ne.jp/ts/language/number.html

5.Fibbonacci Numbers

The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ...
Each number in the Sequence is obtained by summing the previous two numbers.
Observe the sequence and write the next 20 terms.
Explore about it in nature...
For example, when counting the number of petals of a flower, it is most probable that they will correspond to one of the Fibonacci Numbers. It is seen that:o Lilies have 3 petalso Buttercups commonly have 5 petalso Delphiniums have 8 petalso Ragworts have 13 petalso Asters have 21 petalsFind more information of such kind on the internet.
Explore the information about Leonardo Pisano Fibonacci 1170 - 1250
You can take the help from the following link
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

You can make a project on fibonacci sequence and its presence in nature.The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next) .It is called the Fibonacci series after Leonardo of Pisa or (Filius Bonacci), alias Leonardo Fibonacci, born in 1175, whose great book The Liber Abaci (1202) , on arithmetic, was a standard work for 200 years and is still considered the best book written on arithmetic.The following link will help you to gather useful information.http://britton.disted.camosun.bc.ca/fibslide/jbfibslide.htm

6.Symbols in mathematics

In the previous session, one of the students made a project on mathematical symbols,their origin and utility.You can also try this one .Some of the information is given below. Search for more information .

The factorial symbol n!

The symbol n!, called factorial n, was introduced in 1808 by Christian Kramp of Strassbourg, who chose it so as to circumvent printing difficulties incurred by the previously used symbol thus illustrated on the right. The symbol n! for "factorial n", now universally used in algebra, is due to Christian Kramp (1760-1826) of Strassburg, who used it in 1808.

The symbols for similarity and congruency

Our familiar signs, in geometry, for similar, and for congruent) are due to Leibniz (1646-1715.) Leibniz made important contributions to the notation of mathematics .

The symbol for angle and right angle

In 1923, the National Committee on Mathematical Requirements, sponsored by the Mathematical Association of America, recommended this symbol as standard usage for angle in the United States. Historically, Pierre Herigone, in a French work in 1634, was apparently the first person to use a symbol for angle.

The symbol for pi

(This symbol for pi was used by the early English mathematicians William Oughtred (1574 -1660), Isaac Barrow (1630-1677), and David Gregory (1661-1701) to designate the circumference , or periphery, of a circle. The first to use the symbol for the ratio of the circumference to the diameter was the English writer, William Jones, in a publication in 1706. The symbol was not generally used in this sense, however, until Euler (1707-1783) adopted it in 1737.

The symbol for infinity

John Wallis (1616-1703) was one of the most original English mathematicians of his day. He was educated for the Church at Cambridge and entered Holy Orders, but his genius was employed chiefly in the study of mathematics. The Arithmetica infinitorum, published in 1655, is his greatest work. This symbol for infinity is first found in print in his 1655 publication Arithmetica Infinitorum.

The symbols for ratio and proportion

The symbol : to indicate ratio seems to have originated in England early in the 17th century. It appears in a text entitled Johnson’s Arithmetick ; In two Bookes (London.1633), but to indicate a fraction, three quarters being written 3:4.Have fun exploring mathematics.

7.Magic Squares

Click on the given link to know the detail.

http://www.math.hmc.edu/funfacts/ffiles/10001.4-8.shtm

lhttp://members.aol.com/katydidit/numbrfun.htm

http://www.grogono.com/magic/history.php

http://www.markfarrar.co.uk/msqhst01.htm

http://nrich.maths.org/public/viewer.php?obj_id=1337&part=index

http://www.geocities.com/~harveyh/magicsquare.htm

http://www.jcu.edu/math/vignettes/magicsquares.htm

Explore the following:

What is a magic square?

Explore on its historical background.

What is an odd ordered magic square?

Explain methods of making them.

What is a dated magic square?

How to make a dated magic square?

8. Making Koch tetrahedron

Click on the link given below and have fun making Koch tetrahedron http://classes.yale.edu/fractals/Labs/KochTetra/KochTetra.html

The following model of Koch's tetrahedron is made by a student at K.H.M.S. Planet Infinity.

Mathematical Fractal Card, Nine point Circle)

2007-05-06T17:46:00.001+05:30

1.Making a Fractal Card

You can make a fractal card by clicking on this link

http://classes.yale.edu/fractals/Labs/PaperFoldingLab/PaperFoldingLab.html

2. Nine Point Circle

Click on the given link to see the detail

http://www.math.hmc.edu/funfacts/ffiles/10004.2.shtml

Its an interesting activity.