## Tuesday, September 29, 2009

### PROJECT WORK TOPICS FOR CLASS IX AND X

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Dear All
We are well aware that CBSE is acknowledging the concept of internal assessment in Mathematics for the past three years wherein a student studying in class IX and X is supposed to submit a project work in Mathematics. This project can be in the form of extended learning in the subject or related to real life situations as well. Click here to download the evaluation performa for the same.
I have observed that students are usually confused while selecting the topic for their project work. That is why; I want to share a few possible topics to help them pick up a suitable topic which suits their aptitude and attitude (as separate posts). Students will have the liberty to take the decision of taking up individual or a group projects (though they need the consent of their concerned math's teacher!). I would also discuss (in brief) about each topic and share some related resources which may prove to be helpful.
few suggested topics are:
1. day on given date
2. tessellations
3. fibonnaci numbers
4. paper sizes
5. tower of hanoi
6. divisibility rules for prime numbers
7. unit digit of x^y
8. joseph shooting problem
9. magic squares
10. polyominoes
11. platonic and archemedian solids
12. optical illusion in maths
13. some uncommon results in maths
14. great mathematicians and their contributions
15. vedic maths and its relevance
16. various proofs of pythagoras theorem
17. golden ratio in nature / human body
18. generation of solids- 2d to 3d model
19. working model of ellipse
20. square root spiral
21. soma cube
22. common error in maths
23. fractals (sprinski triangle, kosh snowflake etc)
You are welcome to clarify any of your doubts. Also, do suggest other topics you know about. I would want you to share some more trivia related to already suggest topics. I will be waiting for your response…

All the best and happy reading!

### Believe it or not - 10

Dear All

There are certainly at least two peoples in the world with exactly the same number of hairs on their heads!
(There are more people than the hairs on any one head).

### Believe it or not - 9

Dear all

Descartes (1596-1650) wrote his coordinate geometry without the use of negative numbers.

## Sunday, September 27, 2009

### Believe it or not - 8

Dear All

Believe it or not, three legged stool is more stable than any other stool. The principle underlying is this fact is we can draw only one cirlcle through three given points which are not collinear. That is why old people walk with the assistance of a stick (third leg) , or even think of tripod.

### Believe it or not - 7

Dear All

A plane can be filled with squares, equilateral triangles and regular hexagons. No other regular polygons can fill the plane without gaps.
visit this link to know more.

## Saturday, September 26, 2009

### Solve it - Question 8

Dear All

One of my student (now not studying in CRPF School)shared this math problem with me. Let us all try together to solve it.
check website www.shubhamsuman.co.nr (Must Visit)

The question is as follows:

Let two cyclists A and B start from a point 100kms apart from each other with the speed of 10kms towards each other. As they start a bee takes off from the nose of a cyclist a and heads towards B's nose.It turns back and heads towards A's nose.It continues this back and forth movement till it gets squashed between cyclist.in doing this how much total distance does the bee covers? Given speed of bee is 20 km/hr.

Well, he also shared this piece of information. Hope all the readers will like it...

HANGING NECKLACE
Borrow a necklace from a shop and hold it up in the air by its two ends at the same level so that it hangs downwards.The necklace assumes the shape of a curve.This curve is named as catenoid.
the problem posed by jacob bernoulli was to find the equation for the curve.
the curve is not a parabola.
it was found that
y=a(e^(x/a) + e^(-x/a))/2 + b
a and b are constants
a =depends on physicsal characteristics e.g. density how far ends were held .
b =the placement on x axis which can be 0 also.
ITS APPLICATION
Among all possible shapes that hanging string can assume ,catenary is one for which potential energy of string is minimised .
centre of gravity at this shape of string is at the lowest.
Dip the two identical circular hoops of wire into a soap solution in contact with one another along their entire circumference.Let the hoops be pulled out of soap solution and drawn apart carefully.Soap solution produce s a soap film connecting the two hoops, and the shape assumed by the film is a catenoid.The soap film the shape which minimises the total potential energy.

## Monday, September 21, 2009

### Believe it or not - 6

Dear All

What is the largest number of circles that can touch another circle of equal size? The answer is 6. In case of spheres this number is 12 (total 13). Newton discovered this property in 1694. Believe it or not this property was proved by R. Hoppe only in 1874 after 180 years of its discovery.

## Sunday, September 20, 2009

### MOBIUS STRIP

Dear All

If we take a rectangular strip of paper, then make a half twist and join the ends we come up with a Mobius strip. If we were to draw a line through the center of the strip without lifting the pencil off the paper, we would come back to the starting point but on the "opposite" side of the paper. Logically, this is only possible if the surface has only one side and only one boundary, meaning that while the Mobius strip appears to have two sides, it actually has one.FEW EXPERIMENTS WITH MOBIUS STRIP:

Experiment 1: Draw a line through the center of the strip. We would have to go round the loop twice to get back to the starting point. This is a key feature of the Mobius strip because it's what describes it as a non orientable surface.
Experiment 2: Cut through the center line. In general, if we cut a rectangular strip of paper lengthwise through the middle from end to end, we would expect to get two strips. This is not the case with the Mobius strip. Instead of getting two strips, we get one long strip with two full twists in it. If we cut the strip again through the center line, we come up with two strips wound around each other.
Experiment 3: Cut through the line about one third from the edge. (note: we have to go twice round the loop), we get two separate strips, one of which is thinner, but of the same length as the original strip. The other will be a long strip whose length is twice that of the original strip.
Experiment 4: Cut once round the loop through the line about one third from the edge, then cut through the center line of the resultant thicker strip. We get three strips wound around each other, one in the middle and one on either side.

A strip with an odd number of twists will behave the same way as a Mobius strip, that is, it will have one edge and one side. On the other hand, a strip with an even number of twists will have two boundaries and sides.

APPLICATIONS:

Mobius strips have been used as conveyor belts because their one sided nature allows equal wearing of "opposite sides" of the belt. This makes the belts last longer. The strip has also been used in recording tapes to double the playing time without having to manually take out the tape and change the side playing. It is also used in numerous electronic appliances especially those which have resistors and superconductors.

## Saturday, September 19, 2009

Dear All

National Science foundation organises IMO every year. The benefits of participating in IMO are as follows:

• Every participant of Level I is awarded a Certificate of Participation. Toppers are awarded merit certificate.
• Students get a chance to be assessed at international level and are awarded performance-based rankings.
• Students gain confidence to contest at international level in a world where from admission to elite courses to selection for choice jobs is becoming more and more competitive.
• The spirit of competition and sense of recognition inspire students to excel in the chosen field of study and set higher goals.
• Top three students from each class are awarded Gold, Silver and Bronze medals.
• The top 500 winners (class-wise) are endowed with cash prizes and scholarships, courtesy of the official sponsor.
• Every participant who scores 50% or more is awarded a Certificate of Participation. Toppers are awarded merit certificate.

CLASSES: II TO XII

EXAM FEE: RS 100

EXAM DATE: 10 DECEMBER

SYLLABUS: AS PER CBSE

EXAM PATTERN: 50 MULTIPLE CHOICE QUESTIONS (MCQ) TO BE ANSWERED IN ONE HOUR

HOW TO PREPARE: IMO WORKBOOKS FOR II TO X CLASS ARE AVAILABLE

VISIT www.sofworld.org FOR FURTHER DETAILS

LAST DATE OF REGISTRATION: CONTACT YOUR SUBJECT TEACHER

### Believe it or not - 5

Dear All

There are only five Heronian triangles (triangles having integer sides) such that the perimeter is equal to the area. They are : (5, 12, 13) , (6, 8, 10) , (6, 25, 29) , (7, 15, 20) and
(9, 10, 17). The first two triangles are right triangles also.

### Solve it - Question 7

Dear All

Solve the following problem. Is the remainder theorem applicable here?

Solution:

(Click image to enlarge)

## Saturday, September 12, 2009

### Solve it - Question 6

Dear All

A rectangle with perimeter 44 units is partitioned into 5 congruent rectangles, as indicated in the diagram. Find the perimeter of each of the congruent rectangle.

### Believe it or not - 4

Dear All

Do you think that anything and everything in Mathematics has been discovered till date, or is there a scope for NEWER Maths?
Read below and then think again!!!

The number of periodicals that publish mathematical research papers and articles are given below:

 Prior to 1700 AD 17 periodicals 18th Century 210 periodicals 19th Century 950 periodicals 20th Century 2000 periodicals

According to one estimate every year nearly 2,00,000 (two lakhs, no typing mistake) new theorems and methods appear in the journals and the books.

So... What are you thinking? To derive a new maths formula or result!
Good luck!

## Tuesday, September 8, 2009

### Solve it - Question 5

Dear All

Try this question:

The time on electronic digital watch is 11 : 11. How many minutes before this would the watch have shown a time with all digits identical?

Here is the Solution:

The required digits on the clock before 11:11 would be 5:55 (Note that times like 6.66, 7.77 are not possible).
This gives a time difference of 316 minutes (11 : 11 – 5.55).

### Believe it or not - 3

Dear All

Most of us know that the sum of two sides of any triangle is greater than the third side. But very few of us know that the sum of three sides of a triangle is greater than the sum of the bisectors of the angles of the triangle.

Well... whats about the relationship between four sides of any quadrilateral? any guess....
yes, you are right....
The sum of any three sides of a quadrilateral is always greater than the fourth side.

## Monday, September 7, 2009

### Believe it or not - 2

Dear All

A side of a regular pentagon, of a regular hexagon, and of a regular decagon inscribed in the same circle constitute the sides of the right triangle.

## Thursday, September 3, 2009

### Believe it or not - 1

Dear All

Believe it or not there is no equilateral triangle , the coordinates of whose vertices are all integers.
Well... it can be proved very easily. Try it!

### NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)

Dear all, Please do watch my latest video (dated 10-01-2021) on the topic “NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)” VIDEO LINK HERE...