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Unit 14: Geometric. Volume

OBJECTIVES:

• Recognize prisms, pyramids, round bodies and regular polyhedra, and its elements.
• Find the volume of a body with a unit cube.
• Know and apply the relationship between volume and capacity (m3, kl, l dm3).
• Use the relationship between m3, dm3 and cm3.
• Calculate volumes of cuboids and cubes.
• Solve problems starting with other simpler problems.

MUST LEARN:

Prisms: geometric are two equal and parallel faces called bases, and the rest of their faces are parallelograms.

prism elements: Bases

1. : two polygons equal and parallel. The shape of the base indicates the type of prism (hexagonal, pentagonal ...).
2. lateral surfaces: are the faces that are not bases.
3. basic Edges: are the sides of the polygons of the bases. Edges
4. side: are the sides of the lateral edges that are not basic.
5. Vertices: are the points where they join the edges.

Pyramids: are geometric whose base is a polygon and whose faces either side are

triangles having a common vertex.

Elements of the pyramids:

1. Base: is a polygon either. The shape of the base indicates the pyramid
   type (hexagonal, pentagonal ...).
2. lateral surfaces: are the faces that are not the base.
3. basic Edges: are the sides of the circle of the base. Edges
4. side: are the sides of the lateral edges that are not basic.
5. base Vertices: are the vertices of the polygon base. Vertex
6. or top of the pyramid: is the point where are all the lateral edges. Bodies

round:

• Cylinder: has two circular bases and a curved surface.
• Cone: has a circular base and a curved surface.
• Sphere: only have curved surfaces.

The volume of a body: is the amount of space it occupies.

To find the volume of a cuboid or cube is taken as the unit of measure a cube and the number of cubes of each body. This link can practice this concept mentally calculating the number of "cubes" unity "is missing.

are volume units cubic meter (m3) cubic decimeter (dm3) and cubic centimeter (cm3).

1. 1 m3 = 1,000 dm3 1 dm3 = 1,000 cm3
2. 1 dm3 = 1 liter

The volume of a cuboid is equal the product of its length by its width by its height.

PRACTICE:

In the links presented below will have the opportunity to practice and reinforce the concepts used in class. Prisms

• geometric. Polyhedra, developments and sections. Polyhedra
• Learn how to calculate volumes
• volume. Activities
• Test your knowledge on volume measures ..

Miley Cyrus Big Boobs 2010

Hirsch's Conjecture refuted by a

When we take the linear programming course, teach us that the problem is represented by d variables and n constraints seeing

This geometric point of view we have to, for example, two variables (d = 2), a area that is bounded by straight lines that give the sides of a polygon, then we as the axes variables will be two and constraints (eg n = 5) will lead to each side of the polygon, which finally gives us the area where the feasible solutions.

The best we have on one side, which maximize or minimize a function of two variables (the objective function).

If we see three variables we imagine the space within which begin to act planes that cut through one side, and finally we leave an irregular polyhedron (but convex) with vertices, faces or facets and edges.

When operating the simplex method, it moves from one vertex to another through the edges, from one corner to another corner to find a solution that always improves previous and to reach the optimal solution.
recently by the news that publish newspapers, I learned something I had said Warren Hirsch, connected to the above problem, in which he states that the diameter (combinatorial) graph of a polyhedron of dimension "d" and defined by "n" inequalities can never be greater than "nd".

But to understand it referred is necessary to review some graph theory:

• Distance between two vertices: is the number of arcs that connect in the shortest route possible.
• Eccentricity of a vertex: is the longest distance between that vertex and another
• The diameter of a graph: is the maximum eccentricity of any vertex of the graph, ie the longest distance of any pair of vertices. To calculate the distance to be calculated for each pair of vertices and take the value of the calculated value.

Returning to the above would have to if I have two variables (dimension d = 2) and five constraints (inequalities n = 5), the longest distance between any pair of vertices never to exceed 3 (see the initial image to view if true, we see that in any case, we need more than 3 arc to connect two vertices). But it was still

just a guess. Recently the mathematical

Francisco Santos has found a case in which the rule is not met before, built a polytope dimension 43 (variables) with 86 facets (restrictions) spindle-shaped in which the diameter was greater to 43, which honestly is not very encouraging because instead of shortening the number of steps to reach the optimum would indicate that possibly in some cases we need to nd more steps (or edges) to connect the most remote corners.

That usually happens when we start with the worst solution (farthest from the optimum) and seek to reach the optimum in the fewest of steps or iterations as in the simplex.

For more information:

Cantabrian A teacher solves a problem word ...
El Diario Montanes - 26/05/2010
"is part of the Simplex Method, an algorithm that all companies in the world currently used for road design, production planning, ...
A English resolves the conjecture of Hirsch, laid over ... La Vanguardia
Resolved Hirsch's conjecture, a mathematical problem 50 years ABC.es Professor
solves one of the major mathematical puzzles Terra Peru
elmundo.es
the 42 articles »

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Learning Unit 13: Area of \u200b\u200bplane figures

Here you can access a given task that will help you to learn the concepts related to this unit.

OBJECTIVES:
• Calculate the area of \u200b\u200bsquares, rectangles, rhombuses, rhomboids and triangles.
• Calculate the area of \u200b\u200bregular polygons.
• Calculate the area of \u200b\u200bcircles.
• Calculate the area of \u200b\u200bplane figures, breaking them down into areas known figures.
• Solve problems by reducing them first to another known.

MUST LEARN:

Area of \u200b\u200brectangle: is calculated by multiplying its base by its height.
Area of \u200b\u200bsquare: is calculated by multiplying the side itself. Area
diamond: the product of its diagonal diagonal less divided by 2.
rhomboid area: the product of its base by its height.
Triangle Area: is the product of its base by its height divided by 2.
area of \u200b\u200bregular polygons: the product of its perimeter by its apothem divided by 2. Area
circle: it is the product of the number π by its radius squared.
area of \u200b\u200ba plane figure : we must first decompose other figures whose areas we know to calculate and then sum the areas of these figures.

explanatory video:



PRACTICE:

In the links presented below will have the opportunity to practice and reinforce the concepts used in class.

1. What is the area of \u200b\u200ba polygon?
2. Area parallelogram and the triangle.
3. Area rhombus and the trapezium.
4. Areas of polygons.
5. Area of \u200b\u200bthe circle.

In the link below, choose the activity represented in the attached picture "Little Shop" and you can see if you learned to calculate the area of \u200b\u200bthe main plane figures:

http://genmagic.org/mates1/ap1c.html

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