Not always, or even usually, true. The product of two irrationals can be rational or irrational.John McKenna wrote: Also, if two irrationals are multiplied or divided a rational results!
Draughts/Checkers and Chess
-
- Posts: 4837
- Joined: Tue Apr 17, 2007 1:13 am
- Location: Bideford
Re: Draughts/Checkers and Chess
-
- Posts: 147
- Joined: Sat Nov 07, 2009 12:20 pm
Re: Draughts/Checkers and Chess
'them' of course referred to the irrational numbers.John McKenna wrote:Bill Porter >... rational numbers aren't generally purer than irrational(s)... just because there are more of them...<
The rationals and irrationals should the other way round. There's an infinite number of rationals but there's a greater (infinite) number of irrationals.
I've also discovered a wonderful proof that white is in zugzwang at his first move and must lose.
As I'm rather off topic I won't post it.
Re: Draughts/Checkers and Chess
Thanks to Bill for precisely stating that rationals aren't necessarily purer than irrationals just because there are more irrationals. (Ancient Greeks thought the rationals purer and abhorred irrationals.)
Jack's right - the result of multiplication or division of two irrationals can be either rational or irrational. My pronouncement fell short. But, when is it one rather than the other? (Don't know the answer but believe there may be one.)
Back on topic - what's the weight of having 1st move in draughts?
Jack's right - the result of multiplication or division of two irrationals can be either rational or irrational. My pronouncement fell short. But, when is it one rather than the other? (Don't know the answer but believe there may be one.)
Back on topic - what's the weight of having 1st move in draughts?
-
- Posts: 9085
- Joined: Sat May 30, 2009 5:18 pm
- Location: Oldbury, Worcestershire
Re: Draughts/Checkers and Chess
Example off the top of my head: Pi is irrational. Pi squared is Pi*Pi (so it's a multiplication of two irrationals), but Pi squared is also irrational.John McKenna wrote:Jack's right - the result of multiplication or division of two irrationals can be either rational or irrational. My pronouncement fell short. But, when is it one rather than the other? (Don't know the answer but believe there may be one.)
-
- Posts: 4552
- Joined: Tue Apr 03, 2007 11:04 pm
- Location: writer
Re: Draughts/Checkers and Chess
John McKenna >Back on topic - what's the weight of having 1st move in draughts?<
I had already commentated that I had seen it suggested that the second person to move has the advantage in draughts, the 8x8 version.
I had already commentated that I had seen it suggested that the second person to move has the advantage in draughts, the 8x8 version.
-
- Posts: 835
- Joined: Sun Jan 02, 2011 11:48 am
- Location: Bradford
Re: Draughts/Checkers and Chess
As anyone who has manipulated surds will know, sqrt 2 is irrational, as is sqrt 3.IM Jack Rudd wrote:Not always, or even usually, true. The product of two irrationals can be rational or irrational.John McKenna wrote: Also, if two irrationals are multiplied or divided a rational results!
sqrt 2 x sqrt 2 = 2 - rational
sqrt 2 x sqrt 3 = 2.449 etc - irrational
Re: Draughts/Checkers and Chess
My thanks to Alex H, Stewart and Andrew for the above answers. Food for thought.
-
- Posts: 9
- Joined: Wed Mar 21, 2012 10:33 pm
Re: Draughts/Checkers and Chess
I play in what I believe is the only draughts club in the West Midlands. There's only about 12 of us. Tony Hynes, whom many of you will know is one of us. We play on Saturdays. It fits in well with when there is no chess to be played at the weekend. With have a mini league and cup competition !
It's a great game. I love chess, but believe draughts to be a purer game because of the minimal rules. I always say that in our universe you can bet there are more games resembling draughts than chess !
Draughts is a totally unforgiving game. With chess you may get away with something, in draughts no !
Our club has a 10x10 European draughts even minier league than our 8X8 (I don't play this !). Obviously more sophisticated than 8x8 draughts/checkers. Players come up from London to play !
(I would like to volunteer in a clumsy way a more esoteric appreciation of draughts: Musicians are often very good at chess, and intense concentration at mental games does cause the individual to transcend our often banal world ....and I believe there is an associated mental sound/resonance/aesthetic thing going on in the mind when we sit back and admire a knight outpost on e5.....a nice combination..or a well played rook and pawn endgame etc.... I would say that chess is to Beethoven what Bach is to draughts. From my own experience I have achieved deeper transcendence with draughts than chess. Chess I believe is like human law, often arbitary. Moves like castling, en passant, the initial setup of pieces on the backrow creates a more jagged impression in the mind....)
It's a great game. I love chess, but believe draughts to be a purer game because of the minimal rules. I always say that in our universe you can bet there are more games resembling draughts than chess !
Draughts is a totally unforgiving game. With chess you may get away with something, in draughts no !
Our club has a 10x10 European draughts even minier league than our 8X8 (I don't play this !). Obviously more sophisticated than 8x8 draughts/checkers. Players come up from London to play !
(I would like to volunteer in a clumsy way a more esoteric appreciation of draughts: Musicians are often very good at chess, and intense concentration at mental games does cause the individual to transcend our often banal world ....and I believe there is an associated mental sound/resonance/aesthetic thing going on in the mind when we sit back and admire a knight outpost on e5.....a nice combination..or a well played rook and pawn endgame etc.... I would say that chess is to Beethoven what Bach is to draughts. From my own experience I have achieved deeper transcendence with draughts than chess. Chess I believe is like human law, often arbitary. Moves like castling, en passant, the initial setup of pieces on the backrow creates a more jagged impression in the mind....)
-
- Posts: 858
- Joined: Sun Aug 29, 2010 8:26 pm
Re: Draughts/Checkers and Chess
Howard Staunton was not very good at draughts, according to Draughts World (as reported in the Otago Witness, 15 April 1903, p. 59). My book, Notes on the Life of Howard Staunton (pp. 73-74) includes the story of a "bachelor Easter holiday" shared by Staunton, Robert Martins (later to become one of the all-time greats of the draughts board) and Herbert Ingram, joint proprietor of the Illustrated London News, at Ingram's mansion at Swineshead, Lincolnshire. Martins had been introduced by Staunton to Ingram, whom he preceeded to fleece for a week at a sovereign a game, while Staunton stayed on the sidelines. My book also carried some biographical notes on Robert Martins, about whom I would like to know more.
Regards,
John Townsend
Regards,
John Townsend
-
- Posts: 642
- Joined: Tue Mar 02, 2010 12:37 pm
Re: Draughts/Checkers and Chess
Good job I don't play draughts, then.Simon Smith wrote:Draughts is a totally unforgiving game. With chess you may get away with something, in draughts no !