NUMBERS

                                                Ganga  K S

                                                         IX B

 0,1,2,3,4,5...................

NUMBERS THE FIRST STEP OF

MATHEMATICS

  Have BEEN A HELPFUL DEVICE

IN EVERY SUBJECT.

FROM ARYABHATA TILL NOW

WE USE NUMBERS 

IN OUR DAY TO DAY LIFE.

WE USE NUMBERS AS

OUR FRIENDS WHEN 

PLAYING,CALCULATING.....

EVERY WHERE THERE IS A NUMBER

AS A PART OF OUR LIFE

IT DOES NOT HAVE AN END
IT GOES 

ON AND ON........JUST COUNT...... 0,1,2,3,4,5 .......

Math’s Interesting Facts

                                                                                                                  ANILA

                                                                                                                      IX-B

·         The word "mathematics" comes from the Greek máthēma, which means learning, study, science.

·         What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion.

·         Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

·         The = sign ("equals sign") was invented by 16th Century Welsh mathematician Robert Recorde, who was fed up with writing "is equal to" in his equations.

·         Googol (meaning & origin of Google brand) is the term used for a number 1 followed by 100 zeros and that it was used by a nine-year old, Milton Sirotta, in 1940.

·         The name of the popular search engine ‘Google’ came from a misspelling of the word ‘googol’.

·         Abacus is considered the origin of the calculator.

·         12,345,678,987,654,321 is the product of 111,111,111 x 111,111,111. Notice the sequence of the numbers 1 to 9 and back to 1.

·         Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D.

·         An icosagon is a shape with 20 sides.

·         Trigonometry is the study of the relationship between the angles of triangles and their sides.

·         If you add up the numbers 1-100 consecutively (1+2+3+4+5...) the total is 5050.

·         2 and 5 are the only primes that end in 2 or 5.

·         From 0 to 1,000, the letter "A" only appears in 1,000 ("one thousand").

·         'FOUR' is the only number in the English language that is spelt with the same number of letters as the number itself

·         40 when written "forty" is the only number with letters in alphabetical order, while "one" is the only one with letters in reverse order.

·         Among all shapes with the same perimeter a circle has the largest area.

·         Among all shapes with the same area circle has the shortest perimeter .

·         In 1995 in Taipei, citizens were allowed to remove ‘4’ from street numbers because it sounded like ‘death’ in Chinese. Many Chinese hospitals do not have a 4th floor.

·         In many cultures no 13 is considered unlucky, well,there are many myths around it .One is that In some ancient European religions, there were 12 good gods and one evil god; the evil god was called the 13th god.Other is superstition goes back to the Last Supper. There were 13 people at the meal, including Jesus Christ, and Judas was thought to be the 13th guest.

Some beautiful examples with multiplication

12345679 x 9 = 111111111;

12345679 x 8 = 98765432

An interesting fact about primes
Mathematicians of XVIII^th century proved that numbers 31; 331; 3331; 33331; 333331; 3333331; 33333331 are primes. It was a big temptation to think that all numbers of such kind are primes. But the next number is not a prime.
333333331 = 17 x 19607843

     The evolution of mathematics

GIRISH V GOPINATH - X A -

The evolution of mathematics might be seen as an ever-increasing series of abstractions , or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals, was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.

In addition to recognizing how to count  physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons , years. elementaryarithmetic (addition, subtraction, multiplication & division)   naturally followed.

Since numeracy pre-dated writing ,further steps were needed for recording numbers such as tallies or  the knotted strings called Quipu  used by theinca  to store numerical data. Numeral systems have been many and diverse, with the first known written numerals created byEgyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.

Mayan numerals

The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when theBabylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.                         

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Math of drugs and bodies (pharmacokinetics

__   Shahana Moideen  XB  __   

  

  

Pharmacokinetics is the process whereby substances (like food and drugs) are ingested into the body (via mouth or needles) and processed. We’ll concentrate on drugs.

 

The process of pharmacokinetics has 5 steps:

• Liberation – the drug is released from the formulation.

• Absorption – the drug enters the body.

• Distribution – the drug disperses throughout the body

• Metabolism – the drug is broken down by the body.

• Excretion – the drug is eliminated from the body.

Of course, each drug needs to act on the body in a different way. Some drugs need to be absorbed quickly (like nitroglycerin if we are having a heart attack) and preferably eliminated quickly (otherwise toxins build up in the blood). For other drugs, we want slow absorption so we get maximum benefit and don’t lose a lot of it from excretion.

So when your doctor prescribes (say) "take 2 tablets every meal time", this is based on the desirable levels of drug concentration and known levels of distribution, metabolism and excretion in the body.

What’s the math?

When the nurse first administers the drug, the concentration of the drug in the blood stream is zero. As the drug moves around the body and is metabolized, the concentration of the drug increases.

There comes a point when the concentration no longer increases and begins to decline. This is the period when the drug is fully distributed and metabolism is taking place. As time goes on, the drug concentration gets less and less and falls below a certain effective amount. Time to take some more pills.

We can model such a situation mathematically with a differential equation  It has 2 parts – an absorption part and an elimination part. At first, absorption (increasing drug concentration) takes precedence and over time, elimination (decreasing concentration) is the most important element.

We have the following variables:

D = drug dose given

V = volume distributed in the body

C = concentration of the drug at time t

F = fraction of dose which has been absorbed (also called bioavailability)

A = absorption rate constant

E = elimination rate constant

t = time

Absorption part: This depends on the amount of the drug given, the fraction that has been absorbed and the absorption rate constant. It decreases as time goes on. The expression for absorption is given by:

A × F × D × e^-At

Elimination part: The elimination dynamic is affected by the elimination constant, the volume distributed in the body and the concentration left of the drug. The expression for this part is:

E × V × C

For our model, we need to subtract the elimination part from the absorption part (since the absorption part increases the concentration of drug and the elimination part decreases it). Our differential equation is as follows:

We now substitute some typical values for our variables (without units to keep things simple. Note C is a variable, the one for which we seek an expression in t.)

Solving this differential equation (using a computer algebra system), gives the concentration at time t as:

C(t) = 533.3(e^−0.4t − e^−0.5t)

We can see in the graph the portion where the concentration increases (up to around t = 3) and levels off. The concentration then decreases to almost zero at t = 24.

Pharmacokinetics is yet another interesting “real life” application of math.