9 - Charles HAMEL
Contents
1. made those knots and tested those arrays and a lot more of them to verify the programs CA 48GX CA 48GX Before using any of the program and after you are completely finished with a TOTU full run so as to reclaim memory used by the many variables created run the program CLEAN Just after CLEAN ran you need to STOre the array of the knot you want in MALR it is supposed that you know how to RCL and STO a variable using the STACK Let us say that for a first use you use MASEDG Put MASEDG on the stack by just pushing on the button just under MASE in the menu row 3 and inside write MALR capitals and STO it Copyright Charles HAMEL aka Nautile Nov 2009 Page 6 of 16 If MALR does not exist or is not the correct one you want you will get a program crash in the first case or results that are those of the array in the variable MALR but which 1 not the one you really want in the second case Now that you are sure that you have the VALID array in MALR variable run PGSU PACKARD 48GX 48GX PACKARD 48GX You will be asked to enter LEAD and BIGHT numbers for this knot Type the numbers separated by a space then push the ENTER button This HALT the program To resume the running of the program while use Left side violet arrow button ON An hourglass icon appears in the top right side of the screen meaning calculation are Being done2. 10 11 312 13 14 15 ie gt a lt gt 9 9 9 Q 4 4 ae iar Pact E ya 1 9E Sh 1 4 15 12 11 10 S B e gt Copyright Charles HAMEL aka Nautile Nov 2009 Page 16 of 16 Here is this Knot 41 a derivation from the Sedgwick s
3. 9 1 9 1 9 0 9 0 9 11 9 9 0 9 1 9 9 0 9 9 09 0 9 T 1 9 0 9119 9 1 9 1 9 9 1 9 09 1 9 11910 9 1 9 1 9 0 98 1 9 99 9 9 1 9 0 9 0 9 0191s 1 9 1 8 6 1 1 1 94119 0 9 119 1 1910 9 1 9 0 1911 9 1 9 9 1119 1 9 0 9 1019 9 0 19 1 9 0 9 1 1910 9 0 9 9 10 9 0 1911 9119 0 9 1 9 11910 9 1 9 0 911 9 1 9 0 9 1 9 1 9 0 Page 14 of 16 12 13 8 3 141 158 BASKET WEAVE modified from SCHAAKE amp TURNER 2 Copyright Charles HAMEL aka Nautile Nov 2009 KNOT 37 e NN C XX XXXXYX n 3E J o c o i m 2 11 13 Copyright Charles HAMEL aka Nautile Nov 2009 Page 15 of 16 MA41 919091909190919 090909090909090 919191919191919 090909090909090 919091909190919 091919191919190 919091909190919 090909090909090 919191919191919 090909090909090 919091909190919 091919191919190 919091909190919 090909090909090 919191919191919 090909090909090 919091909190919 091919191919190 Knot41 derived from Sedgewicks 16L 9B modified from SCHAAKE amp TURNER T
4. RIGHT TOP amp BOTTOM side of the isometric diagram The SPart WEnd crossing is on the LEFT side Your paper and pencil table will need L 1 columns and 2 rows absence of crossing at an intersection of a vertical line with an horizontal line of crossing is denoted 9 An OVER crossing as noted by an EVEN numbered half period is denoted 1 and an UNDER crossing by 0 Copyright Charles HAMEL aka Nautile Nov 2009 Page 10 of 16 HOW TO WRITE THE FOUR ARRAYS PROVIDED FROM THE KNOT DIAGRAM It is for this type of NEITHER ROW NOR COLUMN CODED knot that this program the most useful IS MASEDG 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919091909190919091909190919 919091919191919191919191909190 190919091909190919091909190919 919090909090909090909090909190 190919091909190919091909190919 919091919191919191919191909190 190919091909190919091909190919 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919091909190919091909190919 919091919191919191919191909190 190919091909190919091909190919 919090909090909090909090909190 190919091909190919091909190919 919091
5. here that would make mandatory a numbering beginning at zero Copyright Charles HAMEL aka Nautile Nov 2009 Page 12 of 16 MAT35 9191909190919190 1909190919190919 9190919190919091 0919190919091919 9190919091919091 0919091919091909 9091919091909191 1919091909191909 9091909191909190 1909191909190919 9191909190919190 1909190919190919 9190919190919091 0919190919091919 9190919091919091 0919091919091909 9091919091909191 1919091909191909 9091909191909190 190919190919091 9 knot N 35 FAST HELIX KNOT 17L 108 MODIFIED FROM SCHAAKE amp TURNER 2 T B 10 711 12 14 14 19 16 NK OY PERKY MAN NN Copyright Charles HAMEL aka Nautile Nov 2009 MAT37 9091909091909 1909091909091 9091909091909 0919190919190 9190919190919 0919190919190 9091909091909 1909091909091 9091909091909 0919190919190 9190919190919 0919190919190 9091909091909 1909091909091 9091909091909 0919190919190 9190919190919 0919190919190 9091909091909 1909091909091 9091909091909 0919190919190 9190919190919 0919190919190 9091909091909 1909091909091 9091909091909 0919190919190 9190919190919 0919190919190 Page 13 of 16 9 0 9 1 9 9 0 9 1 9 9 1 9 019 0 9 1 9 9 09 1 9 9 1 9 0 0 9 1 9 0 9 09 19 11910 9 1 9 1 9 0 9 119 0 9 1 9 11910 9 1 9 0 1911 9 11910
6. 919191919191919191909190 190919091909190919091909190919 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919191919191919191919190919 919090909090909090909090909190 190919091909190919091909190919 919091919191919191919191909190 190919091909190919091909190919 919090909090909090909090909190 190919091909190919091909190919 919091919191919191919191909190 190919091909190919091909190919 919090909090909090909090909190 190919191919191919191919190919 ARRAY will have L 1 Columns numbered left to right from 1 2 B Rows numbered top to bottom from 1 O stands for an UNDER crossing 1 stands for OVER crossing 9 stand for empty space at this particular place of the row or the column in the knot diagram NOTE the type of the crossing OVER UNDER 1 read as the ODD numbered half period going from low left to up right would read it Train yourself with the four examples given Now for the only tricky point Numbering the columns and rows on the knot diagram we use here the horizontal mandrel frame of reference Copyright Charles HAMEL aka Nautile Nov 2009 P age 11 of 16 with the bight rim on the left and on the right vertical cylinder would have the bight rim top and bottom and the half period reading the type of the crossing would b
7. Copyright Charles HAMEL aka Nautile Nov 2009 Page of 16 TOTU HP48GX PROGRAM FOR ANY CODING ON A THK CORDAGE ROUTE single strand knots All along this document have supposed that you own 48 calculator or that an emulator is installed on your computer that you know how to use it if not read user tips manual to get and inkling or read the quick start official Hewlett Packard user manual download available on my web pages just look attentively in Publication 3 page Heading the user s tips of the other programs can do wonder to clarify some points about the use of the HP48 to run my programs all of them follow an identical trail The learning curve of TOTU has been made quite gentle This program is easy to use even if it demands that you perform some work manually with paper and pencil you need to create an array describing the layout of the crossings in the knot With TOTU s help you can find the coding of each halt period of any limit 32L 32 B single strand knot following a turk s head knot cordage route with whatever coding COLUMN coded ROW coded Row AND Column coded NEITHER Row NOR Column coded For the first three types of coding the specialized programs dealing with those already put online are much faster and a lot more user friendly than this one almost no paper and pencil work with them Still with the NEITHER row NOR Column coded type only this pr
8. Wait till the hourglass on the upper part of the screen disappear very fast may be 10 seconds with the emulator slow with the calculator can take 1 to 10 minutes depending on the size of the array Results will be put in the STACK where you can access them with ease Copyright Charles HAMEL aka Nautile Nov 2009 Page 7 of 16 FIRST EASY LESSON ON WRITING THE KNOT s ARRAY made an especially easy diagram 4L 5B regular THK 9 8 7 reading the crossing EP ets L lt ae L gt NOU VYY Y NN NM V M mw ISS L an 10 k 10 __ 77 NO 3 MANDREL FRAME of REFERENCE ON AN ISOMETRIC GRID You MUST make your diagram on an ISOMETRIC GRID to easily see the alignments crossing Please note that the blank white coloured cells in the table are in the same number as are the intersections between the RED lines and the GREEN lines in the diagram The numbering in RED that will be use to write the table are the digits at the top they are also letters for the sake of illustration but array matrix have columns and row identified by digit and not number in the HP48 They are numbered 1 to 3 that is L 1 Note also that the horizontal GREEN lines are numbered 1 to 10 10 2 B Copyright Charles HAMEL aka Nautile Nov 2009 Page 8 of 16 Now we enter the intersection between RED and GREEN lines that show no knot cr
9. e going from bottom right to top left modified from SCHAAKE amp TURNER c 9 wow Ae RT Ay Ac ag 47 a ow de 40 AP UP SP Mp p og P ID SSCS CSCS RITIRARE OK SSS SSS SESS EPS OOS SOS SSS ISOS OSS IST 2 ul SSS 5 4 0 31L 21B SEDGWICK s knot For the ARRAY to be entered in the MALR variable you will number its columns as the columns of crossing are numbered from left to right at the top of the diagram 1 2 3 to L 1 Now the rows of the ARRAY will be numbered from 1 2 3 to 2 BUT how do we find the correct numbering ON THE KNOT DIAGRAM Using the horizontal mandrel reference and remembering that the bight rim of a real knot is a circle in the diagram we put ROW where the Wend cross the SPart and go on upward When at the top ROW then we go down to the lowest ROW and continue the numbering Just study the diagram NOTE this numbering use here has nothing to do with all the numbers SCHAAKE system use made it such so as to be able to write a valid array matrix for the HP in an array numbering or row and column does not begin at 0 but at 1 There is no use of modulus
10. ogram can help you provided that that you have a diagram of the knot made on isometric grid paper in the style promoted by SCHAAKE and TURNER This program is my own mix things learned in THE BRAIDER and in BRAIDING THE REGULAR KNOTS this is the source of the diagram use here In a modified form THE BRAIDING OF LONG COLUMN CODED REGULAR KNOTS THE BRAIDING OF ROW CODED REGULAR KNOTS Now that the programming has been done any one of you can easily with no hard mental work adapt it to any other programming language of your choosing Copyright Charles HAMEL aka Nautile Nov 2009 Page 2 of 16 HOW DOES THIS PROGRAM WORK Simple enough YOU write the array describing the knot in a standardized and symbolic manner That array will be the variable named MALR This matrix describe in an isometric diagram the lay out of the crossings in the knot diagram with their OVER UNDER read as seen by an ODD numbered half period going from low left to up right in the chosen frame of reference horizontal mandrel For the vertical cylinder the ODD numbered HP are running bottom right to top left This MALR array takes care of the ODD numbered half periods reading the parallel bight line column for mandrel row for cylinder from LEFT from RIGHT To provide for the EVEN numbered half periods reading from RIGHT to LEFT the calculator will mirror the MALR matrix oay this one becomes that one It should be ob
11. ossing and are denoted by YELLOW circle in the isometric diagram In the array they will be 9 the OVER crossing being 1 and the UNDER crossing being 0 O 9 0 9 1 9 1 9 0 9 1 9 1 95009 We get that simplified table That you now have to write the HP48 matrix 9 0 9 form ajo 9 0 9 119 1 rows Rown Rown Copyright Charles HAMEL aka Nautile Nov 2009 Page 9 of 16 lt is easy to make a mistake when entering an array Enter it TWICE each time STOre it under a different variable name That done ReCaLl each of the array on the STACK then type SAME push ENTER If the two arrays are identical then you get 1 as answer or O if they are different If they are different AT LEAST ONE is mistaken If they are identical then they are either both correct or both mistaken just verify attentively one of them to see it is exactly as you written table Failing to do that validation of the diagram of the writing of the array on the paper of the writing of the array in the calculator of the concordance between diagram and array entered may lead you to get mistaken half period coding calculation will have been correctly made on the wrong material Now for some real life diagrams and arrays REMINDER In THIS frame of reference horizontal mandrel the BIGHT rim are on the LEFT and on the
12. t and activate VIEW in the menu at the screen bottom and you will see this half period in full What is rocket sciences is the calculation for getting the COLUMN and ROW of each crossing AS IT APPEAR in the laying of the successive HP this is SCHAAKE amp TURNER part In fact the rocket science part was discovering the law governing the crossing but the equations are not really hard any 14 years old of my generation with the usual schooling would have tackled them without undue stress cannot know what say an American or an English school boy can accomplish but certainly it should be at least as good if not better With the TOTU in your HP48 you can export it as ASCII and get to the source in clear T XT format with some special HP characters mistakenly reproduced may be make the correction by reading the object in the EDIT of the HP48 real or emulator If someone want it just email me RPL is a user friendly language and HP did wonder with that HP48 Copyright Charles HAMEL aka Nautile Nov 2009 Page 5 of 16 HOW TO USE THE TOTU HP48 PROGRAM You loaded the TOTU program in either the calculator or the emulator and stored it is in the HOME open the TOTU directory PACKARD 48GX You will be using successively TWO programs PGSU and when PGSU 1 finished an optional TOTAL will be run provided FOUR READY MADE ARRAYS for FOUR KNOTS MASEDG 5 7 and
13. vious for every one that this translate the 1 2 3 n 1 n that is at the top of the diagram which becomes at its bottom 1 It remains to take on account that when an ODD numbered half period read a given crossing as say OVER the EVEN half period contributing in the making of this crossing read it UNDER To take that in account the calculator will be built unit matrix that will be subtracted from the mirrored MALR MALR mirrored Copyright Charles HAMEL aka Nautile Nov 2009 Page 3 of 16 After subtraction MARL Now it just remain to take the ABSOLUTE of this post substraction matrix to get the one that will be the MARL variable created by the calculator for the EVEN numbered half periods The type of each crossing have been changed for its opposite MALR for the ODD numbered HP and MARL for the EVEN numbered HP As this is not rocket sciences and don t envision one having difficulties there Now say that HEWLETT 48GX 128K you will have to look for it in the menu at the bottom of the screen as the variables created by PGSU will have make the list longer again not really rocket science HEWLETT HEMET 4 Packard Copyright Charles HAMEL aka Nautile Nov 2009 Page 4 of 16 Just make use of the ACTIVE STACK feature select the HP you wan
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