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 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.

The Triangle Inequality Theorem

Let us learn Triangle Inequality Theorem :

In Δ TAB (Figure 1 ), if T, A, and B represent three points on a map and you want to go from T to B, going from T to A to B would obviously be longer than going directly from T to B. The following theorem expresses this idea.

Figure 1

Two paths from T to B.

Theorem (Triangle Inequality Theorem): The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Example 1: In Figure 2 , the measures of two sides of a triangle are 7 and 12. Find the range of possibilities for the third side.

Figure 2

What values of x will make a triangle possible?

Using the Triangle Inequality Theorem, you can write the following:

7 + x > 12, so x > 5

7 + 12 > x, so 19 > x (or x < 19)

Therefore, the third side must be more than 5 and less than 19.

Hope the above explanation helped you.