Integars

Integer is a number without any fractional components.

The examples of integer is 1, 2, 3, 4.........

The negative value of any number is also integer. For example -2, -6, -30 is integer.

But 8.5 is not integer,  because it includes fractional components. Zero is also an element of the set of integer.

Positive integer is called counting number or hole number.

Number theory

Number theory is the study of integer and an attractive branch of mathematics.

German mathematician Carl Friedrich Gauss said that "Mathematics is the queen of science and Number theory is the queen of mathematics".

Arithmetic is the older term of number theory that was usually useful for elementary calculation. It is also known as mathematical logic.

Another types of arithmetic is floating point arithmetic which is widely used in computer science.

Euclidean geometry

Euclidean geometry is a mathematical system discovered by an Alexandrian Mathematician Euclid.  These mathematical system Euclid described in his famous book Geometry.

Euclidean geometry consists with a small set of axioms and some propositions derived from these axioms.

Elements of Euclidean geometry is plane geometry and with the time it expanded towards solid geometry with three dimensional space.

Algebra and number theory which is known as geometric language is result from the elements of Euclidean geometry.

Euclidean geometry is an example of synthetic geometry which is contradict with the analytical geometry.  The most of the results in geometry is came out from the axioms point and line.

Pithagorean Theorem

Pythagorean Theorem is also known as the Pythagorus theory. It is a relationship among the sides of a right triangle. Pythagorean theorem is a one of the fundamental relationship of Eucludian Geometry.

Here Right triangle is a triangle whose at least one angle is 90 degree.

Let a, b and c the three side of a right triangle. a and b is the adjunct side of right angle. The Pythagorean equation will be the square of two side is equal to the square of big side.