mathematician

Bhāskara II 

Bhaskara the teacher, Bhaskara Achārya, Bhaskara II, Bhāskarācārya

FAMOUS AS

Mathematician

NATIONALITY

Indian    Famous Indian Men

RELIGION

Hinduism

BORN

1114 AD

DIED AT AGE

71

BORN IN

Bijapur

DIED ON

1185 AD

 Bhāskara II’s mathematical works (written in verse like nearly all Indian mathematical classics), particularly Līlāvatī (“The Beautiful”) and Bījagaṇita (“Seed Counting”), he not only used the decimal system but also compiled problems from Brahmagupta and others. He filled many of the gaps in Brahmagupta’s work, especially in obtaining a general solution to the Pell equation (x2 = 1 + py2) and in giving many particular solutions (e.g., x2 = 1 + 61y2, which has the solution x = 1,766,319,049 and y = 226,153,980; French mathematician Pierre de Fermat proposed this same problem as a challenge to his friend Frenicle de Bessy five centuries later in 1657). Bhāskara II anticipated the modern convention of signs (minus by minus makes plus, minus by plus makes minus) and evidently was the first to gain some understanding of the meaning of division by zero, for he specifically stated that the value of 3/0 is an infinite quantity, though his understanding seems to have been limited, for he also stated wrongly that a⁄0 × 0 = a. Bhāskara II used letters to represent unknown quantities, much as in modern algebra, and solved indeterminate equations of 1st and 2nd degrees. He reduced quadratic equations to a single type and solved them and investigated regular polygons up to those having 384 sides, thus obtaining a good approximate value of π = 3.141666.

What Is Math?

                            By Wendy Petti

What is math? It might seem obvious: We hope we know what we're teaching -- and that our students know what they're learning! But responses to that question can be surprisingly diverse.

Before you read on, please take a few minutes to reflect and record your own thoughts on "What is math?"

Illustration courtesy of Wendy Petti.

I'm a math educator -- I teach grade 4 math, I've created a math Web site, and I write about topics in math education. Yet I cannot easily express what math is. I'm in good company. Bertrand Russell has quipped, "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." Math teacher Sanderson M. Smith observes that "students can gain a tremendous appreciation for mathematics if they understand that the question 'What is mathematics?' has been analyzed and debated since the time of the Pythagoreans, around 550 B.C. "

It is worth pursuing a clear understanding of the meaning and scope of mathematics so that we might provide our students with a richer learning experience and help them more fully appreciate the beauty and power of mathematics.

STUDENTS AND TEACHERS REFLECT ON
"WHAT IS MATH?"

In my math classes, no matter how much attention we pay to the five content standards and five process standards, many of my students seem to focus on number and operation when they share their thoughts and feelings about math. One of my students had an "aha!" moment the morning after a student-led math night: "I look at math a different way now. I've usually thought of math as something we need to do, to know how much money we need to pay, things like that. But this morning I woke up and said, 'Wow! Math is everywhere!'"

A 2005 Math Cats writing contest on "What is math?" produced these reflections:

• From an elementary school volunteer: "Math is more than a subject we learn in school. Math is every breath we take and every second of the day. From the moment we wake up in the morning, math is the core of everything we do..."
• From a first-grade teacher:
  "Math is you.
  Math is me.
  Math is everything we see!
  Infinity and beyond our wildest dreams
  Math encompasses all extremes!"
• From a 13-year-old: "Math is the entire world simplified on a piece of paper... Math is ingeniousness morphed into a tiny simple formula so we can harness its fantastic powers."
• From a 12-year-old: "Math is the universal language of the world."
• From an 11-year-old: "No one can live without math; it means different things to different people. But to me it means love, liberty, learning. I could keep going but to sum it up, math is my life."

mathematical facts

                       Top ten facts about maths

1. In 2010 on World Maths Day, 1.13 million students from more than 235 countries set a record correctly answering 479,732,613 questions. 

2. Americans called mathematics ‘math’, arguing that ‘mathematics’ functions as a singular noun so ‘math’ should be singular too. 

3. They have been calling maths ‘math’ for much longer than we have called it ‘maths’. 

4. ‘Mathematics’ is an anagram of ‘me asthmatic’. 

5. The only number in English that is spelled with its letters in alphabetical order is ‘forty’. 

6. The only Shakespeare play to include the word ‘mathematics’ is The Taming Of The Shrew. 

7. Notches on animal bones show that people have been doing mathematics, or at least making computations, since around 30,000BC. 

8. The word ‘hundrath’ in Old Norse, from which our ‘hundred’ derives, meant not 100 but 120. 

9. “Pure mathematics is, in its way, the poetry of logical ideas.” (Albert Einstein). 

10. “Mathematics [is] the subject in which we never know what we are talking about nor whether what we are saying is true.” (Bertrand Russell).

maths in games

             Everything in the Universe Is Made of Math

interesting facts about maths

Did you know that...

1. π=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 ...
2. A sphere has two sides. However, there are one-sided surfaces.
3. There are shapes of constant width other than the circle. One can even drill square holes.
4. There are just five regular polyhedra
5. In a group of 23 people, at least two have the same birthday with the probability greater than 1/2
6. Everything you can do with a ruler and a compass you can do with the compass alone
7. Among all shapes with the same perimeter a circle has the largest area.
8. There are curves that fill a plane without holes
9. Much as with people, there are irrational, perfect, complex numbers
10. As in philosophy, there are transcendental numbers
11. As in the art, there are imaginary and surreal numbers
12. A straight line has dimension 1, a plane - 2. Fractals have mostly fractional dimension
13. You are wrong if you think Mathematics is not fun
14. Mathematics studies neighborhoods, groups and free groups, rings, ideals, holes, poles and removable poles, trees, growth ...
15. Mathematics also studies models, shapes, curves, cardinals, similarity, consistency, completeness, space ...
16. Among objects of mathematical study are heredity, continuity, jumps, infinity, infinitesimals, paradoxes...
17. Last but not the least, Mathematics studies stability, projections and values, values are often absolute but may also be extreme, local or global.
18. Trigonometry aside, Mathematics comprises fields like Game Theory, Braids Theory, Knot Theory and more
19. One is morally obligated not to do anything impossible
20. Some numbers are square, yet others are triangular

probability

                               PROBABILITY          

INTRODUCTION

—  Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.

—  Probably Kuzhalisai will stand first in the forth coming annual examination. ™

—  Possibly Thamizhisai will catch the train today. ™

—  The prices of essential commodities are likely to be stable. ™

—   There is a chance that Leela will win today’s Tennis match.

—  The words “Probably”, “Possibly” , “Likely”, “Chance” , etc., will mean “the lack of certainty OR uncertainty”

EXAMPLES

—  “Should I carry an umbrella to work today?”, “Will my cellphone battery last until tonight?”, and “Should I buy a new brand of laptop?”. Probability provides a way to make decisions when the person is uncertain about the things, quantities or actions involved in the decision.

DEFINITION

—  Probability is the chance that something will happen - how likely it is that some event will happen.

—  Sometimes you can measure a probability with a number like "10% chance of rain", or you can use words such as impossible, unlikely, possible, even chance, likely and certain.
FORMULA:

—  Probability of an event happening = Number of ways it can happen / Total number of outcomes

EXAMPLES

Throwing Dice  :

•       When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.

•       The probability of any one of them is 1/6.

•       BASIC CONCEPTS:

•       Experiment

•       Trial

•       Sample space

•       Sample point

•       Events

EXPERIMENT:

v  An experiment is defined as a process whose result is

well defined.

v  There are two types of experiment.

1. Deterministic Experiment : It is an experiment whose outcomes can be predicted with certainty, under identical conditions.
2. Random Experiment : It is an experiment whose all possible outcomes are known, but it is not possible to predict the exact outcome in advance.                    

 Trial

A Trial is an action which results in one or several outcomes.

EXAMPLES:

“ Flipping” a coin and “Rolling” a die are trials                          

SAMPLE SPACE:

A sample space S is the set of all possible outcomes of a random experiment.

EXAMPLE:

•       While rolling a die, sample space

•        S = { 1, 2,3,4, 5, 6}                                                        

SAMPLE POINT:

Each outcome of an experiment is called a sample point.

EXAMPLE:

While rolling a die each outcome,

 {1} {2} {3} {4} {5} and {6}

 are are corresponding sample points .        

EVENTS:

—  Any subset of a sample space is called an event.

—  EXAMPLE:

—  When a die is rolled some of the possible events are {1, 2, 3}, {1, 3}, {2, 3, 5, 6}

APPLICATION:

many ways probability used in our life.

Examples:

1. every day you use probability to plan around the weather. Meteorologists can't predict exactly what the weather will be, so they use tools and instruments to determine the likelihood that it will rain, snow or hail. For example, if there's a 60-percent chance of rain, then the weather conditions are such that 60 out of 100 days with similar conditions, it has rained. You may decide to wear closed-toed shoes rather than sandals or take an umbrella to work. Meteorologists also examine historical data bases to guesstimate high and low temperatures and probable weather patterns for that day or week.
2. I’ve Got Your Number:
3. Produced in collaboration with Wales Institute of Mathematical and Computational Sciences, I’ve got your Number is a quiz show with a difference.                                                                                     Thank you.

numbers

Types of Numbers

Compiled by William Tappe

Introduction

         Those ten simple symbols, digits, or numbers that we all learn early in life that influence our lives in far more ways than we could ever imagine. Have you ever wondered what our lives would be like without these 10 elegant digits and the infinite array of other numbers that they can create?

Birthdays, ages,height, weight, dimensions, addresses, telephone numbers, license plate numbers, credit card numbers, PIN numbers, bank account numbers, radio/TV station numbers, time, dates, years,directions, wake up times, sports scores, prices,accounting, sequences/series of numbers, magic squares, polygonal numbers, factors, squares, cubes, Fibonacci numbers, perfect, deficient, and abundant numbers, and the list goes on ad infinitum. Engineers, accountants, store clerks,manufacturers, cashiers, bankers, stock brokers, carpenters, mathematicians, scientists, and so on,could not survive without them.

 In a sense, it could easily be concluded that we would not be able to live without them. Surprisingly, there exists an almost immeasurable variety of hidden wonders surrounding or emanating from these familiar symbols that we use every day, the natural numbers.

Numbers - The Basics Integers - Any of the positive and negative whole numbers, ...,  - 3,  - 2,  - 1, 0,  + 1,  + 2,  + 3, ... The positive integers, 1, 2, 3..., are called the natural numbers or counting numbers. The set of all integers is usually denoted by Z or Z+

Digits - the 10 symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, used to create numbers in the base 10 decimal number system.

Numerals - the symbols used to denote the natural numbers. The Arabic numerals 0, 1, 2, 3, 4, 5, 6,7, 8, 9 are those used in the Hindu-Arabic number system to define numbers.

Natural Numbers - the set of numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,....., that we see and use every day. The natural numbers are often referred to as the counting numbers and the positive integers.

Whole Numbers - the natural numbers plus the zero.

Rational Numbers - any number that is either an integer "a" or is expressible as the ratio of two integers, a/b. The numerator, "a", may be any whole number, and the denominator, "b", may be any positive whole number greater than zero. If the denominator happens to be unity, b = 1, the ratio is an integer. If "b" is other than 1, a/b is a fraction.

Fractional Numbers - any number expressible by the quotient of two numbers as in a/b, "b" greater than 1, where "a" is called the numerator and "b" is called the denominator.

Irrational Numbers - any number that cannot be expressed by an integer or the ratio of two integers.Irrational numbers are expressible only as decimal fractions where the digits continue forever with not repeating pattern. Some examples of irrational numbers are .

Transcendental Numbers - any number that cannot be the root of a polynomial equation with rational coefficients. They are a subset of irrational numbers examples of which are Pi = 3.14159... and e =2.7182818..., the base of the natural logarithms.

ALPHAMETIC NUMBERS Alphametic numbers form cryptarithms where a set of numbers are assigned to letters that usually spell out some meaningful thought. The numbers can form an addition, subtraction, multiplication or division problem. One of the first cryptarithms came into being in 1924 in the form of an addition problem the words being intended to represent a student's letter from college to the parents. The puzzle read SEND + MORE = MONEY. The answer was 9567 += 1085 = 10,652. Of course, you have to use logic to derive the numbers represented by each letter..

AMICABLE NUMBERS Amicable numbers are pairs of numbers, each of which is the sum of the others aliquot divisors. For example, 220 and 284 are amicable numbers whereas all the aliquot divisors of 220, i.e., 110, 55, 44,22, 10, 5, 4, 2, 1 add up to 284 and all the aliquot divisors of 284, i.e., 142, 71, 4, 2, 1 add up to 220.Also true for any two amicable numbers, N1 and N2, is the fact that the sum of all the factors/divisors of both, Sf(N1 + N2) = N1 + N2.