The Perfect Square: Leonardo DaVinci's Renaissance Discovery

[Artit Pongpira]

In the renaissance Leonardo DaVinci discovered that the perfect square is 1:1:618.
I would like to know if there is a perfect square measure, then is there a perfect measure for a triangle or a circle?
If so, could Pi be measured by a new and other calculation system which is similar to circumference divided by diameter? Could the perfect triangle match be 1:1:3?
Suppose there are constants which could lead to a solution of Pi by another way method, might there be a concept of calculating its infinite system to an including possibility in some kind of mathematical solution for calculation from a different formula to find it?

 

[Svein]

In the renaissance Leonardo DaVinci discovered that the perfect square is 1:1:618.

I do not understand. A perfect square is a product of two equal integers. Leonardo's perfect square was his drawing of the "Vitruvian man". Please explain what you mean.

 

[Artit Pongpira]

In the diaries of DaVinci, he wrote a perfect square measures 1:1:618 in frame format and this I know from the documentary of his books from study sources.

 

[Svein]

In the diaries of DaVinci, he wrote a perfect square measures 1:1:618 in frame format and this I know from the documentary of his books from study sources.

I think you have misunderstood. If you had written 1: 1.618, you would have referred to the Golden Ratio, which is something else (it has nothing to do with a square).

 

[Artit Pongpira]

oh, really? I thought it is one divided by one divided by 618? So it really stood written on and maybe I thought it could have meant so as a real perfect square ratio because they really wrote "perfect Square is 1:1:618" as quoted.

 

[Artit Pongpira]

Could possibly a perfect square be 1:1:618 even it looks similar to 1.618 since it could be a circumstance because the golden ratio continues to infinity, right?

 

[Svein]

I thought it is one divided by one divided by 618?

Which is 618. Seriously - a ratio between three numbers does not describe a square (or a rectangle).

Could possibly a perfect square be 1:1:618 even it looks similar to 1.618 since it could be a circumstance because the golden ratio continues to infinity, right?

Again, I don't understand what you mean - but if you ask whether the golden ratio is irrational, it is. The exact value is \frac{1+\sqrt{5}}{2}.

 

[Artit Pongpira]

Yes. I know the Golden Ratio number. But for the perfect square in this case I know too that it is maybe the solution to 618 which could be a unit measure by an amount? How many numbers describe a square? Should be 4 numbers likely? DaVinci wrote it with a secret documenting but those who found it in his diaries let 1:618 which is 0.0016181229773463... and under the calculation 1:1:618 could it be a unit measure for a square and it's origin frame or something? When a ratio is resulting to a number, it actually is like a constant, maybe? For example, if a cube is build with many parts of squares to represent the whole, would it complete for 618 and through that be like the mathematical circuit for the form of a square, perhaps?

 

[Svein]

How many numbers describe a square?

One. The length of a side.

 

[HallsofIvy]

I think you are using the wrong words. DaVinci's "vitruvian man" appears to be, at least approximately, a "golden rectangle", not a square, that has its two sides in ratio 1 to 1.618 (the "golden ratio"). If this documentary said that DaVinci "discovered" the golden ratio or golden rectangle, they were "puffing". There is no evidence that he actually used any specific calculation, other than his eye, for that size and there were earlier painters who used similar sizes. And if they used the term "perfect square" they really didn't know what they were doing!

The "golden rectangle" has the property that if you draw a new line, parallel to the short side, cutting the rectangle into a square and a smaller rectangle, this new rectangle is also a "golden rectangle".

 

[Mark44]

Yes. I know the Golden Ratio number. But for the perfect square in this case I know too that it is maybe the solution to 618 which could be a unit measure by an amount?

What do you mean by "solution to 618"? Equations have solutions, but plain old numbers don't.

How many numbers describe a square?

One - the length of a side.

Should be 4 numbers likely?

No.

DaVinci wrote it with a secret documenting but those who found it in his diaries let 1:618 which is 0.0016181229773463...

This has nothing to do with what is called the Golden Rectangle (http://en.wikipedia.org/wiki/Golden_rectangle), which is probably what you're thinking of. A rectangle for which the ratio of the short side to the long side is 1:618 is very long and extremely thin, not even close to ratio in the Golden Rectangle.

and under the calculation 1:1:618 could it be a unit measure for a square and it's origin frame or something?

No.

When a ratio is resulting to a number, it actually is like a constant, maybe?
For example, if a cube is build with many parts of squares to represent the whole

No. Cubes are three-dimensional and squares are two dimensional. A cube is not made up of squares.

, would it complete for 618 and through that be like the mathematical circuit for the form of a square, perhaps?

The question has been asked and answered, and is now closed. @Artit Pongpira, what you're on about sounds suspiciously like numerology. This is a site for actual science, so discussions about numerology are not permitted here.