My Science School

Pythagoras was a Greek living in the sixth century BC. He was a mathematician and scientist who are now best remembered for Pythagoras’ Theorem, a formula for calculating the length of one side of a right-angled triangle if the other sides are known. However, this theorem was, in fact, already known hundreds of years earlier by Egyptian and Babylonian mathematicians.

Pythagoras was a Greek philosopher who was born in Samos in the sixth century B.C. he was a great mathematician who explained everything with the help of numbers. He gave the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the lengths of legs of any right angled triangle is equal to the square of the length of its hypotenuse. The hypotenuse is known to be the longest side and is always equal opposite to the right angle.

The theorem can be written as an equation where lengths of the sides can be a, b and c. The Pythagorean equation is a2 + b2 = c2 where c is the length of the hypotenuse and a, b are lengths of the two sides of the triangle. The Pythagorean equation simplifies the relation of the sides of the right triangle to each other in such a way that if the length of any of the two sides of the right triangle is known, then the third side can be easily found.

To generalise this theorem, there is the law of cosines which helps in calculation of the length of any of the sides of the triangle when the other two lengths for the two sides are given along with the angle between them. When the angle between the other sides turns out to be a right angle, then the law of the cosines becomes the Pythagorean Theorem. The converse of this theorem is also true. It is that for any triangle with sides a, b and c, if a2 + b2 = c2, then the angle between the two sides a and b would turn out to be 900.

Picture Credit : Google

An abacus is a frame of beads used in China and neighbouring countries for making calculations. A skilled abacus user can produce answers to some calculations almost as quickly as someone using an electronic calculator.

The word abacus is derived from the Latin word abax, which means a flat surface, board or tablet. As such, an abacus is a calculating table or tablet. The abacus is the oldest device in history to be used for arithmetic purposes, such as counting. It is typically an open wooden rectangular shape with wooden beads on vertical rods. Each bead can represent a different number. For simple arithmetic purposes, each bead can represent one number. So, as a person moves beads from one side to the other, they would count, 'one, two, three', etc.

An abacus can be used to calculate large numbers, as well. The columns of beads could represent different place values. For example, one column may represent numbers in the hundreds, while another column may represent numbers in the thousands.

One of the most popular kinds of abacuses is the Chinese abacus, also known as the suanpan. Rules on how to use the suanpan have dated all the way back to the 13th century.

On a Chinese abacus, the rod or column to the far right is in the ones place. The one to the left of that is in the tens place, then the hundreds, etc. So, the columns are different place values and the beads are used to represent different numbers within those place values. For addition, beads on the suanpan are moved up towards the beam in the middle. For subtraction, they are moved down towards the bottom or outer edge of the suanpan. The rules of use are a bit more intricate and complicated, but this is the general idea of how one is used.

Geometry is the branch of mathematics that is concerned with points, lines, surfaces and solids, and their relation to each other. Shapes, both flat and three-dimensional, are an important part of geometry. When we describe something as geometric, we mean that it has a regular, often angular pattern of lines or shapes.

Geometry is a term used to refer to a branch in mathematics that deals with geometrical objects such as straight lines, points and circles and other shapes. However, circles are the most elementary of geometric objects. The term geometry was derived from a Greek word, ‘geo’ which means earth and metron, meaning measure. These words reflect its actual roots. However, Plato knew how to differentiate the process of mensuration as used in construction from the philosophical implication of Geometry. In essence, Geometry in Greek implies earth measurements. Geometry was first organized by Euclid a mathematician who was able to arrange more than 400 geometric suggestions. Being one of the early sciences, it is the substance of most developments and it was believed that it has been in use way before in Egypt. Evidence shows that geometry dates back to the days of Mesopotamia in 3000 BC and is attributed to numerous developments since its discovery.

Geometry is not just a math topic created to make your life harder. It is a topic that was developed to answer questions about shapes and space related to construction and surveying. It answers questions about all the different shapes we see, such as how much space an object or shape can hold. Geometry even has application in the field of astronomy, as it is used to calculate the position of stars and planets. Over time, different people contributed new and different things to grow geometry from its basic beginnings to the geometry we know, use and study today.

The first written record that we have of geometry comes from Egypt back in 2000 BC. Some of the earliest texts that have been discovered include the Egyptian Rhind papyrus, Moscow papyrus and some Babylonian clay tablets, such as the Plimpton 322. These early geometry works included formulas for calculating lengths, areas and volumes of various shapes, including those of a pyramid.

Mathematical formulae are useful rules expressed using symbols or letters. In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of relationship between given quantities. The plural of formula can be spelled either as formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).

In mathematics, a formula generally refers to an identity which equates one mathematical expression to another with the most important ones being mathematical theorems. Syntactically, a formula is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: V = 4/3nr3

Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volume V and the radius rare expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. Mathematical formulas are often algebraic, analytical or in closed form.

In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (?) signs. For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O?

denotes an ozone molecule consisting of three oxygen atoms and a net negative charge.

In a general context, formulas are a manifestation of mathematical model to real world phenomena, and as such can be used to provide solution (or approximated solution) to real world problems, with some being more general than others. For example, the formula F = ma is an expression of Newton’s second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations.

Expressions are distinct from formulas in that they cannot contain an equal’s sign (=). Expressions can be liken to phrases the same way formulas can be liken to grammatical sentences.

Decimal numbers use 10 digits, which are combined to make numbers of any size. The position of the digit determines what it means in any number. For example, the 2 in the number 200 is ten times the size of the 2 in the number 20. Each position of a number gives a value ten times higher than the position to its right. So 9867 means 7 units, plus 6 x 10, plus 8 x 10 x 10, plus 9 x 10 x 10 x 10. As decimal numbers are based on the number 10, we say that this is a base -10 number system.

We have learnt that the decimals are an extension of our number system. We also know that decimals can be considered as fractions whose denominators are 10, 100, 1000, etc. The numbers expressed in the decimal form are called decimal numbers or decimals.

For example: 5.1, 4.09, 13.83, etc.

A decimal has two parts:

(a) Whole number part

(b) Decimal part

These parts are separated by a dot (.) called the decimal point.

• The digits lying to the left of the decimal point form the whole number part. The places begin with ones, then tens, then hundreds, then thousands and so on.


• The decimal point together with the digits lying on the right of decimal point form the decimal part. The places begin with tenths, then hundredths, then thousandths and so on…

Example:

(i) In the decimal number 211.35; the whole number part is 211 and the decimal part is .35

(ii) In the decimal number 57.031; the whole number part is 57 and the decimal part is .031

(iii) In the decimal number 197.73; the whole number part is 197 and the decimal part is .73

The binary system is another way of counting. Instead of being a base-10 system, it is a base-2 system, using only two digits: 0 and 1. Again, the position of a digit gives it a particular value. 1010101 means 1 unit, plus 0 x 2, plus 1 x 2 x 2, plus 0 x 2 x 2 x2, plus1 x 2 x 2 x 2 x 2, plus 0 x 2x 2 x 2 x 2x 2,plus 1 x 2 x 2 x 2 x 2 x 2 x 2. 1010101 is the same as 85 in decimal numbers.

When you learn math at school, you use a base-10 number system. That means your number system consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When you add one to nine, you move the 1 one spot to the left into the tens place and put a 0 in the ones place: 10. The binary system, on the other hand, is a base-2 number system. That means it only uses two numbers: 0 and 1. When you add one to one, you move the 1 one spot to the left into the twos place and put a 0 in the ones place: 10. So, in a base-10 system, 10 equal ten. In a base-2 system, 10 equal two.

In the base-10 system you're familiar with, the place values start with ones and move to tens, hundreds, and thousands as you move to the left. That's because the system is based upon powers of 10. Likewise, in a base-2 system, the place values start with ones and move to twos, fours, and eights as you move to the left. That's because the base-2 system is based upon powers of two. Each binary digit is known as a bit.

Don't worry if the binary system seems confusing right now. It's fairly easy to pick up once you work with it a while. It just seems confusing at first because all numbers are made up of only 0s and 1s. The familiar base-10 system is as easy as 1-2-3, while the base-2 binary system is as easy as 1-10-11.

You may WONDER why computers use the binary system. Computers and other electronic systems work faster and more efficiently using the binary system, because the system's use of only two numbers is easy to duplicate with an on/off system. Electricity is either on or off, so devices can use an on/off switch within electric circuits to process binary information easily. For example, off can equal 0 and on can equal 1.

Every letter, number, and symbol on a keyboard is represented by an eight-bit binary number. For example, the letter A is actually 01000001 as far as your computer is concerned! To help you develop a better understanding of the binary system and how it relates to the decimal system you're familiar with, here's how the decimal numbers 1-10 look in binary:

Picture Credit : Google

The romans had a number system with a base of 10, as we do, but they used different numerals to write it down. For the numbers one to nine, instead of using nine different numerals, they used only three different letters, combining them to make the numbers. This made it very difficult for them to do even simple calculations, so their advances in mathematics and related fields were not as great as might have been expected from such a far-reaching civilization.

Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Modern usage employs seven symbols, each with a fixed integer value:

The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some minor applications to this day.

One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as:

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII

The notations IV and IX can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favoring representation of "4" as "IIII" on Roman numeral clocks.

Other common uses include year numbers on monuments and buildings and copyright dates on the title screens of movies and television programs. MCM, signifying "a thousand, and a hundred less than another thousand", means 1900, so 1912 is written MCMXII. For the years of this century, MM indicates 2000; so that the current year is MMXX (2020).

Picture Credit : Google