Comments on: Phi and the Golden Section in Architecture

By: dfrtryjj

dfrtryjj — Tue, 22 Mar 2022 12:41:39 +0000

thank you. now i have known.

By: Gary B Meisner

Gary B Meisner — Wed, 02 Sep 2020 06:10:52 +0000

In reply to lawrence strauss. I've not analyzed Greek key borders. From the ones I just examined, it appears that the proportions of their lines are based on integer relationships, not the golden ratio or other geometric progressions.

By: lawrence strauss

lawrence strauss — Sat, 29 Aug 2020 12:00:55 +0000

Hello. Have you analyzed Greek Key borfders? I’m actually most interested in how they originated and if the geometric repetition to “infinity” held any special significance in the Ancient Greek mind. With Thanks

By: alines

alines — Sun, 02 Aug 2020 15:33:48 +0000

Once you understand how simply and pervasively the golden ratio appears in geometry, the better question is how could they not have come across it.

By: Carson

Carson — Wed, 26 Dec 2018 13:22:36 +0000

In reply to Steven.

Oh, but carpenters do aim for perfection (I’m a master carpenter), but are often dictated to by existing or architectural designs to adjust their stairs to the space allocated. I was taught early on that the ideal rise and run of stairs equal 18″. Interestingly, a standard 2×12 measures 11.25″, and is the norm for stair treads. A standard 1×8 (typically used for risers) measures 7.25″. That allows 1/2″ to tuck in behind the back edge of the tread. It also allows for adjustment of the rise should there be less than optimal total run space available in any given structure. The point is, 18 is the guide.

By: Brian

Brian — Sun, 26 Aug 2018 13:45:07 +0000

I think it is also worth noting just how mathmatically perfect this number is. The exact number comes from taking the square root of 5 then add 1 and then divide by 2. The number rounded off is 1.618 but is non recurring. Now what is amazing is that if you square this number the decimals do not change, if you take the inverse the decimals do not change. This is the perfect number and appears in many mathmatical series like Fibinacci. The face that the ratio is present in nature is the beauty.

By: Jayden

Jayden — Tue, 31 Jul 2018 00:43:15 +0000

In reply to Wal. Yea

By: Gary B Meisner

Gary B Meisner — Sat, 28 Jul 2018 13:09:33 +0000

In reply to Adam.

This requires a bit more explanation. Spirals in nature are typically logarithmic (aka equiangular or exponential) spirals, which by themselves have nothing to do with the golden ratio. A golden spiral is just a very special case of a logarithmic spiral that expands at a constant rate based on the golden ratio rather on some other ratio. So by analogy, while gold is a metal, not all metals are gold. And technically speaking, connecting the arcs of the golden rectangles creates a spiral known as a volute, which is ever so slightly different than a true equiangular spiral. And the spirals found in plants, such as those in pine cones and seed pods, are based on successive numbers in the Fibonacci sequence. The ratios of Fibonacci numbers converge on the golden ratio as you go further in the series, but are not exactly the golden ratio. See more on this here:

https://www.goldennumber.net/spirals/
https://www.goldennumber.net/nautilus-spiral-golden-ratio/
https://www.goldennumber.net/plants/

By: Adam

Adam — Thu, 26 Jul 2018 01:21:31 +0000

In reply to Daniel. Explore perfect spirals in nature. Seashells and certain types of flowers contain perfect spirals which can be constructed from rectangles using the golden ratio. Happy hunting!

By: Gary B Meisner

Gary B Meisner — Sun, 15 Apr 2018 18:10:19 +0000

In reply to Thomas Gajdek.

Once you understand how simply and pervasively the golden ratio appears in geometry, the better question is how could they not have come across it. They didn’t have to know about irrational constants. All they needed to know was some simply geometric constructions. See https://www.goldennumber.net/geometry/ and the section titled “Many basic geometric constructions create golden ratio proportions” at https://www.goldennumber.net/golden-ratio-misconceptions-by-george-markowsky-reviewed/.