Somewhat beyond the books in maths:

The word 'mathematics' comes from the Greek máthēma, which means learning, study, science.Do you know a word known as Dyscalculia? Dyscalculia means difficulty in learning arithmetic, such as difficulty in understanding numbers, and learning maths facts!In America, mathematics is known as ‘math’, they say that ‘mathematics’ functions as a singular noun so as per them ‘math’ should be singular too.

Do you know ‘Mathematics’ is an anagram of ‘me asthmatic’ (An Anagram is word or phrase made by transposing or rearranging letter of other words or phrase.)

Notches (cuts or indentation) on animal bones prove that humans have been doing mathematics since aroud 30,000 BC.The word ‘hundrath’ in Old Norse (old language from where English language originated), from which word ‘hundred’ derives, meant not 100 but 120.

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

The number 5 is pronounced as 'Ha' in Thai language.555 is also used by some as slang for 'HaHaHa'.Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

Zero ( 0 ) is the only number which can not be represented by Roman numerals.The name 'zero' derives from the Arabic word sifr which also gave us the English word 'cipher' meaning 'a secret way of writing' .

Do you know the magic of no. nine (9)? Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9).

Here is an interesting trick to check divisibility of any number by number 3.A number is divisible by three if the sum of its digits is divisible by three (3).

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.

Have you ever noticed that the opposite sides a die always add up to seven (7).

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").A 'jiffy' is an actual unit of time for 1/100th of a second.

'FOUR' is the only number in the English language that is spelt with the same number of letters as the number itself40 when written "forty" is the only number with letters in alphabetical order, while "one" is the only one with letters in reverse order.

In a group of 23 people, at least two have the same birthday with the probability greater than 1/2 .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.

The word "FRACTION" derives from the Latin " fractio - to break".In working out mathematical equations, the Greek mathematician ,Pythagoreans used little rocks to represent numbers.Hence the name of Calculus was born which means pebbles in Greek.

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.

Have you heard about Fibonacci? It is the sequence of numbers wherein a number is the result of adding the two numbers before it! Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

Have you heard about a Palindrome Number? It is a number that reads the same backwards and forward, e.g. 12421.

@infoprofesormathematics

From grands series mathematics books of London .@divyansh.org

3) Trigonometrical ratios:

In a right-angled triangle, the Pythagoras theorem states

(perpendicular )² + ( base )² = ( hypotenuse )²

There are some properties pertaining to the right-angled triangle. It is to be noted that in the following formulas, P stands for perpendicular, B stands for base and H stands for the hypotenuse.

1. SinA = P / H
2. CosA = B / H
3. TanA = P / B
4. CotA = B / P
5. CosecA = H / P
6. SecA = H/B
7. Sin²A + Cos²A = 1
8. Tan²A + 1 = Sec²A

Cot²A + 1 = Cosec²A

In order to find a relationship between various trigonometric identities, there are some important formulas:
1. TanA = SinA / CosA
2. CotA = CosA / SinA
3. CosecA = 1 / SinA
4. SecA = 1 / CosA

There are some formulas that are very crucial to solving higher level sums.

1. Sin (A +B) =SinA . CosB + CosA . SinB
2. Sin (A – B) = SinA . CosB – CosA . SinB
3. Cos (A + B) = CosA . CosB – SinA . SinB
4. Cos (A – B) = CosA. CosB + SinA . SinB
5. Tan (A + B) = TanA + TanB / 1 – TanA . TanB
6. Tan (A – B) = TanA –TanB / 1 + TanA . TanB
7. Sin ( A + B) . Sin (A – B) = Sin²A – Sin²B = Cos²B – Cos²A
8. Cos (A + B) . Cos (A – B) = Cos²A – Sin²B = Cos²B – Sin²A
9. Sin2A = 2 . SinA . CosA = 2 . TanA / (1 + Tan²A)
10. Cos2A = Cos²A – Sin²A = 1 – 2Sin²A = 2Cos²A – 1 = (1 – Tan²A) / (1 + Tan²A)
11. Tan2A = 2TanA / (1 – Tan²A)
12.  Sin3A = 3 . SinA – 4 . Sin³A
13. Cos3A = 4 . Cos³A – 3 . CosA
14. Tan3A = (3TanA – Tan³A) / (1 – 3Tan²A)
15. SinA + SinB = 2 Sin (A + B)/2 Cos (A – B)/2
16. SinA – SinB = 2 Sin (A – B)/2 Cos (A + B)/2
17. CosA + CosB = 2 Cos(A – B)/2 Cos (A + B)/2
18. CosA – CosB = 2 Sin(B – A)/2 Sin (A + B)/2
19. TanA + TanB = Sin (A + B) / CosA . CosB
20. SinA CosB = Sin (A + B) + Sin (A – B)
21. CosA SinB = Sin (A + B) – Sin (A – B)
22. CosA CosB = Cos (A + B) + Cos (A – B)
23.  SinA SinB = Cos (A – B) – Cos (A + B)

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2).Introduction to pie(π)__.  :::

The number π is a mathematical constant. Originally defined as the ratio of a 

circle's circumference to its diameter, it now has various equivalent definitions

 and appears in many formulas in all areas of mathematics and physics. It is 

approximately equal to 3.14159 not a physical constant.

  π appears routinely in describing fundamental principles of the universe, often  

because π's relationship to the circle and to spherical coordinate systems. A 

 Simple formula from the field of classical mechanics gives the approximate 

period T of a simple pendulum of length L, swinging with a small amplitude (g is the earth's gravitational acceleration):

${\displaystyle T\approx 2\pi {\sqrt {\frac {L}{g}}}.}$

Below is the 100 digits of pie which goes to infinite:-

3.141592653589793238462643383279502884197169399375105820974944592307816406286 .....................

The entire universe exists in pie.
Pie day is celebrated on 14 march and this day is also know as mathematical constant day or maths constant day.
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1) interesting questions on expansion:

If it is given that ::    ( a^2-b^2)=c

   

Then find the value of 'a'  and 'b'.

Solution;

(a^2-b^2) * 1=c*1                  (multiplying 1 both sides) 

(a^2-b^2)=c*1

(a+b)(a-b)=c*1

Therefore:

(a+b)=c -----------------------------------(1st eq.)

(a-b)=1------------------------------------(2nd eq.)

(Adding eq 1 and 2 )

a+b+a-b=c+1

2a=c+1

a=c+1/2

(Substracting eq 2 from 1)

a-a+b+b=c-1

2b=c-1

b=c-1/2

        

Thus:

a=(c+1)/2 .         And .             b=(c-1)/2

Characteristics of these formulas:

1) .When the value of c is even then the value of a and b will be in decimals.

2).  When the value of c is odd then the value of a and b will be an real number.

Note: this formula is applicable for specific numbers .

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Intro.maths.dps

MATHEMATICS

"History has proven ,the one who dares to imagine the impossible are the one who breaks all the human limitations"

Hii  , let me introduce you to myself that's me. My name is Divyansh pratap Singh.I am a student of class 10th. I am a blogger and also I love Mathematics and I have an unsatisfing thirst for maths.
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