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  1. #11
    Join Date
    Apr 2012
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    Default Re: Construction a Golden Rectangle

    Quote Originally Posted by wizard509 View Post
    Acorn , I used to be very aware of the "Golden rectangle" but now a days like handrawn I tend to go by what looks right. I tend to think of the value of Pi as 22/7 or rounded to 3.14159.
    For pi, use 355/113 (3.14159292), c.f. pi at 3.14159265; 355/113 is 2,000 times more accurate.

    Agreed, people do forget that 5/3 (1.6) is very close to Phi (ɸ), around 99% accurate.

    Acorn
    Acorn - My currently active Xara software: occasionally serviced XDPX, purposely unserviced XDPX12 & XDPX11 (32/64-bit), unserviced XWD Premium 15 & 12, XPGD10, X3D7 and lots of 'permanently-owned' licences back through time (to CC's Artworks)

  2. #12
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    Info Re: Construction a Golden Rectangle

    Here is a quick demonstration of the crossed-eyed elephant:

    Click image for larger version. 

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    1. Create a Red circle.
    2. Clone, colour Green and align centres vertically to edges.
    3. Clone again, colour Yellow and double size.
    4. Clone this, colour Cyan.
    5. Align bottom Yellow and Green, top Red and Cyan.

    The (red) length of the Red/Green intersections is taken as unity.
    Extend the right end to the the right-side intersection fo Yellow/Cyan. This (blue) length is Phi (ɸ).

    Note this is the Golden Ratio and a little more would be needed to get a Golden Rectangle but the eyes have it.

    Acorn
    Acorn - My currently active Xara software: occasionally serviced XDPX, purposely unserviced XDPX12 & XDPX11 (32/64-bit), unserviced XWD Premium 15 & 12, XPGD10, X3D7 and lots of 'permanently-owned' licences back through time (to CC's Artworks)

  3. #13
    Join Date
    Feb 2007
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    UK
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    16,033

    Default Re: Construction a Golden Rectangle

    ah now I see what you mean... very good

    [btw the two circles in my eye were in ratio 1:0.618]
    -------------------------------

  4. #14
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    Default Re: Construction a Golden Rectangle

    Quote Originally Posted by handrawn View Post
    ah now I see what you mean... very good
    [btw the two circles in my eye were in ratio 1:0.618]
    handrawn, 'eye' saw that straight away - same as 1.618::1 as Phi (ɸ)'s inverse is ɸ - 1.

    Acorn
    Acorn - My currently active Xara software: occasionally serviced XDPX, purposely unserviced XDPX12 & XDPX11 (32/64-bit), unserviced XWD Premium 15 & 12, XPGD10, X3D7 and lots of 'permanently-owned' licences back through time (to CC's Artworks)

  5. #15
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    Apr 2012
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    Info Re: Construction a Golden Rectangle

    OK, perhaps the concept is a bit too exotic but keep it in mind for future reference.

    Here is a construction that delivers a Golden Rectangle from an initial pentagon.

    1. Create a Red pentagon, with rotation 180.
    2. Clone it, colour it Green and change to a circle.
    3. Place its centre on the pentagon left base corner.
    4. Shift-drag until the circle's edge touches the pentagon's opposite sides. [I used a mixture of Guides and Zooms as there is no snap point unless you add set the circle's rotation as 36 (or rotate all the construction by the same)!]
    5. Clone the pentagon, colour it Blue and change to a square.
    6. Resize and position its base to match the pentagon.
    7. Drag up the top to touch the green circle.

    Click image for larger version. 

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    I have left a simpler approach outstanding should anyone still want to have a go.

    Acorn
    Acorn - My currently active Xara software: occasionally serviced XDPX, purposely unserviced XDPX12 & XDPX11 (32/64-bit), unserviced XWD Premium 15 & 12, XPGD10, X3D7 and lots of 'permanently-owned' licences back through time (to CC's Artworks)

 

 

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