Markov Chain in Every Day Life

The picture shows a subway map.  A team of inspectors verifies passengers’ tickets at a station on a line, or all lines through it if there are many lines.  Then they randomly choose the next neighboring station and move there to make their inspection.

subwaymap2

Subway map

How many times higher is the probability of being inspected at station C than at station A?

Are you eager to know the answer? Try yourself before reading how Markov Chain helps to solve the problem. The answer is here.

 

 

The perfect explanation is given in the PBS Infinite Series video:

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Mathematical Beauty

e + 1 = 0

Euler’s identity is often cited as an example of deep mathematical beauty.

Constance Reid: Euler’s identity is “the most famous formula in all mathematics”.

Euler’s Identity is a special case of his formula from complex analysis suggested by Swiss mathematician Euler in  1748.

The identity links five fundamental mathematical constants:

  • The number 0
  • The number 1
  • The number π (π = 3.141 . . .)
  • The number e (e = 2.718 . . .)
  • The number i, the imaginary unit of the complex numbers.

Euler’s Identity “is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth”. – Benjamin Peirce.

aplusclickEulerIdentity

We Lack Numeracy Skills

Alan Smith reported amazing statistics of adult numeracy:

2011 England Survey: 49 of 100 adults lacked of numeracy Level 1 skills (fractions, percentage, and decimals).  The figure is only shocking for 51% of population.

OECD reported (PIAACX2012) that forty percent of USA young people aged 16-19 were below Level 2.

This is statistics. Statistics is a part of mathematics and it is about us as a group.

There are two categories of people who can and who cannot do numbers.

Are You in a category of people who are comfortable with numbers? Check / train yourself at the website A+Click

The Largest Known Prime Number

The largest known prime number was discovered in 2016 by a computer laboratory of the University of Central Missouri .

257,885,161 – 1

is one of the Mersenne primes that can be written in form 2n – 1, where n is an integer.  They are named after 17-century French mathematician Marin Mersenne.

nums

The number written in the decimal form contains 17 million digits.

Pythagorean Triples Were Known 1,000 Years Before Pythagoras

The Babylonian clay tablet from the collection of Columbia University dating from 1,000 years before Pythagoras’s theorem is a trigonometric table which has 15 pairs of numbers forming Pythagorean triples: three whole numbers a, b and c:

a2 + b2 = c2

The tabet is known as the world’s oldest trig table. Babylonians used the base-60 numbers, which permitted many more accurate fractions than the contemporary base 10. For example, 2/3 = 0.6666… (or 40 minutes) was a finite number. The base-60 system were inspired from such shapes as a circle and the regular hexagon (see an example).

Why Is X The Unknown?

Terry Moore explains that the inventors of algebra were Arabic scientists. Their definition:

X = something, some undefined unknown thing = the unknown thing.

When the books were translated from Arabic to Spanish the Arabic unknown was “SH” that did not exist inSpanish. They replaced it by “X“.  It migrated to other European languages 600 years ago.

X is “X” because Spanish language does not have “SH“.

Selfie Math

Jim is going on a tour around the world. He has 5 tops, 4 bottoms, and 3 pairs of footwear. He wants to post a selfie everyday to show different places and his different outfits to his girl-friend Mary, who stays at home. He does not want to wear the same outfit twice. ## For how many days does he have enough clothing?

married

Leslie Green gives the answer : 96 days.

Can you explain why it is 96? What is logic behind?