Friends | I USED TO WORK FOR THE U.S. ARMY CORPS OF ENGINEERS IN THE MEMPHIS DISTRICT. I WAS ON THE F-21 HYDRO SURVEY PARTY INVOLVED WITH MAPPING OF THE MISSISSIPPI RIVER. NOW THAT WAS A TRIP. IN THE FALL AND SPRING IN THOSE DAYS I WENT TO ARKANSAS STATE UNIVERSITY ;IN JONESBORO ARKANSAS. I STUDIED MATH AND ENGINEERING WITH LIMITED SUCCESS. NOW A DAYS I HAVE INVOLVEMENT WITH ALGEBRAIC GEOMETRY. THAN GOODNESS FOR THOSE GOVERNMENT CHECKS EVERY MONTH. Boomer: I am using Windows 10.0. So gather around children. I've got something to say about the sub calculus as I know it now. Sub means substitution of trig relations in some uncool fractions of algebraic fractions of x.. Now, for integrations of cos(x)^2 and sin(x)^2 one must combine the following trig relations: cos(2x)=cos(x)cos(x)-sin(x)sin(x) and 1=cos(x)^2+sin(x)+sin(x)^2. One can find an expression for cos(x)^2 and sin(x)^2 as a function of cos(x) and sin(x) that one can integrate. I found this left.as an exercise in my 1977 copy of "Calculus and Analytical Geometry" by George B. Thomas of MIT. It was found in chapter 5 with all the other trig in the world. Thats all folks.... Boomer: Sorry, that second equation should be cos(x)^2+sin(x)^2=1. I would like to appypolyogize for my error. Boomer: just went to the line on the back of a bike...i thought we were busted two or three times over Boomer: I recently had to integrate (cos(x))^2. I had to get out the CRC math tables. It worked. Imagine having to use the CRC in a job situation. It could get someone a raise in pay. Boomer: Look up sub calculus. I used Bing to get several worked examples the other night. It seems sub means trigonometric substitution. Boomer to cynthia_zaddy44: I USE AN ENGINEER'S SCALE. THE 10 SCALE THAT IS MARKED OFF IN 10TH S OF AN INCH. THAT IS CLOSE ENOUGH FOR GOVERNMENT WORK. ON EACH CORNER MARK OFF 1 INCH IN EACH DIRECTION. ONCE AGAIN I'M READY FOR MY OVER-SIZED STRAIGHT EDGE AND I USE IT TO ESTABLISH ONE INCH MARGINS. THAT MEANS A 20 BY 20 INCH SURFACE TO BE COVERED WITH INK. I USED TO DREAM OF DOING THIS BACK IN THE 7TH GRAD. NOW IT IS ALL I DO. Boomer: Use a translucent ink on the 1 inch border so as not to obscure the work's title or your signature. BAK15 is of course how I am signing them this year. And I am sticking to the gimic that this year all works so far are titled as "Topic". They are useful compilations of psychedelic colors and style. I like to mail them off to bill collectors by priority mail. I produce just enough to keep my psychiatrist supplied so as to maintain sound relations. There is a distinct disadvantage in supplying my psychiatrist. He is a medical doctor and treats my art as something requiring patient/doctor confidentiality. Distributing work to staff psychologists avoids this pitfall. All ready the psychologists' kids are seeing my work in their mothers' offices. I am also creating hand painted laminated and signed addition and multiplication tables. I have started to write my full mailing address on the back of my work and to be truthful to the act of addressing my work as I promised the local chief of police here in Harrisburg, Ar. You would be surprised at how many times my posters have been found during police raids here and there! Do I want to be famous? Do I want fame and fortune? Would I settle for fortune and infamy? Well I've got gov't. money and damned near every body has infamy. I mean, If I get famous for my psychedelic posters and I don't like it, I'll just quit the fame seeking and become infamously obscure. I'm still trying to find out what Peter Max has done.
Boomer: Allan Baker 302 North Park #404 Harrisburg, Ar 72432-1129 This is my home address where I manufacture posters. A posters take about 4 hours to work out. 4 hours @ $8.00 and hour and $3.00 for materials pushes the total price to $35.00. If people can request works by snail mail I can afford to distribute my work for free by priority mail. Just look at is as U.S. Government sponsored art. Life for life's sake. Art for art's sake. Money for government sake; though that is not an issue for the present time. Thank you for reading me. BAK15 Boomer: I've done 4 posters within the last 7 days. I work with "Sharpy" ink pens. It is good that I work with ink or I would always be jonesing for another couple of tubes of ink. I laminate by overlapping 2 inch wide plastic tape. The result is a 22 inch square poster that uses up to as many colors as one could want that is water and dust proof. I say that one of my posters would last 100 years in a land fill. Boomer: Just remember to do overlapping strokes with your Sharpies and also say It is all in the wrist. Don't hesitate to rotate the paper if that would help you free-hand in a line or bead of ink. It is all in the wrist when you go to outline a penciled in area boarder with an ink marker. Don't forget to lay in concentric beads of ink as if you were welding metal. Be careful not to handle the ink as if it were a wax crayon to fill a small sub-area with color. Boomer to cynthia_zaddy44: My straight edge is 5 inches wide, 32 inches long and an eighth of an inch thick. It was cut to length at a Marked Tree Arkansas factory, Mid South Manufacturing ( which I hear is about to reopen). I took a tool file and scraped of the oil and smoothed out the surface. The 32 inch length steel bar is slightly bowed. The bar goes flat after application of a 1 or 2 or more pounds of vertical force is applied to it's mid-point. Sounds crazy , eh? I learned to use a long straight edge after seeing draftsmen using a combine blade to do particularly close work at the offices of Michael Baker Engineering in Jackson Mississippi. They were drawing up a map of a new pipeline on a twenty foot length of linen. that draftsman, Lamar Bullerton, really knew what he was doing there with those ink pens. That was 1987. Boomer: r= xi+yj+zk r*r=x^2+y^2+z^2=abs(r)^2 1=(x^2)/(r*r)+(y^2)/(r*r)+(z^2)/(r*r) 1=(cos(alpha))^2+(cos(beta))^2+(cos(gamma))^2 Alpha, beta and gamma are angles formed by the position vector and the x, y and z axes respectively. Boomer: r =x i + y j +z k is called the "POSITION VECTOR". I want to believe that the x,y and z can be replaced by functions....crazy huh? r*r is pronounced as "r dot r": the dot multiplication of vector r with itself. (cos(alpha)), (cos(beta)) and (cos(gamma)) are called "DIRECTIONAL COSINES". I believe I heard about that in an engineering statics course one day at ASU several years ago. It was engineering mathematics course in the math department.that really stress that sort of thing. Boomer: In a self esteem class today the staff nurse asked 19 people, damned near 21 of them I'll bet, to say something good about me. Nobody replied. To hell with them all I thought. Finely the staff nurse said I was a good artist and that she liked the work I did that is hanging on her office wall. All the girls on the psychology staff have one or more of my abstracts. Boomer to cynthia_zaddy44: WHAT COMES NATURALLY FROM HAVING A 22 BY 28 INCH PIECE OF POSTER BOARD? I THROW THEM ON MY DRAFTING TABLE, GET OUT MY OVER SIZED STEEL STRAIGHT EDGE AND A RAZOR BLADE. A 22 IN SQUARE POSTER BOARD IS THE RESULT. |
FINITE MATH GROUPS LIKE S3, THE SYMMETRY GROUP , ARE GREAT FUN TO WORK WITH. LET M3 BE THE SET OF 3X3 PERMUTATION MATRIX GROUP. S3 AND M3 ARE ISOMORPHISMS OF EACH OTHER.
A GROUP IS DEFINED BY A SET AND A BINARY OPERATION WHICH HERE IS THE SET FOR S3: S3={123, 231, 312, 132, 231, 321}, THE OPERATION IS P(K)=B(A(K)) FOR K={1, 2, 3}. THERE IS CLOSURE ON THE SET S3 WITH RESPECT TO THE OPERATION. THE IDENTITY ELEMENT IS 123, THE ELEMENTS PAIR AS INVERSES WITH PRODUCTS OF THE PAIRS OF INVERSES IS IDENTITY. I AM INTERESTED IN A FOURTH PROPERTY OF GROUP MULTIPLICATION: ASSOCIATIVITY OF THE OPERATION: A(BC)=(AB)C.
M3 IS CONSTRUCTED FROM S3. IDENTITY 123 OF S3 TRANSLATES IN INTO THE IDENTITY OF M3 AS A 3X3 MATRIX WITH 1 IN THE 1ST 2ND & 3RD POSITIONS IN THE 1ST, 2ND & 3RD ROW OF A 3X3 MATRIX WITH ZERO IN THE 6 OTHER POSITIONS ON ROWS 1 ,2,&3. JUST LIKE PERMUTATION ELEMENT 231 TRANSLATES INTO A 3X3 PERMUTATION MATRIX WITH 1 IN THE SECOND POSITION OF THE FIRST ROW, 1 IN THE FIRST POSITION OFF THE 2ND ROW, 3 IN THE SECOND POSITION OF ROW 2 AND 1 IN THE THIRD LINE OF THE MATRIX WHERE OTHERWISE THE ENTRY IN THE MATRIX IS ZERO.
TO SHOW THAT THE OPERATION OF S3 IS ASSOCIATIVE. HOW DO I DO THAT? WITH M3 THE OPERATION, ASSOCIATIVE OPERATION CAN BE SHOWN TO BE IN EFFECT BY MATRIX ALGEBRA: A(BC)=(AB)C. SINCE THE PRODUCT TABLE OF S3 AND M3 SHOW DIRECT TRANSLATION OF EACH OTHERS ELEMENTS, I THINK THAT S3 HAS AN ASSOCIATIVE OPERATION.
TO END THIS DOG AND PONY SHOW,THE COMMUTATIVE ELEMENTS ON A ROW OR COLUMN OF A GROUP PRODUCT SYSTEM TABLE, SAY S3 OR M3,CAN BE GATHERED OFF EACH ROW OR COLUMN TO FORM A SUBGROUP.
I JUST HAD TO SAY THAT AGAIN. TO GET THAT REQUIRES A TABLE AND THAT ;IS AN EXCUSE TO DRAW ONE, i JUST HAD TO THROW THAT IN. SEE YOU LATER! BAK15