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[edit] Planar Angles : Horizont H

[edit] Metric Unit of planar angles

Visual and triangular parameter

Horizont = 1 dm ( m )

Horizont² = 1 dm² ( m )²

We already know some angular measures in their different dimensions, but always referring or taking as reference point to radial centres on which we measure these angles.

In this case always it gives us radial angles that are circumference arch with such units as degrees or radians in longitudinal way or square degrees and steradians in surface form.

But I think we lack the most important centre or reference frame for us, our eyes.

Our field of vision has a width that many estimate around 50º of lateral width.

In this case I would say that it is rather a field of reception of brightness, but there is other vision field very important for us that it is the observation field.

We don't capture all what happens in our field of vision appropriately, but rather when we want to see any interesting for us, we direct the look toward this place and we observe and frame the object in question inside a small visual field that we could call reception field.

Although if this object is big or it is very close, we cannot capture it appropriately in its entirety and we have to look sequentially to be able to appreciate all its details.

Now then, the question would be this case: How many width of visual field we use as maximum to capture an image appropriately without having to move the eyes?

Because each person will surely have his, but in general we can find a half value for all person.

I have made my own observations and I believe that an angular surface (lineal) acceptable would be about 1 dm² from a meter of distance with almost square form, that is to say, 1 x 1 dm.

Therefore, (if other doesn't exist) we will say that our visual reception of a horizontal field will be of one square horizont, similar to 1 square decimetre for meter, and whose surface will be square (1 dm. x 1 dm. = 1 dm²).

Horizont² = 1 dm²( m )²

But for what reason this parameter can serve us and reason we use centimetre instead of degrees? For the first question, to have a parameter adjusted to our peculiarities of vision. And to second, we use metric measures instead of angular ones with object of being able to adjust the surface that we observe in metric measures that can serve later to adjust the dimensions of objects.

Then would it be necessary to wonder: How many horizonts can have a circumference seen from its interior; and a sphere?

With this type of planar angles we can not embrace circumference nor sphere due to these are curve surfaces and planar angles are plane surfaces.

Nevertheless, we can make successive applications of planar angles, that is to say, to go applying different observations around us and this way embracing the entirety of the celestial sphere o any other ones.

In this circumstance we can say that circumference a sphere have about 20 Pi and 400 Pi horizont approximately, that is to say, 62,8 and 1256 horizonts aprox.

The used formulas with this measure type are very simple as it is glimpsed. The simpler would be:

S = $ x d²

Where S is the surface we want to know of a distant object. $ is the angular surface that can be measured with a simple device for such events (a squared visor), and of course, the necessary distance d from the object to observe.

Considerations:

With the previous formula -maintaining the surface of the observable object that logically is unalterable- if we make diminish the distance, that is to say, we go coming closer gradually to the object, we see that the angular surface goes spreading to infinite which tells us that we are using an eminently visual parameter, which alone can have real value when we mange our observation field and the applied formulas.

In this case, if we could observe with a hypothetical and ideal microscope an atom and comes closer until being next to it, we would have an angular surface of enormous proportions.

But we already know how small an atom is in fact.

[edit] Longitudinal planar angles

Although for reason of its visual foundation we have begun seeing the planar angular surface, the planar angular longitude logically also exists.

This would be that plane and lineal width of our horizon of vision with a magnitude of 1 dm to a meter of distance.

Of course their measure unit would be the horizont = 1 dm (m).

And the usable formula would be then:

L = L X d where

L would be the frontal longitude of any observable object.

L the angular longitude and

d the distance to that the object is.

Of course, all the considerations on the planar angular surfaces are valid for the longitudinal ones.

Definition:

Planar angle is an angular geometric structure that is built and defined uniquely by lines and planes, and subjected to metric measures exclusively.

It consists of:

---A angular vertex where the lines or planes that form the angle cut themselves.

---Sides are the lines or planes that form the angle.

---The angular horizon is the line or plane that cuts perpendicularly to the distance d, and where the objects to observe are located.

---The distance d or bisector of the angle on which the distance units and the distance of the observables objects are measured.

The angular dimensions come determined by the width or opening of the angle and the distance d from the angular vertex until the angular horizon where the observable object is situated.