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
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Here is a quick demonstration of the crossed-eyed elephant:
Attachment 122604
- Create a Red circle.
- Clone, colour Green and align centres vertically to edges.
- Clone again, colour Yellow and double size.
- Clone this, colour Cyan.
- 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
ah now I see what you mean... very good
[btw the two circles in my eye were in ratio 1:0.618]
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.
- Create a Red pentagon, with rotation 180°.
- Clone it, colour it Green and change to a circle.
- Place its centre on the pentagon left base corner.
- 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)!]
- Clone the pentagon, colour it Blue and change to a square.
- Resize and position its base to match the pentagon.
- Drag up the top to touch the green circle.
Attachment 122631
I have left a simpler approach outstanding should anyone still want to have a go.
Acorn
Here goes:
Attachment 122666
- Create a Red square.
- Clone it, change to a circle, colour it Green and place behind.
- Place its centre on the midpoint of bottom edge of the Red circle.
- Shift-drag the circle's edge to touch the top right corner of the Red square.
- Clone the Red square, colour it Blue and place immediately under the Red square.
- Drag its right edge so its top right corner touches the edge of the Green circle.
This construction does rely on a steady hand as there is no snap for the circle radius.
Other suggestions are very welcome.
Acorn
Cheers Keith, that is a good remedy. I will although still look for one that doesn't have a dimension constraint.
Found one!
Attachment 122672
- Create a Red square.
- Half its width.
- Clone it, colour it Green.
- Change the Red square to editable Shapes and delete its top left corner.
- Position the red triangle to the top right of the Green rectangle.
- Rotate it about this point so its longest edge it horizontal.
- Clone the Green rectangle, colour it Blue.
- Drag its right edge to the right end of the Red triangle.
Acorn