Tuesday 12 February 2013




                                                 A WONDER IN EUCLIDEAN GEOMETRY


Years ago, way back in 1980-81, when my daughter Mrs. Mugdhaa was of the age of her daughter Miss. Deekshaa, I was just strolling through a big shop of Toys & Games in Pune, when I spotted a toy containing a square piece of Acrylic, divided into seven pieces as shown below.


                                                     

Just seven plastic pieces of different Geometric shapes, which could be assembled to create a perfect square. That's all there was in the Carton !!
However the toy seemed to be priced quite exhorbittantly at about thirty two rupees. In 1981, that was a pretty stiff price tag.
At least I felt so prima faciae, till I found an instruction booklet  inside the carton, convincing me beyond any doubt whatsoever, that I had accidently found a Goldmine in fact.

The tiny booklet of hardly fifty pages or so, depicted almost fourteen hundred shapes of different objects such as Alphabets, Numerals, Animals, Birds, Boats & Yachts, Aeroplanes, Plants, Buildings.....etc. etc. which can be created with just these seven pieces of a square......... the list is endless.

Even shapes of human beings in different postures also can be replicated with this set of piecs.
The intriguing aspect is the perfect Geometric proportions, of the shapes so created.... it is simply awe inspiring.

After this accident, I have enjoyed literally years of creative pleasure till now, with this gem of a toy.

Next to Chess, I found  this to be the most ingenious game I ever played in my lifetime.
Each one of the shape is a puzzle to be solved, the only conditions being that…..
a>   In every shape all seven pieces are to be used necessarily. There cannot be any left over piece.
b>   The shapes are to be created as exact replicas of the given shape…no deviations are allowed.

Based on the theory of Polygons, and Permutations, it can be mathematically proved that this small toy can create almost 1,58,000 different meaningful shapes & outlines, each one being a puzzle by itself.!!
During last thirty two years, I have been able to solve only 1170 of them. !!!

My daughter was immensely benefitted by this game during her high school age, and presently my grand daughter Miss. Deekshaa, is augering it’s wonderful benefits.

My hats off to the creater of this wonder of Euclidean Geometry, which is a 1200 Yr. old Chinese puzzle, and it is called TANGRAM.
Just click on the link below, to see some of the solved puzzles in this game.

http://ravishankarsgalleryofshapes.blogspot.in/2013/02/awonder-in-euclidean-geometry-years-ago.html


------- R S NANIVADEKAR..
         February 12th 2013.

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