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WORLDS polyhedron (webquest)

INTRODUCTION

"Do not enter here who does not know geometry"

This sentence could read above the entrance to the Academy of Plato (fourth century BC) where they met to discuss problems of philosophy, logic, politics, art, etc. and gives us an idea of \u200b\u200bthe importance of old has been granted to the knowledge of geometry.

The Italian astronomer and physicist Galileo Galilei (1564-1642) referring to the Universe wrote: "This great book that continually We have opened the eyes can not be understood without first learning to understand the language and know which characters are written. It is written in mathematical language and the characters are triangles, circles and other geometric figures . "

One of the most famous theorems applied to the polyhedra is owed to a Swiss mathematician named Leonard Euler , which in 1750 published his theorem on polyhedra, in which indicates the ratio between the number of faces, edges and vertices a simple polyhedron (no holes) either: the number of faces (C) plus the number of vertices (V) equals the number of edges (A) + 2.

C + V = A +2

Why there are only five regular polyhedra? First
to be defined is what a regular polyhedron. "To those polyhedra (volumetric figures formed by polygonal faces) in which all faces are the same regular polygon (triangle, square, pentagon, ...). Given this definition, there are only five possibilities. Why? The answer lies in the construction of the vertices.
In a corner of a regular polyhedron converge a fixed number of polygonal faces and these must be at least three because if they are only two, instead of a vertex which is an edge originates. But there are also faces a maximum of possible, but this number depends on the polygon.

can only make buildings in which they converge at the vertex 3, 4 or 5 equilateral triangles (tetrahedron, octahedron and icosahedron), 3 square (cube) or 3 pentagons (dodecahedron). And if anyone thinks that the design tricks you can make an account to confirm what was said. To be able to make the vertex, the sum of the interior angles of the polyhedra that flow must be less than 360 ° so we left a small gap to unite and to lift the corner. If you do account, you'll see that the only cases in which it occurs are the five regular polyhedra.

In this unit you will begin to study some geometric ubiquitous in nature and works of humans: the polyhedra.

Guggenheim Museum (Bilbao)

We further study of the most common and simple (regular polyhedra) and end up with the bodies of revolution (cylinder, cone and sphere). I will well remember regular polygons and aplicaciones.Esta your work unit will need manual for which we can use cardboard, scissors, glue, sheets of embossed sites, sticks, clay, porous plastic (porespan), etc, but good that I leave to your choice.

A solid is anything that takes place in space. In geometry we study their shapes and sizes (solid or spatial geometry.) Geometric bodies can be of two kinds:

- Incorporating flat faces (polyhedra)
- Having some or all of their curved faces (BODIES ROUND).

With this activity the aim is that you learn in a more dynamic and participatory common polyhedral figures, you join a group, you acquire new knowledge about demostréis polyhedra and also of your wit, but also has your stability.

This activity not only be worth it to know you better polyhedra more entertaining for the exam but also all activities conducted throughout the course will count towards the final grade.

TASK

The presentation of the activities performed by each group shall be in two ways:

1. Be posted on this blog the activity undertaken by each group in Word format, that document will be shown a photograph of each of the figures made, these documents shall be suspended a week before the date prior to exposure.

2. The groups will present the work done in class and it may be used if it aids required by the center offers, for example the projector if they want to make your presentation via Power Point. In this exhibition Debaran to all members of group fairly.

PROCESS

For the successful implementation of the activity should follow the following guidelines:

1. The groups will consist of 5 alumn @ s , these groups will be formed randomly, unless the teacher wish to the modification.

2. Polyhedral figures are compiled from the five regular polyhedra and round bodies seen in class, in each figure should be reflected each of the most significant parts of it. This will require manual work, for which we can use cardboard, scissors, glue, sheets of embossed sites, sticks, clay, porous plastic (porespan), etc, but good that I leave to your choice.

3. Each figure must be accompanied by a sign with your name.

4. Activity also consist of a theoretical part is to write everything you know and have seen in relation to each class of polyhedral figures: description of each polyhedron, parts (indicated in each figure), formulas for volume, area, etc ...

5. Each group will conduct a personal assessment of the activity: difficulties, assessment of group work, usefulness of the activity, media used, etc ...

RESOURCES

To carry out the activity as well as your textbook, you will find interesting and useful information on the following websites:

http://www . kalipedia.com /

http://www.korthalsaltes.com/es/

http://www.matematicas.net/

ASSESSMENT

For the evaluation of the activity will take into account the following aspects:

1. Development of the activity is measured as the share of manual work as the theoretical.

2. Exposure of the activity will take into account the activity posted on this blog and the presentation made in class.

3. Participation of all group members.

All these involve the same assessment criteria for the final of the activity.

CONCLUSION

At the end of the exposures of each activity of the various groups will brainstorm, evaluating the positive and negative activity in order to improve subsequent activities and get to learn more entertaining and cale more knowledge you with these tasks.

Monument Dusseldorf. Eduardo Chillida
1971 (Germany, Dusseldorf, Thyssen Gebäude)

Quote of the Day:

"Nothing happen in the world without that stands out, somehow, the presence of a maximum or minimum rule "Leonard Euler

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NOT ONLY ARE SUFFERING

Situations more than a century ago served as impetus for new mathematical discoveries and developments currently displayed on hobbies.

"A mathematician is worth a good hobby, and contributes more to mathematics than a dozen articles mediocre". John Edensor Littlewood

COLOR MAP

One such situation is that of color maps with certain restrictions.
Coloring a map with the minimum number of colors so that countries with a boundary line (and not just a point) do not have that color was an issue first raised by a student at Edinburgh , Francis Guthrie in 1852. From it came to Augustus Morgan of which he could not solve the problem, but extended the challenge from other mathematicians. The conjecture that four colors were sufficient became famous when Arthur Cayley in 1878 proposed it to the Mathematical Society of London, one of the most important mathematical societies in the world at that time, as a problem to solve.
In 1879, the English jurist and mathematician Sir Alfred Kempe published he believed to be a demonstration, but years later found an error in his proof.
not an easy problem. In the late nineteenth showed that five colors suffice and that three colors are sufficient to color any map. In 1950 it was known that if the map was less than 36 countries can be colored with four colors, and in 1976, with the help of computers, concluded that four colors suffice.

tested with the mainland.

HOURGLASS
have two hourglasses to measure respectively 3 minutes and 5 minutes. These watches do not have as intermediate bar, ie they can only measure the time between the fall of the first grain of sand and the last. Using the clocks we measure exactly four minutes. How can we do?

THE MYSTERY FILES OF THE 7
A fichologo place 7 pieces and draw a circle that contains 4 tabs. You draw two circles so that each tab is separate. Note for perfectionists: it is not making perfect circles, but to round out the chips.

Quote of the Day:
"If time is the most expensive, the loss of time is the greatest of the extravagance" Benjamí n Frankl in