Euler and the bridges of Konigsberg.

The recent edition of NUMB3RS carried a passing mention of the bridge of konigsberg problem. As always no more details a brief mention and couple of graphics.

One of Euler’s popular triumphs was the solution to the problem of bridge of konigsberg. The river Pregel, known now as Pregolya runs through Konigsberg, which in Euler’s day was in Prussia (It’s now in Russia and called Kaliningrad)

The river divides, creating two islands in centre of the town and Konigsberians built seven bridges to span it. It had be a challenge among the citizen to see if any one could walk around the town, crossing each bridge once and only once and return to starting point.

Euler proved in 1735 that the task was impossible. His proof is often cited as the birth of topology where the actual physical distance between points is irrelevant. It was the network of connections between different paths of the town that was important to Euler’s solution.

Romancing the infinity!

The taste of infinity in William Shakespeare’s Romeo and Juliet play.

My bounty is as boundless as the sea, My love as deep; the more I give to thee, The more I have, for both are infinite.  – William Shakespeare

Sure enough weird things happen at infinity!

Andre Weil

Andre Weil on Kurt Godel’s Incomplete theorem.

God exists since mathematics is consistent, and the Devil exists since we cannot prove it.

Chidambara Ragasiyam!

The one of the most sane and intriguing mega serial (Chidambaram Ragasiyam) had come to an end last Sunday. I happened to stumble upon this post in forum hub by Naga. I hope this is the same Naga who directed the serial.

I think this may be of some interest to you all………..
The song which had the ragasiyam………..

” vithiyil valaiyum vayirudan vanthE
vakuththoru yukthi vyAdhiyum muRRa
midhakallenavum makothiramum kAN
madiyumudivinil mAnagalagaluvanE
thiRakka vidaiyithai panaiyathaneNthAn
vekuyirupaththil dhiyAnam mEvininai.……”

And the associated code………….

01010100 01001000
01001001 01001100
01001100 01000001
01001001 01010100
01001000 01000001
01010010 01010101

Incidentally sreeramtcs, i have heard that (if not the binary system as applied in the modern day computers) writing the numerals in base five, base two etc., was known even to Baskara when he wrote “Leelavati”…

[Congrats to one and all for the century!]
_________________
Naga
Aha! magic dramas by “air”

Sum

1 + 1 = 3

For larger values of 1

Gauss – Paucca sed matura

 

It is interesting to note that Gauss’s prime motivation was not fame and recognition but personal understanding of subject he loved. His seal bore the motto Pauca sed matura (Few but ripe). Unless a result had reached full maturity it remained an entry in his dairy or a doodle at the back of his table of logarithms. 

For Gauss, Mathematics was private pursuit. He even encrypted entries in his dairy using his own secret language. For example July 10, 1796 Gauss wrote Archimedes famous declaration ‘
Eureka’ followed by the equation. 

Num = ∆ + ∆ + ∆  

This represents his discovery that every number can be written as sum of three numbers from the list of triangular numbers 1, 3, 6, 10, 15, 21, 28… 

No one is able to unravel what Gauss meant when he wrote on October 11, 1796 ‘Vicimus GEGAN’ . Some blame Gauss’s failure to disseminate his discoveries for holding back the development of math by half a century. 

Source: The Music of Primes – Du Sutoy. You can also read about Gauss at Wolform , Wikipedia 

Sampark

Sampark is a user friendly software prepared and supplied free of cost by the Income Tax Department. It may be used for preparing returns of income from comfort of home or office. Knowledge of tax laws and provisions not essential. Income Tax Department encourages free duplication for multiple usage…

Download link

Wondering why not provide a simple Excel file for the task?