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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Not Knowing Math Can Cost $15,000

 

A big number of people can lack basic math skills.

Follow Your Passion in Math

Grow your passion by motivating practice like the 11-year-old Math Marvel

“Chess is a mathematical poem” – Aarushi Maheshwari 

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).

Formula of Love

Professional dancersLove is like π – natural, irrational, and very important.” – Lisa Hoffman

Certain scientists think that love is a chemical state of mind and the formula for love is as follows:

dopamine + seratonin + oxytocin


C8H11NO2 + C10H12N2O + C43H66N12O12S2 

How many atoms  are there in the formula of love?

Answer

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“.