Patient Advocate Jobs Michigan

TEOREMA DE PITAGORAS

Pythagoras THEOREM

To speak of another proof of the theorem of Pythagoras mention Euclidean movements.


* Rotation: to make a rotation is needed at the point around which will make the rotation and an angle that determines how many degrees is this.

parallel
* Translations:
To make a parallel translation takes a segment AB. If a point Q moves to a point Q 'on AB, then the length of QQ' is equal to the length of AB and QQ 'is parallel to AB, while QA is parallel to Q `B.


* Reflection and symmetry
To make a reflection or symmetry is making a line called the axis of reflection or symmetry axis.
Thus if a point is in the axis of symmetry, the reflection is the same point, ie that the line is reflected in itself. Any other point on the plane is reflected across the axis of symmetry.



Another proof of the theorem of Pythagoras

Three Euclidean transformations can be used to give another demonstration of the Pythagorean theorem, namely: the whole triangle, the sum of the squares of the lengths of the legs equals the square the length of the hypotenuse.

Be A `BC a right triangle where BC is the hypotenuse.
Now make the following changes:


1. By reflection symmetry axis BC, obtain the right triangle ABC.


2. For translation, according to BC, the triangle ABC we subtract the triangle T1.

3. By rotating 90 ° around, we subtract the triangle T2.

4. With the triangle T2 is repeated step 2 and continues until the triangle T6.

is clear that the hypotenuse of the triangle ABC, T2, T4 and T6 are all equal to BC and that two consecutive 90-degree angle form. This means that they form a square.

As the area of \u200b\u200bthe square is (BC) 2 and square area can be found in the area of \u200b\u200b5 parts that compose it, namely the four equal triangles and square then you must:

Simple Diagram Of A Camera

TESELACION HEXAGONAL

regular tessellations

regular tessellation is coverage of the plane with regular polygons and congruent. Are only three regular polygons that cover (or tile) the Euclidean plane: the equilateral triangle, square and regular hexagon.
The only regular polygons that completely cover a flat surface are the equilateral triangle, square and hexagon.
As the union at each vertex must sum to 360 º no gaps, the only regular polygons that add up to 360 when joined by their corners, interior is all three.

equilateral triangles, squares and hexagons

semi-regular tessellation are those containing 2 or more regular polygons in their training. A semi-regular tessellation has the following properties:
1. This consists only of regular polygons.
2. The arrangement of polygons at each vertex is identical.
3. There are only 8 semi-regular tessellations





tiles Construction Method removable

This is a very good technique where you draw a figure on paper and then cut it and superimpose it on another paper take their boundary several times to get a tiling. Method

rabbits
is a method by which they are used only circles and ovals and create figures like rabbits but can only do black and white but is rarely used in the does white tessellation, but many do so in combination with method Encino, francaso "which is a mistake because with that method does not create tessellations but forms of alcohol bottles. With this method it is essential that not a single figure is equal to another but what differentiates the color can be put on a black and white alike in shape and the first tiling to be done with this method was the form of a bunny rabbit with 54 but all different from each other.


IMPLEMENTATION OF THE TILES IN REAL LIFE


The tessellations have been used around the world from ancient times to coat floors and walls, and also as decorative furniture, carpets, tapestries in this case speak of the hexagonal tiling of a soil as shown in the picture.


method to tessellate that has been used on the floor shown in the photograph

tessellation Allen is one of the simplest methods, the construction of your employer, involves turns 60 º and 180 º of two arbitrary lines, to which underlies an equilateral triangle.
As in all cases equilateral pattern, turning it 60 degrees is obtained a hexagonal pattern (based on a regular hexagon), exactly as when turning a triangle of 60 º is generated a regular hexagon.

Since the underlying design a regular hexagon, the tiling is a special case of the previous case, as a regular hexagon is a polygon with even number of sides and has parallel. Therefore, the tiling is generated by translation, as the vectors joining midpoints of opposite sides.


Photograph of a hexagonal floor tiling

One advantage of the hexagonal tessellation is that it be cheaper and performs better.
Indeed, it is easy to see that the ratio between the square of perimeter and area worth:
For the triangle to the square 16 and the hexagon.