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© 2007 The Goddesschess Partnership All rights reserved |
Las Vegas Showgirls II
by Georgia Albert
with Jan Newton
Chess - Tesselations - Knight's Tour - Escher - "Harry Potter
DATELINE
Las Vegas, May 20, 2003
Bambi: Candi, What do you think about our new assignment for Goddesschess?
Candi: Do you mean the" Showgirl Uncovers Chess" article?
Bambi: Yes!
Candi: I like the idea, but I am confused about the title, "Showgirl Uncovers Chess". It reminds me of the all-time classic film "Debbie Does Dallas". Are we going to be reviewing Porn Films?
Bambi: No, sorry to say, no porn this time, but maybe in our next assignment we will get a chance.
Candi: Drats! I suppose we are going to review the chess representation in a PG rated movie instead?
Bambi: Candy, how did you know the movie has a PG rating?
Candi: It's simple, I have ESPN, and some of my friends think I'm psychotic.
Bambi: Candi, it's ESP, Not ESPN, and it's Psychic, not psychotic!
Candi: I am confused.
Bambi: I don't doubt it. I'll explain it later, much later.
Candi: OK, So what film are we going to review?
Bambi: Harry Potter and the Sorcerer's Stone. do you remember anything about the movie? Or should we rent the DVD?
Candi: Sure I remember, It's coming back to me now...Potter...Potter...Oh Yeah! Colonel Potter from "M.A.S.H" is in it..
Bambi: No! Not Colonel Potter! It's Harry Potter!
Candi: Oh Yeah! Now I remember....... the high school teacher from "Welcome Back Potter"....
Bambi: No! Not Kotter, it's Potter, Harry Potter! The young boy who discovers he is a Wizard with magical powers, and goes to Hogwort's Castle for schooling. And while he is there, he plays a couple of games of Chess.
Candi: Oh, that movie....the little boy with the glasses, an owl and a broomstick....there wasn't any sex in the movie. No wonder I didn't remember it.
Bambi: The reason Isis wanted us to review this movie is that it ties into my Tesselation and Chess research.
Candi: Tasselations.....Tassels....Oh! The pasties that exotic dancers wear...
Bambi: Not Tasselations! It's "Tesselations." Go get the MC Escher Book off the coffee table and I will show you what I am talking about.
|
WHAT BAMBI THINKS:
From
The Math Forum, by Suzanne Alejandre A regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A regular tessellation means a tessellation made up of congruent regular polygons. [Remember: Regular means that the sides of the polygon are all the same length. Congruent means that the polygons that you put together are all the same size and shape.] Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons. We can't show the entire plane, but imagine that these are pieces taken from planes that have been tiled. Here are examples of
When
you look at these three samples you can easily notice that the
squares are lined up with each other while the triangles and hexagons
are not. Also, if you look at 6 triangles at a time, they form
a hexagon, so the tiling of triangles and the tiling of hexagons
are similar and they cannot be formed by directly lining shapes
up under each other - a slide (or a glide!) is involved.
You can work out the interior measure of the angles for each of these polygons:
Since the regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees. This works for the triangle, square, and hexagon, and you can show working tessellations for these figures. For all the others, the interior angles are not exact divisors of 360 degrees, and therefore those figures cannot tile the plane. Steven Schwartzman's The Words of Mathematics (1994, The Mathematical Association of America) says:
|
< Elephant and Turret Tesselation, Escher
Candi: Here it is. Escher is one of my favorite designers. I would like to do my new line of thong bikinis with pasties using his fabric designs. Bambi, look at this design!Bambi: Oh, yes! This is one of my favorites. This Classic chess piece design of the "Elephant and Turret" was favored by the ancients...
...and maybe also 21st Century Chicago pub crawlers...
|
WHAT BAMBI THINKS:
"Buffalo are very plentiful in the steppes. They are hunted with elephants. Turrets are placed on the elephant's back, in which several men are hidden. Thus they traverse the plain, and as soon as the elephant comes up with the buffalo he attacks him with his teeth and holds him till the hunters get off his back and capture him." (Emphasis added). Excerpted from the subtitle "My Experiences In Hindustan," from Mirat ul Memalik (The Mirror of Countries), 1557 CE, by Sidi Ali Reis (Piri Reis, originator of the famous map of the globe). |
Candi: Oh, Bambi!
Bambi: What? Are you all right? You are getting pink all over!
Candi: Oh, Bambi! I just had an idea!
Bambi: Oh, Candi! That is wonderful! I knew you could do it! Tell me, what is your idea!
Candi: 4.
Bambi: Oh, Candi! I am so excited. That is sooooo deep!
Candi: Ooooh, I know! I am just shivering all over! 4! 4! 4!
Bambi: Ooooh, stop!
Candi: I can't! I am inspired. Bambi, four to the third power. FOUR TO THE THIRD POWER!
Bambi: Ooooh, stop, stop! I can't take anymore!
Candi: Oh. Well then. Okay. I think I'll paint my toe nails.
Bambi: What! You are going to paint your toe nails? But you just told me one of The Secrets of the Universe!
Candi: I did?
Bambi: Oooooh Candi. Don't use THAT color.
Candi: Well, if you feel that way about it, I won't! Hey - wait a minute. I just told you one of the Secrets of the Universe!
Bambi: Yes, you did.
Candi: Well, in that case, I am going to paint my toe nails -
Bambi: Oh! Forget about your toe nails for one minute, Candi! Don't you understand anything?
Candi: Well, for one minute? Hmmm, I suppose I can do that. And of course, I understand anything. I mean, some things. I mean, I understand - Rooks? Oh oh. I feel dizzy. Oh, Bambi! What is happening to me? I feel so strange, I feel so funny, I feel so oh oh oh oh OH OH OH...
Bambi: Oh Candi! You have just had another revelation!
Candi: What? Two in two minutes? Oooooh, I knew that yoga would do me some good!
Bambi: Oh, where is my The Art of Chess Book, Candi? Darn! Where did I put it... There are some examples of the Elephant and Turret - Rook (Rukh) pieces in it... I also need to go to the Media Store and rent the Harry Potter movie for you to watch. There is a scene in the movie with a fantasy staircase that resembles Escher's "House of Stairs."
| WHAT
BAMBI THINKS:
A challenge to the mathematicians: (1) Can you explain and demonstrate (on a graph of the painting) how the Fibonnaci Spiral is embodied in this painting??? (2) Can you explain and demonstrate the use of the "Golden Mean" in the construction of the various staircases??? (3) What tiling pattern did Escher use in this painting? (4) Put this all on a chessboard (extra bonus points)!!!! |
Candi: Bambi, what is 4 times 4 times 4? Isn't that 64? Isn't that a chessboard? What are tesselations, except the graphical representation of the three-dimensional dichotomy of dark and light? Evil and goodness? Black and white? Bambi! IT'S A CHESSBOARD! THE UNIVERSE IS A CHESSBOARD!
Bambi: Oh, Candi! I am soooo impressed! You are truly inspired! I really do like that checkerboard look for your toe nails. Yes, you are right! Four to the third power is 64, which is the number of squares on the chessboard, both western and Chinese. Although, you know, it is very strange - the Chinese do not play on the squares, they play on the intersections of the lines!
Candi: Oh! Thank you, Bambi. I like the black and white checked look. You know, 4 is a very significant number. Only think, there are four cardinal directions; there are four seasons; according to the ancients, there are four primary elements: earth, air, fire, and water. You know, Bambi, Chaturanga, which is what the chess HIStorians say is the earliest form of proto-chess, means [chatur = four] and [anga = limb]. But there are EIGHT primary angas:
|
WHAT CANDI THINKS:
Anga ("limb"): a fundamental category of the yogic path, such as asana, dharana, dhyana, niyama, pranayama, pratyahara, samadhi, yama; also the body (deha, sharira) |
4 x 8 = 32! That is the number of pieces on the chessboard, Bambi. And 2 x 32 = 64, the number of squares on the chessboard! And 4x4x4 = 64! It is quite possible the ancient Indians used Chaturanga on the Ashtapada board to embody aspects of their religious beliefs. While you're away at the Media Store, I am going to slip into something comfortable...a nice warm Bubble Bath.... Then I think I will do some Yoga. By the way, did you know that yoga can improve your sex life?
Bambi: I was the one who told you about yoga and an improved sex. But Candi, don't you know that Chess HIStorians say that Chatur-anga means "four armies" - or something like that. And that is why they say Chess is a War Game!
Candi: Oooh, now I am getting confused! But the tesselations - they're not wrong, are they?
Bambi: No, of course not!
Candi: Well, then. Bambi, don't you see - if the tesselations cannot lie, then those Chess HIStorians are Wrong! Chess is about mathematics, not silly-dilly armies! I mean, what else is the Knight's Tour about, except mathematics.
|
CANDI'S BRAIN IS NOW IN HIGH GEAR:
|
Bambi: Tessellations are soooo exciting. My toes are tingling, oooh. Candi! Do you think the Knight's Move might be a short-hand way of proving the Pythagorean Theorem? After all, the Knight's Move forms a right triangle -
|
WHAT BAMBI THINKS:
|
Bambi: No, Candi. We will go over the Harry Potter movie when you return from the store. I am off to the Bath!
Two Hours Later..
Bambi: Your Lotus position is beautiful... You are getting real good...
Candi: Thanks Bambi. Ever since I started doing my yoga exercises naked I have been enjoying my exercises more.... You should try it. It feels wonderful!
Bambi: OK, after the Harry Potter movie. We really do need to move on to the Wizard's Chess scenes. The Chess game played in the Great Hall was played with Scandinavian Chess Pieces made of Walrus Ivory, modeled after this piece (image, right). The Chess game was played with huge pieces. Here is a picture of the playing pieces and chess board (image, left). Where are you going? Candi, come back!
Candi: Bambi, I have my priorities....a date with a charming man comes first. Don't stay up waiting for me, if you know what I mean;-)
Bambi: That is a wonderful idea! I am going to call my Sweetheart and invite him over for a game of Goddess Chess;-)
For Your Further Reading and Viewing Pleasure ...... (ooooh!!) .....!Tesselation in Graphic Art
Tilings from Historical Sources:
Images of Tiling from Ancient Egypt, Persia, China, etc.
