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Chemical Combinations Mathematics

MATHEMATICS RESEARCH

1 .- flat-known figures:

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1.1.-concept:

a) Square:

The square is a polygon with four sides, with the peculiarity that they are all equal. Besides its four corners are 90 degrees each.

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b) rectangle:

The rectangle is a polygon with four sides equal in pairs. Its four angles are 90 degrees each.

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c) t riángulo:

The triangle is a polygon formed on three sides and three angles. The sum of all angles is always 180 degrees.

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d) trapezoid:

The trapezoid is a polygon four sides, but four different angles are 90 °

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e) diamond:

The diamond is a polygon four equal sides, but its four corners are different from 90 th

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f) Parallelogram:

The parallelogram is a polygon four sides parallel in pairs.

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g) Circle:

The circle is the region bounded by a circle, being the locus of points which are equidistant from the center

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h) Pentagon:

The regular pentagon is a polygon with five sides and five equal angles equal

hexagon:

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References:

http://www.bbo.arrakis.es/geom/

h http://www.arrakis.es/ ~ bbo / geom / index.htm

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2 .- perimeters of plane figures:

a) Square

Perimeter = 4a

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b) rectangle

Perimeter = 2 (a + b)

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c) triangle

Perimeter = a + b + c

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d) trapezoid

Perimeter = 2 (a + b)

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e) diamond

Perimeter = 2 (a + b)

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f) parallelogram

Perimeter = 2 (a + b)

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g) circle

perimeter: it means

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h) pentagon

Perimeter = 5 (a)

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i) hexagon

Perimeter = 6 (a)

References:

http://www.math2.org/math/geometry / es-areasvols.htm

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3.-Areas of plane figures:

a) Square:

Area of \u200b\u200bsquare = side squared

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b) rectangle:

Area of \u200b\u200brectangle = base.altura

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c) triangle:

Area of \u200b\u200btriangle = (base. Height) / 2

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d) trapezoid:

trapeze Area = [(base + base increased less) . height] / 2

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e) diamond:

diamond Area = (diagonal mayor.diagonal lower) / 2

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f) parallelogram

base.altura Area of \u200b\u200bparallelogram =

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g) circle:

Area of \u200b\u200bcircle = 3.14.

radius squared

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h) Pentagon:

Pentagon Area = (perímetro.apotema) / 2

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i) hex:

Area hex = (perímetro.apotema) / 2

References:

http://sipan.inictel.gob.pe/internet/av/geometri/ areas.ht m

http:// www.educarchile.cl/ntg/sitios_educativos/1618/propertyvalue-23062.html

http:/ / www.educared.cl/e5_area.htm

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4.-Polyhedra and Geometric Solids:

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4.1) Concept and elements (faces, edges, vertices).

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are real bodies that have a place in space, ie a geometric solid is a closed region of space bounded by certain surfaces may be flat or curved.

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Elements:

• Faces: The faces are external parts of a given solid. Ex: The faces of the Egyptian pyramids are 4.

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• Arista: is any line segment where two planes intersect. Ex: The faces that converge on the same edge of the pyramids of Egypt.
  
• Vertex: The apex is the point of convergence between two or more line segments. Ex: The apex of the pyramid of Cheops reached 146.59 meters above sea level.

4.2) regular polyhedra:

-Concept:

regular polyhedra are called all those who all their faces are formed by equal regular polygons, which are interconnected polyhedra equal angles. Classes:

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a) Characteristics of regular polyhedra:

- Types of regular polyhedra:

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a) regular tetrahedron :

is anyone who has four equilateral triangles together threes, form a regular tetrahedron. Has six edges and four vertices.

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b) regular hexahedron or cube:

is that polyhedron having six faces, who joined together form 4 right angles. It has 12 edges and 8 vertices

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c) regular octahedron:

is anyone who has eight-sided polyhedron regular bound together due to Nouméa they can be concave or convex. Has 12 edges and 6 vertices

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d) regular dodecahedron:

polyhedron has 12 faces in total, all equal. It also has 30 edges and 20 vertices also

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e) regular Icosahedron

polyhedron is anyone that has 20 faces, all composed in a regular polygon equilateral triangles. It has 30 edges, 12 vertices also .

References:

www.wkipedia.es

http://upload.wikimedia .org/wikipedia/commons/8/80/Ikosaeder- Animation.gif

http://es.wikipedia.org/wiki/Dodecaedro

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5 .- base area, lateral area, total area and volume of regular polyhedra,

a) Prisms:

-Concept:

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The Prism is a polyhedron composed of two parallel copies of some polygonal base joined by faces that vary between rectangles and parallelograms.

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In the case where joint faces are rectangular, the object is called a right prism.

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The rectangular prism or better known as a cuboid, and the octagonal prism are among the types of prism with a rectangular and octagonal base, respectively.
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Volume a prism is the product of the area of \u200b\u200bone of the bases to the length of the sides of joint.

Volume = (Area of \u200b\u200bBase ) * (Distance between bases )

-Name of prisms or classification :

• Prisma oblique: An oblique prism is a prism whose lateral edges are oblique to the bases

• Roof prism: is classified as having two congruent sides in parallel planes and the sides are rectangles. The height is the distance between parallel faces.

• regular Prisma: This solid is limited by two regular polygons which are known as base and as many rectangles as sides have base.
  

b) parallelepiped:

-Concept:

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Is usually two horizontal faces (which are the upper and lower bases, or floor and ceiling) rectangular, with four sides (flat walls) vertical, parallel and perpendicular to the bases.

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Rating:

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• straight parallelepiped: If its lateral edges are perpendicular to the bases. The faces are rectangular regions

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• Rectangular parallelepiped : ste E parallelepiped has the Following features where all sides are rectangular regions. It is also called a cuboid or rectoedro . When all the edges are congruent, called cube or regular hexahedron.

• rectoedro:

• cuboid: The cuboid is a rectangular parallelepiped basic right.
  
  
• Cube or hexahedron regular : A hexahedron is a six-sided polyhedron called a cube, all sides are equal.

• Rhombohedral: parallelepiped is all that is rhombohedral bases or regions of a polygon-shaped diamond.

6 .- base area, lateral area, total area, volume of prisms and parallelepipeds.

Tataedro:

base area: anywhere in this polyhedron can be the basis:

Base x height / 2

lateral area: any face in this polyhedron can be a side face:
Base x height / 2

Total Area:

Volume:

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regular hexahedron:

Base Area:

depends on the square or pentagon, depending on their shape.

lateral area:

4 x squared edge.

Total area:

Volume:

V = a3

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regular octahedron:

Base Area:

Base x height / 2

Total area:

Volume:

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regular Dodecaedo:

Area Base: is the area of \u200b\u200ba square or a pentagon depending.

Total Area:

Volume:

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Icosahedron:

Volume:

Pyramid:

Concept:

The pyramid is any solid figure formed by triangles as sides, which join at the same vertex. Also one of their faces is a polygon anyone who is called the base.

Formulas to find the:

Area base: Base x Height

lateral area: is the total of all areas of the sides.

Total area: is total between the lateral area between the base area.

Volume: is by multiplying area and squared by height, all three.

References:
http://es.wikipedia.org/wiki/Piramide_ (geometri-a)

Elements of the pyramid:

Faces : The faces of the pyramids are the external parts of said parallelepiped, with additional feature that the number of faces is equal to the sides of the base of the pyramid.

Sides: The sides of the base of the pyramid are called basic edges.

Base: The base plays an important role in the name of the pyramid, and on the number of sides that has

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types of pyramids:

• regular pyramid: got its name when the base is a regular polygon as well all lateral edges are congruent, that is of equal length. From this definition we deduce that all faces of a regular pyramid are congruent isosceles triangles and the height falls in the center of the base.

• triangular pyramid: this triangle has the properties that the base has the shape of an equilateral triangle, and their faces side of an isosceles triangle.

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• The Tetrahedron: is a pyramid formed by four equilateral triangles. Any face, therefore, may be the base. Also as a solid geometric figure.

References:

http://www.educared.cl/e5_volumen_piramide.htm

www. juntadeandalucia.es/averroes/iesarroyo/matematicas/materiales/4eso/geometria/poliedros/actividadespoliedros.htm

cylinder revolution

Concept: straight cylinder is also known as cilindor of revolution. Say yes to the cylinder is formed by a rectangle that rotates around one of its sides. The side opposite the rotation axis is the generating and generates the lateral surface of the cylinder, the sides perpendicular to the axis of rotation generated by the basic circles.

• base area: The formula used to determine the area of \u200b\u200bthe base of a cylinder is a circle, as their bases are circular. Its formula is:

• lateral area:

If we call L to the length of the generatrix and R is the radius of the base, the lateral area be. A = 2 (3.14) (r) (l)

• Total area: To determine the total area of \u200b\u200ba cylinder of revolution. We have to find your area lateral and basal area and added these areas gives us the total area of \u200b\u200bthe cylinder which is called: The total area.

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• Volume: The opposite to the rotation axis is the generating and generates the lateral surface of the cylinder, the sides perpendicular to the axis of turn generate basic circles.

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Cone of revolution:

• concept: Called cone of revolution or simply cone, a portion of space bounded by a conical surface of revolution and a plane perpendicular to the axis.
  

base area: The cone has a single base and has a rectangular shape, it can also determine your area of \u200b\u200bthe base is by formula to find the area of \u200b\u200ba circle like a cylinder. The difference being that the cylinder is 2 bases.

Àrea lateral : The lateral area of \u200b\u200ba cone of revolution : Height. radio. generating

Sl = 3.14 (r) xh

base area, lateral area, total area and volume of a cylinder of revolution

Cone of revolution : concept
base area, lateral area, total area and volume of the cone of revolution

Sphere: concept
area and volume of the sphere.

Exercises and problems of implementation problems where measures are determined using the clearance unknown variables in a formula.
Pythagorean Theorem.

Pagina de problemas:

http://www.juntadeandalucia.es/averroes/iesarroyo/matematicas/materiales/4eso/geometria/poliedros/poliedros.htm