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    What are tessellations?

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    Andrea Mills

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    What are tessellations?

    In plane geometry, tessellations are the ways of covering the plane with one or more geometric figures repeated indefinitely without overlapping. These geometric figures, called "tiles", are often polygons, regular or not, but they can also have curvilinear sides, or have no vertex.

    How are tessellations done?

    Tessellation consists in repeating a figure several times with one of the isometries until you get a plane covered by the same figure drawn several times. How did we do it? this figure repeated several times. By doing so we have obtained a TASSELLATION.

    What are regular tessellations?

    Regular tessellations. Regular (or periodic) tessellations are those that respect the following rule: there are two independent translations that send the tessellation into itself (with "independent" we mean that the two translations must not have the same direction).

    What are tessellations for?

    In plane geometry, tessellations (sometimes tessellations or pavements) are the ways of covering the surface with one or more geometric figures repeated indefinitely without overlapping. ... In mathematics, the tessellations of space have also been studied a lot, where the pieces are solid (→ origami).

    What is geometry for in life?

    Galileo and Descartes attribute to geometry the ability to understand a large part of the phenomena of the world and observe how it allows us to formulate and solve many problems and produce knowledge.

    The regular tessellations of the plane

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    Why study geometry?

    Geometry studies the properties of geometric figures and their mutual relationships both in space and in the plane. Why is it so difficult to study geometry? Simple. Our brains, by nature, more easily record and store images than letters or numbers.

    What would a world be like without mathematics?

    Life would be overwhelmed by total chaos and men would live in a disoriented and destabilized world! In fact, numbers, logic and rationality are present in everything we do every day in real life.

    Why do only some polygons cover the floor?

    In order for a regular polygon to plug the plane, its internal angle must in fact be a divider of 360 ° 360 ° 360 °. And this applies to the triangle (60 ° 60 ° 60 °), the square (90 ° 90 ° 90 °) and the hexagon (120 ° 120 ° 120 °), but not the pentagon (108 ° 108 ° 108 °) ).

    What are the figures that cover the top?

    The regular polygons that can fill the plane by themselves, without the help of another polygon are the triangle, the square and the hexagon.

    Which polygons tile the plane?

    • equilateral triangles.
    • squares.
    • regular hexagons.

    Which regular polygons tile the plane?

    The task of establishing which regular polygons are all congruent with rules and properties. we have constructed the tessellations using the rip reflection discovering that IT IS POSSIBLE TO TILE THE PLANE WITH THE SAME POLYGES ONLY IN THREE CASES: EQUILATERAL OILS (60 ° · 6) Cabri Géomètre ”, which is possible to construct regular isometric polygons.

    What do you do in geometry?

    Geometry is the science that studies geometric figures, their properties and their transformations. Any set of points is called a geometric figure.

    Why is Euclidean geometry studied?

    Euclidean geometry helps us to easily study the world we live in and the properties of the geometric figures we draw. We can say that we live in a Euclidean world.

    How do you learn geometry?

    1. Study constantly.
    2. Always review what you have learned in the past, so as not to forget the postulates and theorems.
    3. Check out other websites and watch videos to better understand the more complicated concepts.
    4. Write down the formulas on the flashcards to help you remember them.

    What is Euclidean geometry based on?

    Euclidean geometry is based on primitive axioms and concepts (also called primitive entities). * Axioms are propositions taken as true and indisputable (Postulates). * The primitive concepts do not have a mathematical definition, but they are: the point, the line and the plane.

    What does Euclidean geometry mean what does it deal with?

    Euclidean geometry The term used in the first place to refer to the arrangement on hypothetical-deductive bases of the geometry of the plane and of space operated by Euclid (XNUMXrd century BC) in the Elements.

    What is projective geometry used for?

    Projective geometry is the part of geometry that models the intuitive concepts of perspective and horizon. It defines and studies the usual geometric entities (points, lines, ...) without using measurements or comparing lengths.

    What are the fundamental points of geometry?

    There are three fundamental geometric entities: the point, the straight line and the plane. They constitute abstractions.

    How many geometries are there?

    Saying that the three different types of geometry in dimension 2 are elliptical geometry, Euclidean geometry and hyperbolic geometry means that on any surface (ie variety of dimension 2: see this article by Barbara Fantechi on the website) you can put a metric " modeled "on one of these three ...

    What is middle school geometry?

    geometry is the discipline that studies properties and measurements of geometric figures. Geometric figures are parts of space, of various shapes, made up of sets of points.

    What does third grade geometry study?

    Geometry is often referred to as the science that studies the properties of geometric figures. That is, it deals with the study of forms both in the plane and in space and their mutual relations.

    How many non-Euclidean geometries are there?

    The three geometries have been more correctly defined by F. Klein, respectively, parabolic, hyperbolic and elliptical geometry. To imagine the two geometries distinct from the Euclidean one, 'models' can be used.

    What does Euclid's fifth postulate say?

    The statement: If a straight line cuts two other straight lines, determining internal angles on the same side whose sum is less than that of two right angles, extending the two straight angles indefinitely, they will meet on the side where the sum of the two angles is less than two right angles.

    Who is it that invented mathematics?

    Greek mathematics is believed to have begun with Thales of Miletus (c. 624-546 BC) and Pythagoras of Samos (c. 582 - 507 BC).

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