Euclid: Father of Geometry

Who is called The Father of Geometry ?

Perhaps one of the most difficult things about studying great men of the past is the lack of available information on many of them. Facts about one of our greatest mathematicians are shrouded in mystery. There is so much mystery around him that some people think he did not really exist. Who is this mystery math man? He was Euclid of Alexandria.

Euclid is thought to be a Greek man who lived while Ptolemy I reigned in Egypt (323 BC- 283 BC). He worked in the Library of Alexandria. It was considered to be the greatest library in the world at the time.
Some people believe that there was a team of mathematicians working in Alexandria. As the leader of the team, Euclid could have been given the credit for all of the work. However, no records exist to prove or disprove this idea.

I hope the above explanation was useful, now let me explain Geometry symbols.

Explain Linear Function Concepts

Let us study about Linear Functions,

Introduction to Linear Functions:

A polynomial functions of single degree is defined as a linear functions. It relates a dependent variable with an independent variable in a simple way. Mathematical equation in which there is no independent-variable is raised to a power greater than one. A simple linear function with one independent variable (y=a+bx) traces a straight line when plotted on a graph. It is also called as linear equation.
Forms of Linear Functions:

The function is defined by f the first degree equation:

f = { ( X, Y)/ Y = mX + b }

where m and b are constants, x and y is called a linear functions. The function derives a straight line while graphing.

Functions such as these gives graph that are straight lines, and, thus, the name linear. There are three main forms in linear functions. They are as follows,

1. Slope-Intercept Form is given by y = mx +b.
2. Point Slope Form is given by m = (y - y1) / ( x – x1).
3. General Form is given by Ax + By + C = 0.

I hope the above explanation was useful, now let me explain about Radicals.

Square Roots

Square Roots:Square root method is derived from the process of long-hand division. The symbolic representation of the term square root is [sqrt(x)] .Square root is a constant number. Square root is not a fractional number. The multiplication of a given number is said to be square root of that number. We also find square root for the imaginary values. The imaginary values in square root are represented as ‘i’. For example square root of -1 is ‘i’.

Solving square root inequalities involves the process of solving square root equation with inequalities in detail. The square root can be easily solved by performing squaring operation for the given equation. The comparison process is carried out with the help of inequality sign.Hope you like the above example of Square Roots.Please leave your comments, if you have any doubts.

Slope

Slope of a Line:
The slope of a line is defined as the tangent of the angle made by the line with the x-axis in the positive direction (anti-clockwise).
The lines are said to be intersecting lines only when one line intersect with the other line. These lines are also said to be perpendicular to each other but it is not mandatory that it should be perpendicular .
It can also be said that all the perpendicular lines are intersecting lines but not all intersecting lines are perpendicular lines . The lines that are parallel to each other are not intersecting lines.
Hope you like the above example of Lines.Please leave your comments, if you have any doubts.

Explain intersecting circles

Let us study about intersecting circles,
The following formula for using finding a intersection point on a circle.

The line intersects circle can be defined as,

Y – Y1 = m(x-x1)

Y=m(x-x1) + y1

R2 = (x-h) 2 + (y-k) 2

R = [sqrt((x-h) 2 + (y-k) 2)]

The r is a intersection point of a line.

Here, the x and y are the co ordinates of the point of an intersection.

The x1 and y1 are the co ordinates of appoint on the line

The h and k are the translation between the center of the circle and also the origin of the coordinate system in the x and y directions respectively.

Angle and Angle Pairs

Angles and Angle Pairs :

Easily as significant as rays and line segments are the angles they form. Without them, there would be none of the geometric figures that you know (with the possible exception of the circle).


Angles

Two rays that have the same endpoint form an angle. That endpoint is called the vertex, and the rays are called the sides of the angle. In geometry, an angle is measured in degrees
from 0° to 180°. The number of degrees indicates the size of the angle. In Figure 1 , rays AB and AC form the angle. A is the vertex. and are the sides of the angle.

Figure 1

∠BAC.
I hope the above explanation was helpful.

Central Limit Theorem

Let us learn about Central Limit Theorem,
If the population of all subscribers to the magazine were normal, you would expect its sampling distribution of means to be normal as well. But what if the population were non-normal? The Central Limit Theorem states that even if a population distribution is strongly non-normal, its sampling distribution of means will be approximately normal for large sample sizes (over 30). The Central Limit Theorem makes it possible to use probabilities associated with the normal curve to answer questions about the means of sufficiently large samples.

According to the Central Limit Theorem, the mean of a sampling distribution of means is an unbiased estimator of the population mean.
Similarly, the standard deviation of a sampling distribution of means is
Note that the larger the sample, the less variable the sample mean. The mean of many observations is less variable than the mean of few. The standard deviation of a sampling distribution of means is often called the standard error of the mean. Every statistic has a standard error, which is a measure of the statistic's random variability.
I hope the above explanation was useful.