Construction a Golden Rectangle

[Acorn]

This Challenge allegedly has deep connections to art, geometry and our psyche.

The Golden Ratio is calculated to be 1.618::1.
It describes a pattern that is found in sunflowers, playing cards, architecture and web design layout.

Here are two presentations of a Golden Rectangle where the sides are in Golden Ratio proportion:

Attachment 122576

Now it can be shown that the Golden Ratio is integral to the pentagon, where it is Diagonal Length::Edge Length:


It is therefore possible to construct the blue Golden Rectangle from this knowledge, as shown.

In this Challenge, I wish you to uncover a simpler construction of the Golden Rectangle.

Acorn

P.S. Phi (ɸ) is (√5 + 1) / 2 ≃ 1.6180339887498948482045868343656

[handrawn]

first attachement not showing here... unless you have a deleted image broken link...

[handrawn]

well at least you spared us the fibonacci sequence

how accurate do you want it - 1.6 is usually ok for this lowly cartoonist, and since that is one:three-fifths makes it all a whole load easier... but I tend not to use it that much, I go by what looks right..

[Acorn]

well at least you spared us the fibonacci sequence
how accurate do you want it - 1.6 is usually ok for this lowly cartoonist, and since that is one:three-fifths makes it all a whole load easier... but I tend not to use it that much, I go by what looks right..

I actually slipped in the Fibonacci Sequence through the sunflowers.

The attachment got deleted instead of the one wrongly enumerated in the second diagram.

The diagram should have been:



Acorn

This one had two typos:

[handrawn]

I actually slipped in the Fibonacci Sequence through the sunflowers.

don't tell me... next up is the golden spiral

[Acorn]

don't tell me... next up is the golden spiral

Nope, only pink elephants:



Acorn

[wizard509]

This Challenge allegedly has deep connections to art, geometry and our psyche.

The Golden Ratio is calculated to be 1.618::1.
It describes a pattern that is found in sunflowers, playing cards, architecture and web design layout.

Here are two presentations of a Golden Rectangle where the sides are in Golden Ratio proportion:

Attachment 122576

Now it can be shown that the Golden Ratio is integral to the pentagon, where it is Diagonal Length::Edge Length:


It is therefore possible to construct the blue Golden Rectangle from this knowledge, as shown.

In this Challenge, I wish you to uncover a simpler construction of the Golden Rectangle.

Acorn

P.S. Phi (ɸ) is (√5 + 1) / 2 ≃ 1.6180339887498948482045868343656

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.

[Acorn]

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]

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

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

[handrawn]

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

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