# It is a turn

It is a turn to the elegant solutions. I want to describe in this site my opinions and my proposals about the elegant solutions of the different problems.

### •

I agree with Bob Palais that the definition of the well known mathematicel constant pi
(𝜋 = C / D) represents a wrong definition of the circle constant.
But the number "pi" is not only a confusing and unnatural
choice for this constant.
*There is a deeper theoretical meaning* behind
the new definition C / r of the circle constant! ...

If one turn is always one turn, and a circle is defined by the turn in a distance r,
the turn is the circle constant. The circumference of a circle C is given by a turn 𝜃₀
and a radius r: C = 𝜃₀ r

My point of view about the circle constant is in the article

Circle constant is a turn (itisaturn.pdf, updated 2019-04-08).

### •

Maybe you want to see my methods of Squaring the circle.

### •

A modified and simple method for the drawing of the golden ratio is given in my article Golden ratio and the angle turn/10 (updated 2020-07-22).

### •

Angle unit degree is defined as 1° = 1 turn/360.

Can we have a better definition of the angle unit?

See: A better angle unit

(updated 2020-09-28, a minor text change).

### •

I have to write about the length units of the pixel grid devices. A pixel of a pixel grid device is always a device pixel. Thus, a pixel is not device independent! The display screens have the different pixel sizes! And the length units are already defined by the metric system. But, the "absolute" length units for the pixel grid devices are redefined by the "device independent pixel". This is the source of many problems. The length unit "device independent pixel" is a problem! A "device independent pixel" represents a constant length value, and it can not represent the device pixels with the different pixel sizes! And there are also many other problems of the "device independent pixel"!

The article Pixel grid device units has a solution for the length units of the pixel grid devices. (updated 2020-08-29, MIT license for the files pixelgrid.js and pixelgrid.min.js)

### •

My opinion about the decimal clock is given by the article Decimal clock (Updated: 2020-09-23. The Sun symbol is now independent from a font.).