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Thread: Has anyone seen this Before? Infinite Summation Question

  1. #1

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    Has anyone seen this Before? Infinite Summation Question

    A few years back, I thought of this method as a way of
    representing a numbers inverse as an infinite summation. I doubt
    its original, so Let me describe it and maybe you can tell me if you've seen this before.

    VB Code:
    1. Given a Base number, and a Number to get its inverted infinite expansion based on the base number,
    2.  
    3. Start with 6 columns:
    4.  
    5. Col1    Col2a   Col3    Col4    Col5    Col2b
    6.  
    7. Where:
    8. Col1 = Line #, Initial condition = 0
    9. Col3 = Number to convert
    10. Col4 = Number of times Col3 value can be subtracted from Col2a or Col2b
    11. Col2a and Col2b : Alternate between Base * (Value of Col2a or Col2b of last line), empty, or
    12.  col2a = col2b - col3*col4, or col2b = col2a – col3*col4
    13. Col5 : Inverse sequence of Col1, Built when:
    14. value of Col2a or Col2b previously in Col2a or Col2b. Ignored when Col2a or Col2b ends at 0.

    ok. I don't want to turn this into a midterm essay, so I'll go strait to an example.
    Lets say you wanted to express 1/11 as an infinete summation of 2^(-n1) + 2^(-n2) + 2^(-n3) + ...
    {2 is the base}
    The Col’s initial conditions are:
    0, 1, 11, 0, Blank, Blank.
    Watch This:


    The reason I put the 1* in is if you were using a different base, ie 3, 5, etc… you can have a number from 1 to (Base – 1) as a Multiplier.

    Has anybody seen this Or something similar before?

    -Lou

  2. #2
    PowerPoster beachbum's Avatar
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    Take your dog for a walk Lou!!!!
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  3. #3
    PowerPoster sail3005's Avatar
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    copy...paste....interesting

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  4. #4

  5. #5
    PowerPoster beachbum's Avatar
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    Originally posted by NotLKH
    [B]Hmm,
    Doggy jokes and LSD Hazes the best you can do?
    Well, we could ask for some nicer colours... but i do like the arrows... nice size and style.
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  6. #6

  7. #7
    PowerPoster beachbum's Avatar
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    Homer: "They did what to who now?"

    Yeah of course I understand it. It is a new design for that Twister game. Hope it goes well.. do u need any links to the major toy manufacturers or are u right with the search engine?
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  8. #8

  9. #9
    PowerPoster beachbum's Avatar
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    Originally posted by NotLKH
    Hey BB!
    Long time no C!
    Thought you Bailed!
    Twister! Whats their Theme Song?
    OOOOOh! Shrew it!

    When is 1 + 1 = 3?

    -Lou
    Well no i didnt bail.. unless u count getting bailed.. but that is a different story... honestly i thought she was older

    When does 1+1 = 3.. there are a number of answers
    a) In that song (i forget the name) about love and babies
    2) In your average Intel processor
    E) In boofhead business textbooks about synergy
    iv) In 1984 when big brother deems it so...

    I could go on and on but i just finished my coffee and it looks like beach time now ... where I will no doubt spend my time pondering over mathematical equations!!
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  10. #10

  11. #11

    Thread Starter
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    One More Thing!

    Hey, Beach, What do you think of this?

    (Press the buttons on the right hand side to see what happens.
    Don't play with the dimension box with values > 10. Really Slow!}

  12. #12
    PowerPoster beachbum's Avatar
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    Public Displays of Furniture... emm not recently... well that isnt true either.. yes i have sat out on the balcony on my chair with my laptop programming... and come to think of it i did get some odd looks.. hmmm maybe u are onto something here...
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  13. #13

  14. #14
    PowerPoster beachbum's Avatar
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    Ok back to serious maths...
    Nice proggy (and i like the Mike Oldfield reference). I wonder if it may be an idea to start the cubes at an offset value ... i was a bit underwhelmed by clicking on the first few buttons until the cubes were formed from a diff angle. Did u make urself? Might be a good thing to throw at the gamers forum.
    Ok time to fly now... sun surf and sand...
    Regards
    Stuart
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  15. #15

    Thread Starter
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    Originally posted by NotLKH
    One More Thing!

    Hey, Beach, What do you think of this?

    (Press the buttons on the right hand side to see what happens.
    Don't play with the dimension box with values > 10. Really Slow!}
    3d Rotational Cubular Example.

    Whole n X n rotates,
    Individual Rows Rotate.

    Hit Stop the Motion to get the Quit button.
    At the moment, Don't remember what that Rogue button does.
    sooooo,
    DON'T PRESS IT!!!!

    -lou
    Attached Images Attached Images  

  16. #16

    Thread Starter
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    Originally posted by beachbum

    (and i like the Mike Oldfield reference).
    Thanks!
    Didn't know you'ld pick up on that! {Mike Oldsfield, that is!}
    BTW, It looks physically impossible, but there is a way to actually
    construct this.
    20 years ago {Or longer} when rubiks came out, I thought of this.
    The physical Mech is pretty impressive. But...
    Costly to develop. However, nothing beats the actual feeling of holding
    it in your hands, twisting and turning...
    Err, ehh,
    I'm talking about a toy!!!

    Your suggestions are really good! If I release the Progie, I'll be doing that.

    Yepp!, I made it myself. I'm humble, though, its not anything really.
    BUT
    Once I'm finished, It'll really be a Blueprint to make the actuall Mechanism.

    -Lou

  17. #17

    Thread Starter
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    BTW,
    Did you play with the Zoom?
    Its not live action, I haven't built that in, although its simple enough. Just a call to refresh the image. Just didn't bother to do it yet.


    Anyways,

    Isn't math the most UnderVisited Forum here?
    Nobody'ied even know if it became another chit-chat area.

    heh,heh.

    -Lou

  18. #18

    Thread Starter
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    OOPS, I forgot to tell you.

    To select a Cube, Click on the Picture.
    Whichever Cube has a Vertex closest to the Mouse pointer
    when you click, becomes the "Selected" cube. {It'll become
    outlined.} This cube is the anchor for any of the three potential
    row manuevers.

    -Lou

  19. #19
    PowerPoster beachbum's Avatar
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    Hi again Lou... yeah i found out what the rogue button does.. well, me and the fire brigade that is

    Yeah i had a play around with it, including zoom etc. I havent yet looked thru all ur coding. It is excellent proggy for 3d stuff. Minor criticism and hope u take right way.. or would u prefer me to beat around the bush??? if u do decide to go further with it u gotta burn that GUI and start again!! Too brutal? Hope not. I gather that it is just a test model anyways... but urgh dont go into interior design work!!

    I didnt originally know about clicking on the cubes but will try it out for sure. And just so i dont leave on a bad note I repeat that i think that the code and modelling is most excellent.

    Oops forgot to bash u one as well about Oldfield vs Oldsfield!!!!! It is Oldfield


    Cya!!
    Stuart
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  20. #20
    PowerPoster sail3005's Avatar
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    hey NotLKH, do you have an exe for the program? i don't have VB at the moment.

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  22. #22
    PowerPoster sail3005's Avatar
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    alright, thanks a lot. sorry i don't have vb.

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  23. #23

    Thread Starter
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    Here you go.
    I tweaked it a little, added a couple of labels, and killed that
    dummy button.
    All it is is a Cube of Cubes, where you can rotate the Main cubular
    structure, and also select an Anchor Sub cube which is the key to
    rotating any of its 3 columns. Rearrange the cubes, then try to put it back with all the cubes colors synchronized again.

    It's really a pre-release, scratch project, as Beach was hoping. Again, I was developing it to be more of a blueprint for a Physical
    Puzzle and Demo.

    But, the 3Ding was a fun, tough nut to crack.


    -Lou

  24. #24

    Thread Starter
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    Originally posted by beachbum
    ... if u do decide to go further with it u gotta burn that GUI and start again....Oops forgot to bash u one as well about Oldfield vs Oldsfield!!!!! It is Oldfield
    Cya!!
    Stuart
    Stuart,
    Bash away!
    I can take it!
    re: Oldsfield- Have you ever noticed the proximity of the s key
    to the d key? A combination of Big fingers, and a nip or two resulted in that tragic slander of the Oldfield name.


    re: GUI- You must be talking about the PlaySkool Color Theme.
    Heh, I like intense Blueishness!
    Most of my tools are colored that way. Deep Dark Blue Background,
    Bright Yellow TextFields, and Pale Blue Buttons!

    But if this does get released, there'll be a UserPanel to Customize
    the Colors.
    Also, The cubes will be floating right on the desktop, with a little
    bit of BitBlt magic.

    AnyWays, Back to the Original Topic.
    Anybody seen that methed to convert a number to an infinite series before?

    Or, is it too nebulously explained?

    -lou

  25. #25
    PowerPoster beachbum's Avatar
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    Originally posted by NotLKH
    Stuart,
    Bash away!
    I can take it!
    re: Oldsfield- Have you ever noticed the proximity of the s key
    to the d key? A combination of Big fingers, and a nip or two resulted in that tragic slander of the Oldfield name.
    Uh huh .....
    re: GUI- You must be talking about the PlaySkool Color Theme.
    There's a blue in there, and a yellow as well, and a scary red, that sometimes goes blue, open wide come inside, it's designed by Lou... designed by Lou
    AnyWays, Back to the Original Topic.
    Anybody seen that methed to convert a number to an infinite series before?

    Or, is it too nebulously explained?
    Sowwy!
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  26. #26

    Thread Starter
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    Just so ya KNOW,
    THE BUTTON COLORS GO FROM pALE bLUE TO sCARY RED TO SIGNIFY (aaaggghhh! caps lock on!!!) Much better now.
    Ok. They change color because it signifies rotation in one direction versus another.

    BTW, I'm not a big fan of that red color either, but as stock colors go, the reds are pretty meager. None of them I like!!!!.


    -Lou

  27. #27
    PowerPoster sail3005's Avatar
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    thanks for uploading the exe.

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  28. #28
    PowerPoster sail3005's Avatar
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    WOW, thats AWESOME!!! i gotta get VB installed so i can see the code! thanks a lot for uploading it!

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  29. #29

    Thread Starter
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    {<- BTW: Does anybody else think these smilies look more bored than embarrassed? }
    Thanks!

    Sorry, but I really didn't comment the code up, so I wouldn't be surprised if its a little overwhelming.
    If you want some explanations of the code, just ask!

    -Lou

  30. #30
    PowerPoster sail3005's Avatar
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    Yeah, i'll be sure to ask. Man, i GOTTA get VB installed.

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  31. #31

    Thread Starter
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    If all you want to do is inspect the code, All the VB files, the frm,
    the vbp, can be viewed in a text editor, such as WordPad,
    NotePad, or you can even use Word or any of the other higher
    level apps.

    -Lou

  32. #32

  33. #33
    PowerPoster beachbum's Avatar
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    Was that a bump or a push in the back accompanied by a trip and a kick to the guts?
    Stuart Laidlaw
    Brightspark Financial Software
    http://www.gstsmartbook.com

  34. #34
    PowerPoster sail3005's Avatar
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    Someone deserves the "Old Thread" award

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  35. #35
    sql_lall
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    Talking Try this:

    No, i haven't seen it before, but here is a simple one:

    1/x written with lots of (i.e. Base) y:

    = the sum of (k=1 to infinity) of:
    y^(-k) * (y-1) / x

    This is because:
    the sum of (k=1 to infinity) of y^(-k) = (y-1)^-1

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