Wedding Program Wording Brother Gives Away

orientation can be considered as the ability to recognize the location of the cardinal points, as well as the different objects with respect to oneself and other landmarks.
To help in this task are used mainly two elements: the compass and the plane. You can also locate through the use of natural signs and the position of the sun and stars. There is a sport called
Guidance Sports (video) that con ste
a tour in the shortest possible time through different checkpoints intermiedios which houses a beacon that should be listed on a tab control.
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POWER POINT See explanatory.

What Do Those Gel Bracelets Mean?

real and not imaginary-triangles

Recently, a reader cienciasyletras wondering if it was possible to calculate the angles of a scalene triangle knowing the three sides. My response was that use the law of sines and taking into account that the sum of the three angles must be 180 º. With this you can get two equations with two unknowns to be two of the breasts wanted ... But immediately, I realized that there was a much more elegant and fast (large slip on my part to forget the law of cosines ).


As I thought of that solution was moving into the world "imaginary" numbers that are based on the value i (the square root of minus one). Suppose an isosceles triangle (the different base and two equal sides) and play to increase and decrease on both sides. As we make greater height of the triangle is increasing, and decreasing them also decreases. In the limit, when each side is equal to half the base and we have no triangle, the height is zero.

From there we enter the "world" of imaginary numbers. The results do not belong to the set of real numbers, but of the imaginary and therefore we do not exist, that the sides do not touch. But as both sides continue to decline increases the value of the height "imaginary" of this non-triangle to a maximum equal to half the base, when the two sides tend to zero (without turning it). As lower side of the non-imaginary triangle same height increases up to a maximum may not exceed .

This no longer a curiosity without , but hypothetically we could consider as a phenomenon of reality by which from an arbitrary distance there are two arms of variable length, trying to touch. Assuming this fenómento in the field of quantum mechanics, the possibilities are imaginary component not be ruled out and that contributes finally to the real score. If so the strange "world" of non-imaginary triangles may be telling us that they are as real as triangles themselves, or at least strange world is essential for our real world is as unique as mechanics tells us quantum.



real triangle sides touching each other and determine the length of the height, which can be arbitrarily large, up to infinity. The sides of the non-imaginary triangle, however, without touching each other in the real world seem to figure out the distance that separates them. When you are just an infinitesimal at both ends of the base, determine a non-triangle with a height equal to half of the same base. Is it an indication of the holistic properties presented by quantum mechanics, or the role that appears to be the "world" imagined it?.

Development (only for those who are curious):
If you look at the figure, we rest the base of the triangle in the x-axis. From one end build a circle of radius equal to one side, and from the other end another circle of radius equal to the other side. With the values \u200b\u200bfound in the point y (y is the height of the triangle obtained) we can easily calculate the tangent of the two angles C and A, and B is 180 º-A - C.




The tangent of the angle C is the ratio y / x . The tangent of the angle A is: and / (bx ).

far so very normal, but what would happen if sum of the two sides and c is less than the b-side of the base of the triangle? Obviously there would be no triangle, since the two circles would not get to touch. What results would get to proceed as we have done? The values \u200b\u200bwould be imaginary, which means they do not exist in reality, but in the "world" of so-called imaginary numbers whose base is the value i, corresponding to the square root of -1. Only in this "world" would make sense, but that does not prevent us from studying what happens.

For simplicity, we will change the triangle. The base is b , but the two sides to and c be equal and we will call the two a. The results will always imagined that to be less than b / 2 .

Proceeding in a similar way as we have found that the height of the triangle h (the value of the and ) function of the ratio n = b / a be:
y = h = + - b / √ 2n (4 - n 2)

The lower level is where the value of each side to tend to the middle of the base. The greatest height h we have when the sides tend to zero and, therefore, the value of n becomes infinite. Then the height will b / 2 .


Finally:
In the "world" real as they get older sides will also increase the height as much as we want, to infinity. When the lower side will decrease the height to be zero when the sides are equal to half the base. As sides are becoming less than half of the base we enter another "world", the imaginary numbers and the height will increase as both sides decline to be highest, with the value b / 2 (half base) for values \u200b\u200bof the two sides tend to zero. The highest point b / 2 non-triangle is obtained for a value base b and two sides of value "practically zero."