# Mathematics Local News Update

## Breaking news!!! New mathematical way has been discovred

People are thrilled by the astonishing mathematical way in geometry mainly, it is the Pythagorean theorem ,our good friend Pythagoras had did it again blowing our minds, a little backstory about him, he was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,"and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities.

## But what is the Pythagorean theorem about?

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angled) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation"

## But what is a hypotenuse?

In geometry, the hypotenuse is the longest side of a right-angled triangle, the side opposite of the right angle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem.
Pythagorean Theorem

## Radicals have been introduced to math!!!

"Roots" (or "radicals") are the "opposite" operation of applying exponents; you can "undo" a power with a radical, and a radical can "undo" a power.Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. The term whose root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign,Every positive number a has two square roots: √a, which is positive, and −√a, which is negative. Together, these two roots are denoted.

The mathematical concept of square roots has been in existence for many thousands of years. A square root of a number can be defined as a number that when multiplied by itself produces the first number. For example, 2 is the square root of 4, 3 is the square root of 9. Exactly how the concept was discovered is not clearly known, but several different methods of exacting square roots were used by early mathematicians. Recently discovered Babylonian clay tablets from 1900 to 1600 b.c. contain the squares and cubes of the integers 1 to 30 in Babylonian base 60 Akkadian notation. Whole number roots were specifically stated, while irrational roots were expressed in surprisingly accurate approximations.

Egyptian papyrus dating from about 1700 b.c. have revealed that the Egyptians were knowledgeable of square roots, using a hieroglyphic symbol similar to ⌈ to denote square roots. By the Greek Classical Period (600 to 300 b.c.), square root operations were improved upon by the use of better arithmetic methods. However, because Greek mathematicians were unsettled by inharmonious phenomenon such as irrational numbers (e.g., the square root of 2 is 1.4142135...), they regarded geometry more highly than algebra and arithmetic for its elegance and harmony.

When Hindu mathematics became significant about a.d. 628, mathematicians accepted irrational numbers and used square root operations freely in their equations. They used the term ka, from the word karana, to denote a square root. Thus, ka 9 would equal 3. Borrowing much from Hindu mathematics, Arabian mathematicians continued working with irrational number operations. It is the Middle Eastern mathematician al-Khwarizmi who developed our familiar term root to denote a solution to a problem. In the sixteenth century, the German mathematician Cristoff Rduolff was the first to use the square root symbol, , in his book Coss, written in 1525.

Square Root Tricks

## And for the last subject today, we have Quadrilaterals!!

Well, first quadrilaterals are polygons and Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon comes from Greek. Poly- means "many" and -gon means "angle". Quadrilateral just means "four sides" (quad means four, lateral means side). There are five main types of quadrilaterals the rectangle, parallelogram, square, rhombus, and the trapezoid.

-Rectangle: A rectangle is a four-sided shape where every angle is a right angle (90°).

Also opposite sides are parallel and of equal length.

-Rhombus:A rhombus is a four-sided shape where all sides have equal length.

Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals meet in the middle at a right angle. In other words they "bisect" (cut in half) each other at right angles. A rhombus is sometimes called a rhomb or a diamond.

-Square:A square has equal sides and every angle is a right angle (90°)

Also opposite sides are parallel.A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

-Parallelogram: A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "a" are the same, and angles "b" are the same).

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

-Trapezoid:A trapezoid (called a trapezium in the UK) has a pair of opposite sides parallel.It is called an Isosceles trapezoid if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown. And a trapezium (UK: trapezoid) is a quadrilateral with NO parallel sides

## Who discovered them and when did they show up?

Quadrilaterals were invented by the Ancient Greeks. It is said that Pythagoras was the first to draw one. In those days quadrilaterals had three sides and their properties were only dimly understood. It was the genius of the Romans to add a fourth side and they were the first to make a list of the different kinds of quadrilaterals but it wasn't until 1813 that an English mathematician, J.P. Smith, discovered the trapezium. Quadrilaterals remain a rich source of investigations for researchers, the best known unsolved problem being to find a general formula for the number of interior angles.