Hip to be square: rubik's cubes and sudoku

Magic squares may seem esoteric, but their cultural impact is evident whenever you open the newspaper or walk into a toy shop. The two most popular puzzles of recent years – Sudoku and the Rubik's Cube – are both consequences of a centuries-long preoccupation with them.

In the 18th century, Leonhard Euler, the greatest mathematician of his day, was devising ways to create magic squares. In order to do this he started looking at another type of square that could be used as a kind of template for producing magic squares.

Euler's new concept was a square in which every number, or symbol, would appear once and only once in each row and column. While these squares had been known about since at least a few centuries before, Euler was the first mathematician to analyse them systematically and he coined their name "Latin square".

He also invented the sister concept in which two Latin squares are superimposed on each other, and such that each cell in the grid is unique. This he called a "Graeco-Latin Square".

In 1782, Euler set the "36 officers problem", a frivolous puzzle that led to much deep academic work and discoveries. Can you make a 6x6 Graeco-Latin made up of six regiments of six officers each of different ranks so that no rank and regiment is repeated in any row or column? Only in 1901 was it proved that this was impossible.

Unlike magic squares, Latin and Graeco-Latin squares have found many uses and applications in non-mathematical settings, for example in cryptography and biological experiments, experimental design.

The best-known occurrence of Latin squares now, however, is in newspapers and puzzle books. Sudoku is a puzzle to complete a partially completed 9x9 Latin square that contains the digits one to nine in each column and row, with the added specification that the 3x3 sub-squares also contain the numbers from one to nine.

The previous puzzle craze to Sudoku was the Rubik's Cube, whose history can also be traced back to the magic square. In the mid-19th century in upstate New York, Noyes Palmer Chapman, an amateur puzzle enthusiast, made a physical model of a magic square such that the numbers from 1 to 16 were on small wooden squares that could be fit in a 4x4 box. He realised that if he left out one of the squares, it was possible to slide the other 15 squares around. This became known as the "15 Puzzle", which was an international fad in 1880 – and is the original sliding block puzzle, versions of which you can still find in toyshops.

In the 1970s Hungarian designer Ernö Rubik was trying to reinvent the 15 Puzzle in three dimensions when he came up with the idea of the Rubik's Cube.

From the magic square to Sudoku we seem to have always liked our puzzle crazes to come in squares – although this is a matter not for mathematicians, but for psychologists.

UNIT 9

Physics

Physics (from Ancient Greek means “nature”) is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.

Physics is one of the oldest academic disciplines, perhaps, the oldest physics was a part of natural philosophy, chemistry, certain branches of mathematics, biology. New ideas in physics often explain the fundamental mechanisms in other sciences. Physics also makes significant contributions through advances in new technologies and in understanding of electromagnetism or nuclear physics led directly to the development of new products, which have transformed modern society, such as television, computers, domestic appliances, nuclear weapons, advances in thermodynamics led to the development of industrialization, and advances in mechanics inspired the development of calculus.

Physics is used to understand the behavior of natural phenomena and proved that every event has a natural cause.

Natural science was developed in China, India and Islamic World between the fourth and tenth centuries BC. Experimental Physics had its debuts with experimentation by medieval physicists.

Classical Physics became a separate science when early modern Europeans used experimental methods to discover laws of physics.

Kepler, Galileo, Newton discover and unified the different laws of motion. Modern Physics started with the works of Einstein both in relativity and quantum physics.