BITS AND PIECES |

AuthorShifa Somji enjoys learning, playing, and reading about chess. Chess4Girls held a chess strategy session with Grandmaster Greg Serper at the Bellevue Public Library. In an engaging session, GM Serper discussed his famous game against Ioannis Nikolaidis. The game was played in 1993 and is endearingly named “The Usurper.” The game highlights an aggressive style of play, one Chess4Girls would like to inculcate in all chess playing girls. Here, I analyze some of the best positions from the game.
The set of moves, leading to the first position found below, are as follows: 1. c4 g6 2. e4 Bg7 3. d4 d6 4. Nc3 Nf6 5. Nge2 Nbd7 6. Ng3 c6 7. Be2 a6 8. Be3 h5 9. f3 b5 10. c5In the first position, even ten moves into the opening, White has a clear advantage. White’s pawns dominate the center and White pieces are far more active than Black pieces. The next set of moves, leading to the second position found below, are as follows: 10. … dxc5 11. dxc5 Qc7 12. O-O h4 13. Nh1 Nh5 14. Qd2 e5 15. Nf2 Nf8 16. a4 b4 17. Nd5This Knight sacrifice, the first example of aggressive play in the game, further demonstrates White’s advantage. The next set of moves, leading to the third position found below, are as follows: 17. … cxd5 18. exd5 f5 19. d6 Qc6 20. Bb5 axb5 21. axb5 Qxb5 22. Rxa8 Qc6 23. Rfa1 f4 24. R1a7 Nd7 White’s rooks dominate the last two ranks of the board, highlighting the benefits of playing aggressively. Most of Black’s pieces are controlled simply by White’s rooks and queen and Black needs to tread cautiously. The final position, 1-0, is the fourth position in the gallery below. While White won convincingly, the amazingly bold style of play made the game a memorable one. Overall, the session was very insightful. Through Serper’s beautiful game, girls who attended the session learned about the power of an aggressive style of chess and how it can be incorporated to win tournament games. Chess4Girls hopes to host more sessions in the future.
0 Comments
AuthorShifa Somji enjoys learning, playing, and reading about chess. The Fibonacci numbers were first introduced by Fibonacci in his book
Liber Abaci. As he was considering the growth of an idealized rabbit population, he noticed that there was one pair of rabbits at the end of the first month, two pairs of rabbits at the end of the second month, three rabbits at the end of the third month and five rabbits at the end of the fourth month. The first ten Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and 55.The rule of the Fibonacci sequence can be viewed in the following way: F0 = 0, F1 = 1, Fn = Fn−2 + Fn−1.The Lucas numbers are very similar to the Fibonacci numbers – the only difference is the starting term. The Lucas numbers were studied by the mathematician Francois Edouard Anatole Lucas. Whereas the Fibonacci numbers start with 0, the Lucas numbers start with 2. However, both the Lucas and Fibonacci numbers have the property that the ratio between two consecutive terms converges to the golden ratio. The first ten Lucas numbers are: 2, 1, 3, 4, 7, 11, 18, 29, 47 and 76. The rule of the Lucas sequence can be viewed in the following way: L0 = 2, L1 = 1, Ln = Ln−2 + Ln−1.The “period” of Fibonacci when reduced modulo n, or Ψ(n), for all integers greater than 1, is the number of terms in the Fibonacci sequence before the sequence repeats when reduced modulo n. One of the first patterns regarding the period is that the period of some composite numbers is equal to the product of the periods of its prime factors. There are also many common patterns between the Lucas and Fibonacci sequences. Each Lucas number can be expressed as the sum of two Fibonacci numbers: Theorem 5.1. Ln = Fn−1 + Fn+1 for all n>1.However, the equation can be generalized further. Conjecture 5.2. For any odd number k ∈ N, Ln · Fk+1 = Fn−k + Fn+kNumerical Examples: n = 6 and k = 5: L6 · F5+1 = F6−5 + F6+5 ⇒ L6 · F6 = F1 + F11 ⇒ 11 · 5 = 0 + 55n = 8 and k = 3: L8 · F3+1 = F8−3 + F8+3 ⇒ L8 · F4 = F5 + F11 ⇒ 29 · 2 = 3 + 55n = 9 and k = 7: L9·F7+1 = F9−7+F9+7 ⇒ L9·F8 = F2+F16 ⇒ 47·13 = 1+610 ⇒ 611 = 611What about for even differences? Conjecture 5.3. For any even number j ∈ N, Lj+1 · Fn = Fn−j + Fn+jNumerical Examples: n = 6 and k = 4: L4+1 · F6 = F6−4 + F6+4 ⇒ L5 · F6 = F2 + F10 ⇒ 7 · 5 = 1 + 34 ⇒ 35 = 35n = 10 and k = 2: L2+1 ·F10 = F10−2 +F10+2⇒ L3·F10 = F8+F12 ⇒ 3·34 = 13+89 ⇒ 102 = 102n = 7 and k = 6: L6+1·F7 = F7−6+F7+6 ⇒ L7·F7 = F1+F13 ⇒ 8·18 = 0+144 ⇒ 144 = 144For some even natural number k − 2 (where k > 2), we assume that:Fn−(k−2) + Fn+(k−2)= Lk−1· FnWe also know that k − 1 will be odd, and so:Fn−(k−1) + Fn+(k−1) = Ln · FkIs it possible to prove that Fn−k + Fn+k = Lk+1 · Fn (k is even, as k − 2 is even)and that Fn−(k+1) + Fn+(k+1) = Ln · Fk+2 as k + 1 will be odd? The Fibonacci and Lucas Sequences are two of the most powerful sequences in mathematics. Using these sequences, mathematicians and scientists have discovered patterns in bracts of a pine cone, number of petals in a flower and scales of a pineapple. In addition, these sequences have enhanced our understanding of the Golden Ratio and its significance in our lives. AuthorShifa Somji enjoys learning, playing, and reading about chess. Mir Sultan Khan was born in Sargodha in modern-day Pakistan. He was a family servant in the house of Sir Malik Muhammad Umar Hayat Khan. His only occupation in life was to look after Major General's haveli. Mir Sultan Khan taught himself chess and won the All-India Chess Championship in 1928 . He subsequently travelled to England in 1929. In England, he defeated many masters of the game before bidding farewell to the game forever. His successes in international chess largely remain unknown in modern times. He won the British Chess Championship twice by defeating Grandmasters Alexander Alekhine and Jose Capablanca. Despite these brilliant victories, he always remained remarkably humble.American grandmaster and psychologist, Reuben Fine narrates his meeting with Mir Sultan Khan in his book: “When we entered the home of Maharaja (Malik Umar Hayat Khan), he welcomed us and said: ‘You’re very lucky that I am meeting you, otherwise I prefer spending this time with my greyhounds.’ He then handed over to us a booklet, covering his life and times. By now, we had ascertained that the only feather in his hat was being born as a Maharaja. Then we saw Mir Sultan Khan, who was our real host, and the Maharaja was treating him as his slave. We were in an odd situation, when a chess grandmaster was in front of us as our waiter.” World Chess Federation did not bestow upon Mir Sultan Khan the title of 'grandmaster'. However, his contemporaries do regard him as the first grandmaster from Asia and consider Anand as his spiritual successor. |
## AuthorShifa Somji is the Founder and CEO of Chess4Girls. She is an Avid computer scientist and researcher with a deep interest in science, technology, chess and mathematics. ## Archives
November 2017
## Categories |