Apparently there’s free wine at CES

Sorry for writing all these,but i could not help writing all these since i saw the word pixel..and wanted to elaborate on it..

Calculation of monitor PPI

Theoretically, PPI can be calculated from knowing the diagonal size of the screen in inches and the resolution in pixels (width and height). This can be done in two steps:

1. Calculate diagonal resolution in pixels using the Pythagorean theorem:

d_p = \sqrt{w_p^2 + h_p^2}

2. Calculate PPI:

PPI = \frac{d_p}{d_i}

where

* dp is diagonal resolution in pixels,
* wp is width resolution in pixels,
* hp is height resolution in pixels and
* di is diagonal size in inches. (This is the number advertised as the size of the display.)

Pythagorean theorem:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

As pointed out in the introduction, if c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, Pythagoras’ theorem can be expressed as the Pythagorean equation:

a^2 + b^2 = c^2\,

or, solved for c:

c = \sqrt{a^2 + b^2}. \,

If c is known, and the length of one of the legs must be found, the following equations can be used:

b = \sqrt{c^2 – a^2}. \,

or

a = \sqrt{c^2 – b^2}. \,

The Pythagorean equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found. A generalization of this theorem is the law of cosines, which allows the computation of the length of the third side of any triangle, given the lengths of two sides and the size of the angle between them. If the angle between the sides is a right angle, the law of cosines reduces to the Pythagorean equation.

PROOFS:

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1.Proof using similar triangles
This proof is based on the proportionality of the sides of two similar triangles, that is, upon the fact that the ratio of any two corresponding sides of similar triangles is the same regardless of the size of the triangles.

Let ABC represent a right triangle, with the right angle located at C, as shown on the figure. We draw the altitude from point C, and call H its intersection with the side AB. Point H divides the length of the hypotenuse c into parts d and e. The new triangle ACH is similar to triangle ABC, because they both have a right angle (by definition of the altitude), and they share the angle at A, meaning that the third angle will be the same in both triangles as well, marked as θ in the figure. By a similar reasoning, the triangle CBH is also similar to ABC. The proof of similarity of the triangles requires the Triangle postulate: the sum of the angles in a triangle is two right angles, and is equivalent to the parallel postulate. Similarity of the triangles leads to the equality of ratios of corresponding sides:

\frac{a}{c}=\frac{e}{a} \mbox{ and } \frac{b}{c}=\frac{d}{b}.\,

The first result equates the cosine of each angle θ and the second result equates the sines.

These ratios can be written as:

a^2=c\times e \mbox{ and }b^2=c\times d. \,

Summing these two equalities, we obtain

a^2+b^2=c\times e+c\times d=c\times(d+e)=c^2 ,\,\!

which, tidying up, is the Pythagorean theorem:

a^2+b^2=c^2 \ .\,\!

This is a metric proof in the sense of Dantzig, one that depends on lengths, not areas. The role of this proof in history is the subject of much speculation. The underlying question is why Euclid did not use this proof, but invented another. One conjecture is that the proof by similar triangles involved a theory of proportions, a topic not discussed until later in the Elements, and that the theory of proportions needed further development at that time.

2.Euclid’s proof

3.Proof by rearrangement

4.Proof using differentials..they have a proof for everything..

the video was taking along time to play..i heard till cholera..never download your videos but just save it in facebook..i will download your videos only when i have the safest place to keep it somewhere..

Ashley was speaking loudly…guess this is my novel number 100

Alcohol and new technology… I don’t think you can technically fail with that combination, but I now see why they had cases on those.
= )