NAME - HARSHIT GOEL ROLL NO. - 02UPBFSSCP0917 CLASS - IX

1. NAME - HARSHIT GOEL ROLL NO. - 02UPBFSSCP0917 CLASS - IX SCHOOL. - FATHERSON Sr. Sec. SCHOOL CHANDPUR MOBILE NO. - 7417367384

2. MATHEMATICS CONTENTS ORIGIN OF MATHEMETICS Prehistoric mathematics Babylonion mathematics Egyptian mathematics Greek mathematics IndiAN mathematics Importance of mathematics in study Importance of mathematics in our daily life Methods to improve our calculation speed

3. Prehistoric mathematics • The origin of mathematical thought lie in the concepts of number, magnitude, and form The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between "one", "two", and "many", but not of numbers larger than two • The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC • The Ishango bone, found near the headwaters of the Nile river (northeastern Congo, may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone • Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. It has been claimed that megalithic monuments in England and Scotland, dating from the 3rd millennium BC, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design.

4. Babylonian mathematics • Babylonian mathematics refers to any mathematics of the people of Mesopotamia (modern Iraq) from the days of the early Sumerians through the Hellenistic period almost to the dawn of Christianity. • In contrast to the scarcity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from more than 400 clay tablets • Babylonian advances in mathematics were facilitated by the fact that 60 has many divisors. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system

5. Egyptian mathematics • Egyptian mathematics refers to mathematics written in the Egyptian language. From the Hellenistic period • The most extensive Egyptian mathematical text is the Rhind papyrus dated to 1650 It is an instruction manual for students in arithmetic and geometry In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge including composite and prime numbers; arithmetic, geometric and harmonic means • Another significant Egyptian mathematical text is the Moscow papyrus, It consists of what are today called word problems or story problems, which were apparently intended as entertainment

6. Greek mathematics • Greek mathematics refers to the mathematics written in the Greek language from the time of Thales of Miletus (~600 BC) to the closure of the Academy of Athens in 529 AD • Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. • The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them • The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them • Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem • Archimedes (c.287–212 BC) of Syracuse, widely considered the greatest mathematician of antiquity, used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series • The Pythagoreans are credited with the first proof of the Pythagorean theorem though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers

7. Indian mathematics • The oldest extant mathematical records from India are the SulbaSutras,appendices to religious texts which give simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms, and others. • they compute the square root of 2 to several decimal places , list Pythagorean triples, and give a statement of the Pythagorean theorem • In the 5th century AD, Aryabhata wrote the Aryabhatiya, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration • In the 7th century, Brahmagupta identified the Brahmaguptatheorem, Brahmagupta's identity and Brahmagupta's formula, and for the first time, in Brahma-sphuta-siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu-Arabic numeral system • In the 12th century, BhāskaraII lived in southern India and wrote extensively on all then known branches of mathematics • In the 14th century, Madhava of Sangamagrama, the founder of the so-called Kerala School of Mathematics, found the Madhava–Leibniz series, and, using 21 terms, computed the value of π as 3.14159265359

8. IMPORTANCE OF MATHEMATICS CONTENTS Importance of mathematics in study importance of mathematics in our daily life

9. IMPORTANCE OF MATHEMATICS INSTUDIES Math is a very important and it has its importance in almost every field means either you choose any field in education you have to study math • Importance in Science • Science is incomplete without math there are many calculations used in the science. • Importance in Art • If you chooseart then for measurement you need math • Importance in social science • If you choose social science then to calculate years etc. you need math

10. IMPORTANCE OF MATHEMATICS IN OUR DAILY LIFE • Math is used in everyday life – • To count up the answers to things like how much of an ingredient to add when you're cooking, how much money you have in your bank account, how big a rug will you need for your bedroom, and what size tires should you put on your car • Math helps you decide - • If something is a good idea - when you know how to calculate the odds or percentage of something, you can decide if it is a good risk or not • Math helps you be creative – • Without a good understanding of basic math, you can't create good art, wallpaper your room, figure out how to mix paints, or do any sort of needlework

11. IMPORTANCE OF MATHEMATICS IN OUR DAILY LIFE (page 2) • Math is used to get the most bang for your buck – • if you can do simple math, you can compare prices and get the best deals, you can plan out a good budget so that you save money, and you can plan out your trips to save gas and time • Math is used to predict the future – • if you can do simple math, you can figure out what your grade average will be, how long it will take to save up for that new laptop, and when to buy or sell stocks and make a killing on the market • Math helps you play sports – • what, you didn't think jocks had to study math? How else can you keep score, figure out the odds, calculate a batting average or basket percentage, and decide which yard line your team is on?

12. METHODS TO IMPROVE MATH CALCULATION

13. METHODS TO IMPROVE CALCULATION • Use of vedic methods – • Vedic methods can be very helpful in fast calculation so lets take a look in an example with this method we can calculate square of a no. faster than a calculator For ex- we have to calculate the square of 55 Then 552 = 52+5…………………52= 25+5………………..25 = 30………………..25 = 3025 • DON’T USE CALCULATOR • Never use calculator while doing math calculators are made for our convenience but use them every time may harm us. • PRACTICE MAKES A MAN PERFECT • We should practice more and more to improve our calculation speed because more you practice more you will speed up your calculation

14. METHODS TO IMPROVE CALCULATION (PAGE 2) • TRY TO USE YOUR FINGRES TO SPEED UP CALCULATION • We should use our hand fingers for calculation it helps us to speed up calculation • USE YOUR BRAIN TO FIND SHORTCUTS IN CALCULATIONS • We should use our brain because the real shortcut are hidden in our brain • USE OF FORMUAES • Formulas are made for our convenience for ex If we have to calculate (a+b)2 then we should use a2 + b2 + 2a*b instead of solving with long methods.

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