Bet geometric [ School ]

Retrieving some items from my students, they could disappear erase your blogs experience educational innovation, I saw this group pi-tágoras joining the polygons and playful very successful way.

The educational approach in the form of competition is a valuable resource that does not have to lose the rigorous training approaches. On the contrary, knowledge to explore critically and entertaining couple. This group of students has been successful in its approach, already quoted at the time.

We begin a new year and what better way than to learn from our students

Bet geometric

The other day, being the most suitable place for the free exchange of ideas, we, in what is still the bar, proposed the following game, we propose to all readers.

• A man, significantly higher, certainly, gave us, ten coins of one euro, and we said: -If you are able to do with those ten coins, five rows of four coins each row, not only give os los 10 euros, but in addition, I invite you to what you want right now-.

Poor us, Happy thinking: “bah, students like us, what we get fixed”.The case, spent an hour and did not get anything clear.

• Insurance of our abilities and with the face of outrage, look at that man and told: -This is impossible- to which he replied: -True, I forgot to tell you that a coin can belong to multiple rows, eso si, I do not do a row of ten coins and me-you subdividais.

Now if we think our. Poor us, again. The match ended (if, we went to watch the game) and Mr. announced he was leaving, taking with the coins and the solution. Hours later, and already at home, paced, in the minds of some the solution. A geometric solution (What a coincidence!).

Dear reader, if you want to think the solution, we recommend you do not pass these lines that will be here where exposed (and where finally start talking about drawing, that is already good…).

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As we have often done in drawing class, we simplify the problem we are asked to solve, much simpler one.

In this case it is the same, and for the analysis and solution of this problem we follow a similar procedure.

Try the coins as points, and rows will not be anything other than segments determined by these points. So we are asked to determine five known segment ten points, and that each segment is formed from four points, namely, each point is common to the segments.

Obviously, and as we have indicated, this is not general for any ten points, if the problem is to find the specific position in which this is true. Let us now begin the analysis of this interesting problem.

If we select 10 points in the plane, unaligned'm sure that most people comes to mind the idea of ​​a polygon, ten-sided polygon.

When we asked to do five lines, dotted lines in Several many of us can think of the idea of ​​multiple paths to a common point as two lines that intersect at a point.

Pentagon

And from these ideas began to fight with this little game geometric.

Taking the limit situation the idea of ​​straight,comes a time when, as we have to place five segments occurs to us to place five points, knowing that those five points, common across two segments are completely determined the five segments, note that five points define a polygon with five sides:

a pentagon.

But we still have five more points that determine, and all of them common to two segments, now comes into play when the idea of ​​the star polygon inscribed the Pentagon.

We now turn our starry polygon inscribed the Pentagon.

We have placed our lines whose intersections are the points, and with them certain segments.

Returning to the initial problem we will have determined, five rows of four coins each row.

Sincerely, we are left without money and without drinking, so that, at least we hope that you have enjoyed.