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THE BEAUTY OF MATHEMATICS- Collected from The Internet and Various Books to enrich The students and Teachers. SUPPORT with YOUR COMMENTS ...

Tuesday, November 2, 2010

CHOCOLATE PUZZLE

A shop sells chocolates @ Re.1 each. You can exchange 3 wrappers for 1 chocolate.


If you have Rs.15/- how many chocolates can you get totally????
 
 
Find the solution..
 
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SOLUTION:
 
22 CHOCOLATES

 for  15 rupees you get 15 chocolates.
on returning 15 wrappers you get 5  chocolates.
on returning 3 wrappers  (keeping two wrappers in hand) you get 1 chocolate.
now this one  chocolate. wrapper and the twp wrapers you had will add on three.
atlast on returning 3 wrappers you get 1 chocolate.


i.e.,   15+5+1+1 = 22

Monday, August 30, 2010

MATHS AND NATURE

"The laws of nature are but the mathematical thoughts of God"
                                                                                      - Euclid

Mathematics is everywhere in this universe. We seldom note it. We enjoy nature and are not interested in going deep about what mathematical idea is in it. Here are a very few properties of mathematics that are depicted  in nature.
SYMMETRY

Symmetry is everywhere you look in nature .

Symmetry is when a figure has two sides that are mirror images of one another. It would then be possible to draw a line through a picture of the object and along either side the image would look exactly the same. This line would be called a line of symmetry.

There are two kinds of symmetry.

One is bilateral symmetry in which an object has two sides that are mirror images of each other.

The human body would be an excellent example of a living being that has bilateral symmetry.




Few more pictures in nature showing bilateral symmetry.










The other kind of symmetry is radial symmetry. This is where there is a center point and numerous lines of symmetry could be drawn.

The most obvious geometric example would be a circle.



Few more pictures in nature showing radial symmetry.























SHAPES

Geometry is the branch of mathematics  that describes shapes.

Sphere:

A sphere  is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball.

The shape of the Earth is very close to that of an oblate spheroid, a sphere flattened along the axis from pole to pole such that there is a bulge around the equator.






















Hexagons:

Hexagons are six-sided polygons, closed, 2-dimensional, many-sided figures with straight edges.

 
For a beehive, close packing is important to maximise the use of space. Hexagons fit most closely together without any gaps; so hexagonal wax cells are what bees create to store their eggs and larvae.
















Cones:

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.

Volcanoes form cones, the steepness and height of which depends on the runniness (viscosity) of the lava. Fast, runny lava forms flatter cones; thick, viscous lava forms steep-sided cones.















Few more cones in nature:

































Parallel lines:

In mathematics, parallel lines stretch to infinity, neither converging nor diverging.

These parallel dunes in the Australian desert aren't perfect - the physical world rarely is.

















Fibonacci spiral:

If you construct a series of squares with lengths equal to the Fibonacci numbers (1,1,2,3,5, etc) and trace a line through the diagonals of each square, it forms a Fibonacci spiral.

Many examples of the Fibonacci spiral can be seen in nature, including in the chambers of a nautilus shell.




 
 
 
 
 
 
 
 
 
 
 
 

Thursday, July 29, 2010

VAMPIRE NUMBER

The vampire numbers were introduced by Clifford A. Pickover in 1994.

A Vampire number z  is a number which can be written as a product of two numbers x and y  containing the same digits the same number of times as the vampire number. Here x and y are called FANGS.

FOR EXAMPLE:

1827 can be written as a product of two numbers 21 and 87.
i.e., 1827 = 21 * 87
Here the digits 1,8, 2,7 are repeated  the same number of times but in different order. 21 and 87 are called fangs.

A true Vampire number isa number which can be written with 2 fangs having the same number of digits not both ending in zero.

FOR EXAMPLE :

1260 is a vampire number, with 21 and 60 as fangs, since 21 × 60 = 1260. However, 126000 – 210 × 600 – is not, as both 210 and 600 have trailing zeroes.

All vampire numbers must clearly have an no. of digits.


Some vampire numbers:
 117067 = 167*701
124483 = 281 * 443
536539 = 563 · 953
23287176 = 2673 * 8712.




Vampire number having two distinct pairs of fangs :


125460 = 204 *615 = 246 * 510

Vampire number having three distinct pairs of fangs :

13078260 = 1620*8073 = 1863*7020 = 2070*6318

Tuesday, June 22, 2010

SIMPLE MATH PUZZLES

PUZZLE 8

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

PUZZLE 9

The following multiplication example uses every digit from 0 to 9 once (not counting the intermediate steps). Fill in the missing numbers.
7 _ _  *   4 _  =  _ _ _ _ _

PUZZLE 10

Here's a simple multiplication problem in which each letter represents a different digit. Can you solve it?
IF * AT = FIAT

PUZZLE 11:

Write down the next number in this series:

18,46,94,63,52, ?

PUZZLE12:

Find the next letter in the series:

O,T,T,F,F,S,S,E,?

PUZZLE 13:

How many two-digit positive whole numbers are there?

PUZZLE 14:

Find four consecutive prime numbers that add up to 220.





SOLUTIONS
 
PUZZLE 8 : A Decimal Point. 5.9
 
PUZZLE 9 : 715 * 46 = 32890
 
PUZZLE 10 : IF = 41. AT = 35. FIAT = 1435.


PUZZLE 11 : 61. Each is a perfect square read from back to front


PUZZLE 12 : N –  The series is the first letter of the numbers 1, 2,3,4,5,6,7,8, ? .so the next letter is N the first letter of Nine.  1[One],2[Two], 3 [Three], … 8[Eight], 9 [Nine].


PUZZLE 13: 90


PUZZLE 14:  47,53,59,61.
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