You are currently browsing the tag archive for the ‘cassini’s identity’ tag.

I thought I would share with our chess-loving readers the following interesting (and somewhat well-known) mathematical chess paradox , apparently proving that 64=65, and the accompanying explanation offered by Prof. Christian Hesse, University of Stuttgart (Germany).  It shows a curious connection between the well-known Cassini’s identity (related to Fibonacci numbers) and the 8 \times 8 chessboard (8 being a Fibonacci number!). The connection can be exploited further to come up with similar paradoxes wherein any F_n \times F_n -square can always be “rerranged” to form a F_{n-1} \times F_{n+1} -rectangle such that the difference between their areas is either +1 or -1. Of course, for the curious reader there are plenty of such dissection problems listed in Prof David Eppstein’s Dissection page.

Advertisements

Our other blog

Visitors to this blog

Blog Stats

  • 338,531 hits

Wikio Ranking

Wikio - Top Blogs - Sciences

Current Online Readers

Recent Comments

prof drd horia orasa… on My first post
prof dr mircea orasa… on Inequality with log
notedscholar on Self-referential Paradoxes, In…
prof dr mircea orasa… on Inequality with log
prof dr mircea orasa… on Inequality with log
prof dr mircea orasa… on 2010 in review
kenji on Basic category theory, I
prof dr mircea orasa… on Solution to POW-10: Another ha…
prof drd horia orasa… on Continued fraction for e
prof drd horia orasa… on Inequality with log
prof dr mircea orasa… on Solution to POW-12: A graph co…
prof dr mircea orasa… on The Character of Physical…
prof dr mircea orasa… on Milk and Tea puzzle
prof drd horia orasa… on Inequality with log
prof dr mircea orasa… on The Character of Physical…

Archives

June 2019
M T W T F S S
« Jan    
 12
3456789
10111213141516
17181920212223
24252627282930
Advertisements