vilokanam autumn 2014

8/11/2019 Vilokanam Autumn 2014

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Unsung

Mathematician

heorem Simplied

Dot.Net

Konstant story

Puzzles

Eden Project

Dont worry about your difculties in Mathematics. I can assure you mine are stillgreater! -Albert Einstein

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Would you believe it!

QUOTED

The Fibonacci Sequenceis encoded to be 1/89because1/89 = 0.1 + 0.01 + 0.002+ 0.0003+ 0.00005 +0.000008 + containingthe Fibonacci numbers inthe same fashion.

According to the BirthdayProblem, in a room of just23 people, there is a 50%chance that two peoplewill have the same birth-day.

If you shufe a deck ofcards, chances are thatthe exact sequence ofcards appearing backhas never been seen inthe whole history of theUniverse.

There is not enough

space in the Universe towrite down the numberGoogolplex which is 100raised to 100100.

There are 10! or 3628800seconds in exactly 42daysor 6 weeks.

Vi

lokan

am

Axiom

,TheMathematicsClub

IN ISSUE

UNSUNG MATHEMATICIAN

P.C. MAHALANOBIS

AUTUMN ISSUE 2014

Prasanta Chandra Mahalanobis (29 June1893 28 June 1972) was an Indianapplied mathematician precisely a

statistician. He is well-known for his D2statistic and pioneering contributions to

large scale sample surveys. He played a his-toric role in modernizing the Indian Statisti-

cal System including 5 year economic plansand contributions to Statistical Systems

of other countries as Chair of the UN Subcommission on Statistics. He is known as

Father of Indian Statistics.He graduated in Mathematics and

Physics from Cambridge University and at therequest of the Indian Government

undertook some work on prevention of

oods in various regions of the country.His recommendations resulted in allevia-

tion of the problem of ooding to a greatextent. Agricultural surveys, Economic and

Population census, and various other largescale and in depth samples and surveys

that have been admired for their scope andaccuracy owes its popularity and world-

wide acceptance to the genius of this man.He was a visionary entrepreneur who loved

innovation. It is betting that we celebrateThe Statistics Day on June 29, to honor

his memory on his birth anniversary whichprovides us a great opportunity for creating

public awareness about importance of sta-tistics and taking lessons from his outstand-

ing contributions in the eld of statistics andeconomic planning.

The sciences do not try to explain, theyhardly even try to interpret, and they mainly

make models. By a model is meant a math-ematical construct which, with the addition

of certain verbal interpretations, describes

observed phenomena. The justication ofsuch a mathematical construct is solely and

precisely that it is expected to workP.C.Mahalanobis proved this.


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FOUR COLOUR THEOREM

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We all have seen the graph paperson which we draw and plotegularly. It is a simple grid of boxes

and lines. In general, any diagramon a two-dimensional surface, be itormed out of loops, straight or curvedines and common points can roughlybe called a graph. It has two features-he lines called the edges and theirntersection points called the vertices.Graphs are of verymportant utility for usbecause any analysiswe perform on not-

so-simple patternsike fractals comerom our knowledge

of graphs. Theirstudy is called GraphTheory or EuclideanString Theory. Withhe development

of Set theories,

graph theorieswere formulated ataccelerating rates and nally came toa halt. The reason for the halt was nothat mathematicians had reached the

end of the topic (which they NEVERdo, by the way), it was because athis point, the theories had become so

complex that it was nearly impossibleo prove them by hand as they wouldequire thousands of pages of hand

work. The science came to an endabruptly due to human incapacity.

t was only in the late 1900s that theequisite technology was developedo continue work in this eld. This made

graph theory win the prize to possesshe rst ever theorem to be proved

using a computer. This theorem is the

amous Four Colour Theorem. It is a very

simple conjecture proposed in 1852,stating that any contiguous (meaninglogically covering the available areacompletely) graph can be colouredcompletely using only four distinctcolours such that no two adjacentparts of the graph (which share atleast two vertices and an edge) arecoloured same. It was proved by K.Appel and W. Haken who used a

computer algorithmand a compositemap of 1,936 graphsto prove the theorem

in 1976, more than acentury later than itwas proposed. When itwas proved, most of themathematicians refusedto believe in it, becausethe computer aidedproof was impossible toverify using hand work.

The duo argued thatthe technique used bythe program was simple and reliable-it simply coloured the maps in fourcolours and used the smallest fourcolour patch to show that this patchformed the subset of all of the 1,936maps, making it true for the completemap as a whole and thus proving itsvalidity.

The theorem is a very interesting one- ithas the record for most numbers of falsecounter-examples and disproves! Thereason for this is that when they triedto prove it, they were simply dejectedwith the length and effort of the proof.This encouraged mathematicians tobelieve that this theorem must be falseand thus gave many counterexamples

which were actually false.


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Ask your friend to choose a number between 1 and 9 but is not allowed to choose

the number 8. Multiply the number by 9. Multiply this product by 12345679 (no 8!).Example: Take 7, multiply with 9 and then with 12345679.

7 x 9 x 12345679 = __________Find the product and see for yourself what you get! Have fun with your friends!!

Have an interesting trick or fact to share? Wanna ask a question to us?? Dont

hesitate to drop a mail at [email protected]

TRICK OF THE EDITION!

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KONSTANT STORYFor an instance, the easiestway to get an idea is tothink of a graph in whichall the parts or divisionsof the graph touch eachother. Lets say that thereare two concentric circlesand there are four sectionsof the annulus so formed.If we colour the centralcircle with a particularcolour, we tend to thinkthat we have to colourthe four adjoining partsin four different colour,

tricking us believe that theTheorem cant be true. Butwhen we look closely, wesee that we just need tocolour the adjacent partsin different colours and notthe whole gure. The latestproof for the theorem, alsousing a general purposetheorem-proving software,

was given in 2005.The theorem has foundseveral applications,especially in gene mappingand development in theprocessor architecture. It isnow succeeded by manyother statements of GraphTheory which relates

the colour of the edgesrather than the regions.


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QUEST

GREATER THAN SUDOKU

BANACH-TARSKI PARADOXEver wished to break your cell phone into two when you are too angry or

frustrated? Well, lets do it in an awesome way! How about breaking it into

some number of pieces and, if you liked your phone and you want it back,reassembling those pieces into two exactly identical phones? As strange it

may sound but mathematically speaking, this is very much possible. This iswhat the famous Banach- Tarski Paradox says for a solid ball that can be

thought to consist of innitely many points. It is one of the most intriguing

theorem of set- theoretic geometry and is called a paradox because it

dees normal sense of geometry. Go gure!

Find the next numbers in the sequence:

120, 602, 403, 304, _, _

Do send us your answers in our facebook page (look for QR code on last

page)

Each of the numbers 1 to 9 must

appear exactly once in each

row, column, and block. In

addition, adjacent cells mustobey any greater than (>)

or less than (


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Geometry begins with a measly lildot,

Smallest of thing-the faintest ink blot.

Tinier than the brain of a bee,Of the order of a drop in the sea.

As Emaciated as the thinnest hair,

Minutely minute like its not even

there.

Adjoining to one if other is sent,Together they constitute a line

segment.

If 3 such sticks are joined end to end,A Triangle is formed with 3 bends.

Adding one more when u say its 4,

Square stands outside knocking our

door.

Dot after dot build a circular place,

But 3-D view would take more space.

And when these dots step out of the

ring,The nal shape is an interesting thing.

When all are connected; what does

appear?

A big ball of points-a genuinesphere!!!

Empower imagination with dots from

the

super-set,For the geometry of the world is a big

dot.net

Te Dot.NetKEN-KEN

HITORI

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Numbers allowed are from 1 to the Gridsize. Do not repeat a number in any row

or column. The numbers in each heavi-ly outlined set of squares, called cages,

must combine to produce the targetnumber in the top corner of the cage us-

ing the indicated operation. A numbercan be repeated within a cage as long

as it is not in the same row or column.

Black out some of the digits in the grid so thateach row and each column contains distinct

digits. Black cells must not touch each otherhorizontally or vertically. It must be possibleto visit any white cell from another white cell

using horizontal or vertical paths.


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ABOUT US

E

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E

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P

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O

J

EC

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AXIOM- a statement or idea which people accept as being true. Going by that no-tion, The Mathematics club of National Institute of Technology, Rourkela is proudly

named as AXIOM.

AXIOM tries to explore the fun part of Maths and solve riddles pertaining to real lifescenarios. All the things around us are in some way or the other connected to Math-

ematics and AXIOM tries to seek this symbiotic connection. In accordance with that,

a lot of events, workshops and lectures are also endorsed for both the institute and

school-going students at various levels. All in all, AXIOM is the perfect blend of grow-ing through learning with an assortment of Mathematics involved!

Designed by:

AXIOM, Te Mathematics ClubGet Connected:www.facebook.com/axiom.nitr

The Eden Project, in South West England has geodesic domes made up of

hexagonal and pentagonal cells. The building has taken its inspiration from plants,

using Fibonacci numbers to reect the nature within the site! Theres even more math

to be found in the building structure, which is derived from Phyllotaxis, the mathemat-ical basis for most plant growth (opposing spirals are found in many plants, from pine

cones to sunower heads).

vilokanam autumn 2014

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