# Mathematics

## Markow chain explained in simple words

Markow chain is a probabilistic process used to predict the next step based on the probabilities of the existing related states. Its called a chain because the probability of the next step is dependant on the other steps in the group. For example, if the weather is cloudy then its highly likely that it might rain (The next …

## The Four Color Theorem

Four color theorem states that any given plane figure separated by lines can be colored using not more than 4 colors! First proposed in 1852 when a man named Francis Guthrie who was coloring a map of the counties of England discovered that he was able to color all the adjacent countries using only 4 colors …

## The mysterious and beautiful 6174

My favorite will always be 1.618 (The Golden Ratio) but 6174 fascinated me recently mainly because of the mystery it carries. It was in 1949 when an Indian mathematician named D. R. Kaprekar, devised a process now known as Kaprekar’s operation. This was published in “Scripta Mathematica” which was a quarterly journal published by Yeshiva University. …

## Achilles & The Tortoise Paradox

“In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.” —Aristotle, Physics VI:9, 239b15 Here is another interesting paradox which proves that mathematics can be beautifully strange sometimes. This is a story of Achilles …