Tessellations

Hello friends today we will discuss about tessellation which you need to study in grade VII. Generally in mathematics you didn't heard this term but it has a relation with mathematics. A tessellation is a pattern made by repeating shapes. Making Tessellations require a creativity of an art with capability of solving puzzles. In this world there are many natural tessellations also present.
In modern world very few people are aware of the term Tessellations. The connection between math and art is very strong and frequent but very few people are aware of that. Tessellation also covers a regular space without overlapping and without leaving any space. For example a chessboard is a Tessellation, made of squares with no gap in between and without overlapping. The pattern of the brick on a wall is a Tessellation made by rectangle.
Whenever we deal in mathematics we aware of terms like algebra, calculus, trigonometry ...etc. if we talk about the term tessellation we are not aware of this term. But as we know that there is a very strong relation between art and mathematics and that is only because of the term like tessellation, so we can say that Tessellations has a relationship with mathematics. The tessellation definition is that shape of repeated things. (know more about cbse latest sample papers, here) The repeated things can be anything, if we take an example of a chessboard then it is a pattern made by squares as squares are repeated regularly in the chessboard but the thing we need to notice is that there is no gap between the square, so if we are drawing any tessellation then the thing we need notice that there is no overlapping between the figure and there is no gap between the figure. In the next session we will discuss about Reflections/translations on a coordinate plane. 

Geometric concepts

As we all are very well aware that geometry is the one of the oldest branch of mathematics. It plays an important role in mathematics to solve various kinds of problem. The term “geometry” is comes from the Greek word “Geometron” which is formed by the combination of two word “Geo” and “Metron”. The word “Geo” refers to Earth and the word 'Metron' refers to measurement. The need of the  Geometric concepts was felt in several years ago when person realizes to measure their land when they want to sold or buy their land. The basic application of geometrical construction were made centuries before the mathematical principles on which construction were based and recorded.
In the basic concept of geometry we generally studied about the points, lines, planes, closed flat shapes and many others. These are the most basic concept of geometry that provides the helps in describing, designing and constructing any type of visible objects. In todays life, the concept of geometry used in various field like architects, engineers field, planning for constructing the buildings, bridges roads and many other geometrical architecture cal things. In the below we show you the some of the basic
Concepts of geometry:
A) Point: In geometry a point can be defined as a mark of point which has no length, no breath and no height. It occupies the position and location but no magnitude. This point helps in creating various other type of geometrical shape.
B) Line: The line can be defined as a distance between the two points. A line has no width. Usually a line refers as a straight line. (know more about icse board, here)
C) Line – segment: This line segment different form the line. In line segment, the part of a line with two definite end points is defined but in line these definite points are not define. These line segments are very helpful to form various geometrical shapes like square, rectangle and so on.
As like above there are other geometrical concept are defining in mathematics. Like interesting lines, parallel lines, perpendicular lines and so on. In the next session we are going to discuss Grade VII, Tessellations.

Tessellations in Grade VII

Previously we have discussed about list of rational numbers and In today's session we are going to discuss about Tessellations which belongs to grade VII of maharashtra state education board. Generally in mathematics you didn't heard this term but it has a relation with mathematics. A tessellation is a pattern made by repeating shapes. Making Tessellations require a creativity of an art with capability of solving puzzles. In this world there are many natural tessellations also present.

In modern world very few people are aware of the term Tessellations. The connection between math and art is very strong and frequent but very few people are aware of that. Tessellation also covers a regular space without overlapping and without leaving any space. For example a chessboard is a Tessellation, made of squares with no gap in between and without overlapping. The pattern of the brick on a wall is a Tessellation. made by rectangle.

Now let’s see how we can solve math problems for free related to Tessellations,

Now we have a task that  we want a cover a floor with tiles. We can cover it with square tiles since square tiles never leave gaps and always fit together. But in this activity we will try it with a rectangle where we will provide some very good shapes to that and then make a Tessellation by repeating its shape over and over again. It is a very interesting thing to do.

We require following things for making this Tessellation.

Ruler

Pencil

Scissors

Index card 3” *5”

Transparent tape

Colored marker and pen

2.5” *3” grid paper

Now we need to follow the steps below

Cut the index card in half and create rectangle

Fix the area of the rectangle (area=length * breadth)

Now draw a line between two adjacent corners on one of the longer side of a rectangle. Your line must be straight.(want to Learn more about ,click here),

Cut along the line you draw. Now take the piece you cut outside and slight it across the opposite side of the triangle.

Now you find a new shape that you never seen before. Now you just need to take this piece out and now draw another line that connects two adjacent corners on one of the short size of the shapes.

Now you need to cut it along new line and you will get a shape which is little smaller than the previous one. Take the piece out and now combine all the pieces, now you can see you made a Tessellation.  

Now let’s move to four color theorem. According to this theorem if we have a Tessellation of four colors in such a manner that no same color is together in such a manner no tiles of same color meet at the curve of positive length.

If we talk about intuitive statement of four color theorem that any given separation of the plane in to contiguous regions called as map, the region can get colored using most four color such that no two adjacent regions have the same color.

Note: each region of the map should be contiguous otherwise we add new demand to the statement, which the theorem doesn’t have.

If we talk about real world, not all countries are contiguous. Countries like Russia, USA, Alaska are not contiguous because the  territory of particular country must be of same color. Four colors are not sufficient

This is all about tessellations and if anyone want to know about Representing probability

then they can refer to internet and text books for understanding it more precisely .Read more maths topics of different grades such as Pythagorean theorem  in the next session here.