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Category Mathematics

HOW ARE ROMAN NUMERALS USED?

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).

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What is infinity?

  

               Infinity is a number, or value, which is so huge that it cannot be measured. For instance, the distance to the end of the Universe is called infinity, because if there is an end, it is so far away that it could never be measured.

               Sometimes infinity can be the result of a mathematical calculation. For example, the formula for calculating the distance around the outside of a circle is pi times the diameter. Pi is a Greek letter, and it represents a value of approximately 3.14159. Pi can never be fully calculated, because you would finish up with a string of numbers extending to infinity.

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What is geometry?

 

                    Geometry is a part of mathematics that deals with the shape, position and size of things of geometric forms such as squares, triangles, cubes and cones. Its name comes from the Greek words meaning ‘earth measuring’, because it was probably originally invented as a means of surveying and measuring land.

                   The ancient Egyptians also used geometry when constructing buildings and tombs. Nowadays, geometry is important to engineers and architects. It is also essential in navigation because geometry is used to follow charts and maps.

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Who invented our modern numerals?

               Our numbers are called Arabic numerals, although they probably appeared first in India around AD600. By the 800s the Arab numbering system was use throughout Europe because it was much easier to use than the old Roman system. At first the numbers varied in the way they were written, but with the invention of printing the numbers became standardized. The basic Arab numbers are 0 to 9, and can be used to write any combination of numbers.

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How did Roman numbering work?

   

                 In some ways, Roman numbering worked like the modern Arabic numeral system where, starting from the left, there are thousands, hundreds, tens and individual units. However, Roman numerals are quite different. One thousand is written as M, five hundred as D, one hundred as C, fifty as L, ten as X and five as V.

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What are decimals?

               The decimal system describes a numbering system for calculation based on multiples of ten. Multiplying or dividing a number by ten is very easy because only the decimal point needs to be moved. In the decimal system, each number has a value ten times that of the next number to the right. For instance, 5,283 means five thousands, two hundreds, eight tens and three ones. The decimal point simply separates the main number from numbers less than one. The number ten has always been important in mathematics — you can easily count it on your fingers.

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What is the metric system?

               The metric system is a group of various units of measurement. Its name comes originally from the metre. It is a decimal system, which means that each unit is ten times bigger, or smaller, than the next unit. Previously, measurements were difficult to calculate; in measurements of length, for example, there were 12 inches in one foot and three feet in one yard, while weight was calculated using ounces and pounds (16 ounces in one pound).

               The metric system was devised in the 1790s in France, and is now used in most countries in the world for all scientific and technical measurements.

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Why do we need to use numbers?

               Numbers are used to describe the amount of things. We can express numbers in words, by hand gestures or in writing, using symbols or numerals. When we talk about a number we use words (‘five’) rather than the numeral (5), but when we write we use both words and numerals.

               Numbers can describe how many objects there are or their position among lots of objects, such as 1st or 5th for example. Other types of numbers describe how many units of something there are, for example how many kilograms (weight) or metres (length).Numbers are just a convenient way to describe ideas.

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Why are there only ten numbers with single figures?

               All numbers are made from ten figures. These are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. All decimal numbers are also made from the above ten figures.

               Now the question arises, why are there only ten numbers with single figure? Although it cannot be precisely explained, yet some had concluded that this is because ancient people began counting by using their ten fingers. This was easier for them to learn how to handle numbers, as they could use their ten fingers to count.

               It is an established fact that right from ancient times, people tried various systems to write numbers. They showed numbers by marking separate indications. For a number like 10 for instance, they showed 10 lines or 10 drawings of birds or animals. This system was used by Egyptians which are still to be found in ancient monuments or structures. In fact, all civilizations have had their own way of writing and using numbers. Romans invented special signs or alphabets for counting. Such signs are called numerals. For centuries, people used Roman numerals. But they are rather clumsy. They did not have zero.

               But counting became easier after invention of zero. Zero was invented in 6th century in India and was brought to Europe by Arab travellers at a later stage. Having a figure for zero, any number can be made in a simpler way. It may continue in decimal system. Fractions like or  may be written as decimal fractions like 0.50, 0.25 or 0.75. In fact there are many ways of expressing numbers. In everyday terms numbers are used with units like kg; litre or metre and so on.

               It is most interesting to note that computers use a system that use only two digits — 1 and 0. This is called binary system. They play a key role in a modern digital computer. A computer changes numbers and words into codes made up of 0s and 1s. It makes calculation with these codes.

               The earliest known written numbers were those used by Babylonians about 5000 years ago. The symbols used today in English for the ten numbers (0, 1, 2,…) are called Arabic or Hindu-Arabic numerals because they came from India through the Arab countries and reached Europe in the 12th century.

 

What is a prime number?

          Any positive integer which is greater  than one and divisible by only itself is called a prime number. For example 2,3,5,7,11,13,17,19,23,29, etc. are all prime number – numbers that cannot be split by division by any other number except 1 and the particular number itself.

          The prime numbers lie at the very roots of arithmetic and have always fascinated those dealing with figures. We can take the sequence of the above given series of prime numbers as far as we like, but we will never find a prime number divisible by another. Over the centuries, the world’s greatest mathematicians have tried to do so and always fail, although they have also been unable to prove that no such number exists.

          Every positive integer greater than one can be expressed as the product of only a single set of prime numbers. Despite the fact that prime numbers have been recognized since at least 300 B.C. when they were first studied by the Greek mathematician Euclid and Eratosthenes. Still these numbers have not yet unfolded certain mysteries relating to them.

          There is infinity of prime numbers and in theory anything may happen in infinity. But so far theorists have not been able to even find any particular rule or theory governing the gaps between prime numbers, which still remains a great mathematical mystery.

          However, the highest known prime number was discovered in 1992 by analysts at AEA Technology’s Harwell Laboratory, Oxon. The number contains 227832 digits, enough to fill over 10 fullscap pages.