Philosophical geometry, Part 2. The root of the three and its practical application

Now I will show you something, rock. Be sure to look under the cat, the most interesting pictures I hid there.

I continue the story about the application of philosophical geometry in practice. The last part was a review, she said that for many centuries geometry was used to search for universal ideal laws of nature. These laws were universally used in works of art, architecture, and spiritual life.

Today I will talk about the remarkable proportion of "the root of the three." I will show its sacred meaning, and under the cut I will demonstrate an example from modern design that will shock you;)
')
Let's start with building proportions. Take the segment AB.



Take it for the radius and build a circle with center in A.



Now we will build a second circle with the same radius, but with center B.



We have an ACBD figure, which is of great importance for our ancestors. It is called Vescica Piscis (bubble fish). The simplest and most important example is that it has long been a symbol of Christianity.



I will continue under the cut. I bet never guess what it will all end :)



Well, since we are already under the cut, I will start to pour pictures. We settled on Vescica Piscis and the symbol of Christianity. Here Christ is inscribed in this figure.



Here is a lot of symbolic fish.



By the way, for the first time I found out about it, having bought just such a pendant in the Uppsala Cathedral. So the symbol is quite used now.



But what is so remarkable figure? Let's go back to the constructions. Connect points C and D, and from their intersection draw another circle with radius AB. Draw a rectangle HKLM.



This rectangle has a wonderful property. Its height refers to the width of exactly three of them (√3 / 1). The root of three is one of the basic irrational numbers, but the basis of which was built a lot of paintings, buildings and just objects.

But if you think this is all old, sad and rotten, then you are mistaken. I promised a surprise. Ready? Just do not laugh out loud.



Yes, yes, this is it. The iPhone doesn't fit perfectly in this rectangle, but its dimensions are extremely close. It seems to me that this is not a coincidence that's why.
The root of three is about 1.732050 ...
The ratio of the sides of the first-generation iPhone (115x61) is approximately equal to 1.88524.
iPhone 3G (115.5x61.8) - 1.8599
iPod Touch (110x61.8) - 1.779

See, they strive for the ideal! Only thousands of technical reasons can disturb them.

Surprised? Embarrassed? Do not believe? There will be more now. Head over to apple.com



Hmm ... Something reminds me of this central unit. Well ka ...



Aha So you got caught. Let's take a closer look.



Notice how awesome Apple designs use this grid. This geometric construction, I do not even know how many hundreds of years. It was used in icons, temples, sculptures. Modern designers skillfully use it in ordinary commercial things and it continues to work flawlessly. Their things are buying against all sorts of reasons.

What is this mystic? Payment? Geometry? Philosophy? We can only practice and try to find out for ourselves.