Perimeter of a Rectangle

A rectangle is any quadrilateral with four right angles. A rectangle is a special case of a parallelogram, whose opposite sides are equal in length and parallel to each other.

Perimeter of a Rectangle can be calculated by the below formula:-

P = 2(L+W)

Where, L = length and W = width

A rectangle is cyclic. All the angles of a rectangle are congruent. The two diagonals of a Rectangle are equal and bisect each other. All the four interiors angles of a Rectangle measure 90° (right angles). The opposite sides of a rectangle are parallel to each other.

Volume of a Rectangle can be calculated by the below formula:-

V = l*w*h

Where, L = Length, W = width and H = Height.

Like wise there are many other geometrical objects, like Circle, rhombus, triangle, etc

FATHER OF GEOMETRY

Eulicid is considered the father of geometry. There are a number of other early contributors to this branch of mathematics, but it is Euclid who gave us the extraordinary mathematical text, Elements. Euclid taught for 20 to 30 years. He wrote Elements as he taught. Euclid influenced Archimedes and Appollonius, students at the library.

Geometry is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. In Euclid's time there was no clear distinction between physical space and geometrical space.

Ancient scientists paid special attention to constructing geometric objects that had been described in some other way. Classical instruments allowed in geometrical shapes constructions are those with compass and straightedge.

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, whose elements is the earliest known systematic discussion of geometry.

CONCENTRIC CIRCLES

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A collection of circles is said to be concentric if they have the same center. The region formed between two concentric circles is therefore an annulus.

Concentric circles are simply circles that all have the same center. They fit inside each other and are the same distance apart all the way around. In the figure above, resize either circle by dragging an orange dot and see that they both always have a common center point.

Concentric circles definition: Two or more circles which have the same center point, circles of different diameters but with the same centre point

Circles, tubes, cylindrical shafts, disks, and spheres may be concentric to one another. Concentric objects generally have different radii, as concentric object with the same radius are equal.

Below is an example image of concentric circle art.

AXIOM DEFINITION

Axiom definition is as follows:-

An axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self evident, or subject to necessary decision. Axiom is a rule or a statement that is accepted as true without proof. An axiom is also called a postulate.

There are two different kinds of Axioms:-

Logical Axioms and Non Logical Axioms.

Logical axioms, being mere formula, are devoid of any meaning; but the point is that when they are interpreted in any universe, they will always hold no matter what values are assigned to the variables.

Non-logical axioms are formulas that play the role of theory-specific assumptions. Reasoning about two different structures.

Postulate definition is as follows:-

A statement whose validity is accepted without proof is called a postulate. In addition to point, line plane etc, it is also necessary to start with certain other basic statements that are accepted without proof. In geometry these are called postulates.
A postulate, though itself is an unproved statement, can be cited as a reason to support a step in a proof.

To know more about Postulates click here.

PERMUTATIONS AND COMBINATIONS

INTRODUCTION TO PERMUTATIONS AND COMBINATIONS

The topic for today is Permutations and Combinations.

Certain types of probability calculations involve dividing the number of outcomes associated with an event by the total number of possible outcomes. For simple problems it is easy to count the outcomes, but in more complex situations manual counting can become laborious or impossible.

Fortunately, there are probability formula for determining the number of ways in which members of a set can be arranged. Such arrangements are referred to as permutations and combinations, depending on whether the order in which the members are arranged is a distinguishing factor.

Permutation means arrangements of things. The word arrangement is used, if the order of things is considered. The permutation of a number of objects is the number of different ways they can be ordered; i.e. which is first, second, third, etc. If you wish to choose some objects from a larger number of objects, the way you position the chosen objects is also important.

Combination means selection of things. The word selection is used, when the order of things has no importance here we need not consider the order in which objects were chosen or placed, just which objects were chosen. We could summarize permutations and combinations (very simplistically)

For information on Probability Model click here.

CONCENTRIC CIRCLES

Circles are simple closed curves which divide the plane into two regions, an interior and an exterior. Circles is one main topic under geometry basics. The circle has been known since before the beginning of recorded history. It is the basis for the wheel, which, with related inventions such as gears, makes much of modern civilization possible. The circle is a highly symmetric shape: every line through the center forms a line of reflection symmetry and it has rotational symmetry around the center for every angle.


Concentric circles are simply circles that all have the same center. They fit inside each other and are the same distance apart all the way around. In the figure above, resize either circle by dragging an orange dot and see that they both always have a common center point. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric by inversion by picking the inversion centre as one of the limiting points. The figure below shows a concentric circles art.

Learning Probability

In the theory of probability we deal with events which are outcomes of an experiment. The word 'experiment' means an operation which can produce some well defined outcome(s):

There are two types of experiments:

(i) Deterministic (ii) Random or Probabilistic.

Deterministic Experiment: Deterministic Experiments are those experiments which when repeated under identical conditions produce the same result or outcome. When experiments in science and engineering are repeated under identical conditions, we obtain almost the same result every time.

Random or Probabilistic Experiment:If an experiment, when repeated under identical conditions, do not produce the same outcome every time but the outcome in a trial is one of the several possible outcomes, then it is known as a random or probabilistic experiment. For example, in tossing of a coin one is not sure if a head or a tail will be obtained, so it is a random experiment. Similarly, rolling an unbiased die and drawing a card from a well shuffled pack of card are examples of a random experiment.

Construction of Circumcircle of a Triangle

Today's topic is related to Construction of Circumcircle of a Triangle. Before we get into construction let us first try to know what is meant by Circumcircle of a Triangle.

Circumcircle of a Triangle: A circle passing through the vertices of a triangle is known as Circumcircle of a triangle. The centre of the circumcircle of a triangle is the point of concurrency of perpendicular bisectors of any two sides of the triangle and is known as circumcentre. The circumcentre of a triangle is equidistant from the three vertices. The distance between the circumcentre and any vertex of the triangle is the circumradius.

Listed below are the steps followed in constructing circumcircle of a triangle:-

Step 1:- Draw the given triangle ABC with the help of the given data.

Step 2:- Draw the Perpendicular Bisector of any two sides, say AB and AC of the triangle.

Step 3:- Obtain the point of intersection of the bisectors drawn in step 2 and let this point be O.

Step 4:- Draw the circle with O as centre and OA or OB or OC as radius.

The circle obtained is the required Circumcircle of Triangle ABC