- How many sides does a circle?
- Two, inside and outside.
mathematician may seem a joke, throughout this post you'll find that it is not at all. We talked about
topology : is a branch of geometry that studies only the properties of solids that remain invariant when subjected to changes ..
without action is a geometry, also called geometry of the rubber membrane or gum, since the figures remain the same even if subjected to deformations (twist, distort, stretch, get ...) but tears or breaks, it's as if they were made of rubber or clay.
For example, the size and shape are not topological properties: a balloon can be inflated or deflated, deformed in a bucket or take the form of a giraffe without tearing.
However, a rope that is attached by both sides with a knot or not, it would be a topological property. One of these properties of space curves is a closed curve divides the plane that contains two parts: the interior and exterior.
The number of dimensions of a shape, proximity, type of texture, having border or not, the number of holes ... are also topological properties.
The number of holes presenting a figure is what is known as the gender (the maximum number of cuts that can be done without splitting it into two pieces).
-A solid sphere is of genus 0, since no holes and only requires a court to break it into two parts.
-A donut has genus 1, it has a hole and you can make a cut without breaking it into two pieces.
-pair of spectacles without glasses have genus 2, because they have two holes to make two cuts can not break into two parts.
A sphere, a cube and a pyramid are topologically the same because we could transform one into another without break or join parties.
However, a circle is not the same as a segment, since it would have to cut it somewhere.
A typical example is the bagel and cup of coffee, figures topologically equivalent gender 1.
- Two, inside and outside.
mathematician may seem a joke, throughout this post you'll find that it is not at all. We talked about
topology : is a branch of geometry that studies only the properties of solids that remain invariant when subjected to changes ..
without action is a geometry, also called geometry of the rubber membrane or gum, since the figures remain the same even if subjected to deformations (twist, distort, stretch, get ...) but tears or breaks, it's as if they were made of rubber or clay.
For example, the size and shape are not topological properties: a balloon can be inflated or deflated, deformed in a bucket or take the form of a giraffe without tearing.
However, a rope that is attached by both sides with a knot or not, it would be a topological property. One of these properties of space curves is a closed curve divides the plane that contains two parts: the interior and exterior.
The number of dimensions of a shape, proximity, type of texture, having border or not, the number of holes ... are also topological properties.
The number of holes presenting a figure is what is known as the gender (the maximum number of cuts that can be done without splitting it into two pieces).
-A solid sphere is of genus 0, since no holes and only requires a court to break it into two parts.
-A donut has genus 1, it has a hole and you can make a cut without breaking it into two pieces.
-pair of spectacles without glasses have genus 2, because they have two holes to make two cuts can not break into two parts.
A sphere, a cube and a pyramid are topologically the same because we could transform one into another without break or join parties.
However, a circle is not the same as a segment, since it would have to cut it somewhere.
A typical example is the bagel and cup of coffee, figures topologically equivalent gender 1.
And if you think human beings are also gender 1. We are topologically equivalent to the donuts, our digestive tract correspond to the hole of a donut.
Here you have a funny video:
more topics on the blogs of our partners: problems of the bridges of Königsberg and Möbius strip.
Finally, a break from such geometry to teach this cartoon:
Here you have a funny video:
Topology is of course a mathematical discipline, and as such often in theoretical work is not necessary to have a method to find the solution, but the important thing is knowing that there is such a solution.
For example, whenever is a pair of diametrically opposite points (antipodal) on the surface of the Earth that have exactly the same temperature and pressure. These points vary and there is no way to find them, but we can show that there always.
Historically, the first mention of a geometry without measures derived from Leibniz, who called geometry of position. But not until the resolution of the famous problem of the bridges of Königsberg by Euler, when speaking of "topology." Here For example, whenever is a pair of diametrically opposite points (antipodal) on the surface of the Earth that have exactly the same temperature and pressure. These points vary and there is no way to find them, but we can show that there always.
more topics on the blogs of our partners: problems of the bridges of Königsberg and Möbius strip.
Finally, a break from such geometry to teach this cartoon:
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