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Chicle geometry [ School ]

topologiaOne wrote my first articles that students in the group “Geometry Hicks” was about the most basic aspects of geometry: Topology. To them I was curious to the concept and, inadvertently, were deepening in the main aspects of an axiomatic logical system geometric: continuity.

We started the experience introducing innovative educational blogs as a dynamic tool in the group and we came across this gem. I never fail to learn from them.

I leave your article, as we wrote. (Certainly, the video is great)


– How many sides does a circle?
– Two, the inside and outside.
Although it seems a mathematical joke, throughout this post you will find that it is not todo.Hablamos topology: is a branch of geometry studying only the properties of geometric figures that remain invariant when undergo transformations.
It is a geometry without measures, also called geometry of the rubber membrane or gum, Figures since they remain the same even if the submit to deformations (retorcer, distort, stretch, contract…) but no tears or breaks: it is as if they were made of rubber or clay.

For example, the size and shape are not topological properties: a balloon can inflate or deflate, deformed into a cube or take the form of a giraffe without tearing.
Sin embargo, a rope which is attached by the two sides not tied or, would be a topological property. One of these properties of the space curves, is a closed curve which divides the plane into two parts containing: the inner and outer.

The number of dimensions of a figure, proximity, the type of texture, having no edge or, the number of holes… are also topological properties.

The number of holes having a figure is what is known as the genus (is the maximum number of cuts that can be done without split it into two pieces).

  • A solid sphere is gender 0, since it has no holes and a cut is only necessary to break it into two parts.
  • A donut is genderless 1, it has a hole and you can make a cut without breaking into two pieces.
  • A rimless glasses have gender 2, because having two holes were two cuts can be made without breaking into two parts.
A sphere, a cube and a pyramid are topologically the same because they could transform into each other without breaking or join parts.
Sin embargo, a circle is not the same as a segment, since it would have to cut it somewhere.A typical example is the donut and cup of coffee, topologically equivalent figures, Gender 1.

And if you think, humans are also gender 1.

We are topologically equivalent to donuts: our digestive tract correspond to the hole of a donut.

Here you have a funny video:

The topology is of course a mathematical discipline, as such, often in the theoretical work need not have a method to find the solution, but the important thing is knowing that there is such a solution.
For example, there is always a pair of diametrically opposite points (antipodales) on the surface of the Earth that have exactly the same temperature and pressure. These points will vary and there is no way to find, but we can show that there always.

Historically, The first mentions of a geometry without measures come from Leibniz, whom llamógeometría position. But it is not until the resolution of the famous problem of the bridges of Königsberg by Euler, when discussing “Topology”.

Here are more topics of our fellow blogs: problem of the bridges of Königsberg and Mobius strip .