Fast Maths Trick of Calculation

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Edgar Allan Poe's "The Raven" @ Π value

Edgar Allan Poe's "The Raven", was one of the longest texts ever written using the π constraint, in which the number of letters in each successive word "spells out" the digits of π (740 digits in this example)

Π = 3.14159265358979323846264338327950288419716939937510..

Poe, E.
Near a Raven

Midnights so dreary, tired and weary.
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap - the weirdest tap!
An ominous vibrating sound disturbing my chamber's antedoor.
"This", I whispered quietly, "I ignore".

Perfectly, the intellect remembers: the ghostly fires, a glittering ember.
Inflamed by lightning's outbursts, windows cast penumbras upon this floor.
Sorrowful, as one mistreated, unhappy thoughts I heeded:
That inimitable lesson in elegance - Lenore -
Is delighting, exciting...nevermore.

Ominously, curtains parted (my serenity outsmarted),
And fear overcame my being - the fear of "forevermore".
Fearful foreboding abided, selfish sentiment confided,
As I said, "Methinks mysterious traveler knocks afore.
A man is visiting, of age threescore."

Taking little time, briskly addressing something: "Sir," (robustly)
"Tell what source originates clamorous noise afore?
Disturbing sleep unkindly, is it you a-tapping, so slyly?
Why, devil incarnate!--" Here completely unveiled I my antedoor--
Just darkness, I ascertained - nothing more.

While surrounded by darkness then, I persevered to clearly comprehend.
I perceived the weirdest dream...of everlasting "nevermores".
Quite, quite, quick nocturnal doubts fled - such relief! - as my intellect said,
(Desiring, imagining still) that perchance the apparition was uttering a whispered "Lenore".
This only, as evermore.

Silently, I reinforced, remaining anxious, quite scared, afraid,
While intrusive tap did then come thrice - O, so stronger than sounded afore.
"Surely" (said silently) "it was the banging, clanging window lattice."
Glancing out, I quaked, upset by horrors hereinbefore,
Perceiving: a "nevermore".

Completely disturbed, I said, "Utter, please, what prevails ahead.
Repose, relief, cessation, or but more dreary 'nevermores'?"
The bird intruded thence - O, irritation ever since! -
Then sat on Pallas' pallid bust, watching me (I sat not, therefore),
And stated "nevermores".

Bemused by raven's dissonance, my soul exclaimed, "I seek intelligence;
Explain thy purpose, or soon cease intoning forlorn 'nevermores'!"
"Nevermores", winged corvus proclaimed - thusly was a raven named?
Actually maintain a surname, upon Pluvious seashore?
I heard an oppressive "nevermore".

My sentiments extremely pained, to perceive an utterance so plain,
Most interested, mystified, a meaning I hoped for.
"Surely," said the raven's watcher, "separate discourse is wiser.
Therefore, liberation I'll obtain, retreating heretofore -
Eliminating all the 'nevermores' ".

Still, the detestable raven just remained, unmoving, on sculptured bust.
Always saying "never" (by a red chamber's door).
A poor, tender heartache maven - a sorrowful bird - a raven!
O, I wished thoroughly, forthwith, that he'd fly heretofore.
Still sitting, he recited "nevermores".

The raven's dirge induced alarm - "nevermore" quite wearisome.
I meditated: "Might its utterances summarize of a calamity before?"
O, a sadness was manifest - a sorrowful cry of unrest;
"O," I thought sincerely, "it's a melancholy great - furthermore,
Removing doubt, this explains 'nevermores' ".

Seizing just that moment to sit - closely, carefully, advancing beside it,
Sinking down, intrigued, where velvet cushion lay afore.
A creature, midnight-black, watched there - it studied my soul, unawares.
Wherefore, explanations my insight entreated for.
Silently, I pondered the "nevermores".

"Disentangle, nefarious bird! Disengage - I am disturbed!"
Intently its eye burned, raising the cry within my core.
"That delectable Lenore - whose velvet pillow this was, heretofore,
Departed thence, unsettling my consciousness therefore.
She's returning - that maiden - aye, nevermore."

Since, to me, that thought was madness, I renounced continuing sadness.
Continuing on, I soundly, adamantly forswore:
"Wretch," (addressing blackbird only) "fly swiftly - emancipate me!"
"Respite, respite, detestable raven - and discharge me, I implore!"
A ghostly answer of: "nevermore".

" 'Tis a prophet? Wraith? Strange devil? Or the ultimate evil?"
"Answer, tempter-sent creature!", I inquired, like before.
"Forlorn, though firmly undaunted, with 'nevermores' quite indoctrinated,
Is everything depressing, generating great sorrow evermore?
I am subdued!", I then swore.

In answer, the raven turned - relentless distress it spurned.
"Comfort, surcease, quiet, silence!" - pleaded I for.
"Will my (abusive raven!) sorrows persist unabated?
Nevermore Lenore respondeth?", adamantly I encored.
The appeal was ignored.

"O, satanic inferno's denizen -- go!", I said boldly, standing then.
"Take henceforth loathsome "nevermores" - O, to an ugly Plutonian shore!
Let nary one expression, O bird, remain still here, replacing mirth.
Promptly leave and retreat!", I resolutely swore.
Blackbird's riposte: "nevermore".

So he sitteth, observing always, perching ominously on these doorways.
Squatting on the stony bust so untroubled, O therefore.
Suffering stark raven's conversings, so I am condemned, subserving,
To a nightmare cursed, containing miseries galore.
Thus henceforth, I'll rise (from a darkness, a grave) -- nevermore!

-- Original: E. Poe
-- Redone by measuring circles.

Amazing fact about π

“ Gopi bhaagya madhu vraata/ Shrngisho dadhisandhiga/ Khalajivita khaataava/ Galahaataarasandhara.”

This is apparently a hymn in the praise of Lord Vishnu.
For your astonishment, it gives the value of π (Pi) to the 32 decimal places as 3.1415926535897932384626433832792.

Ancient Indian mathematicians used a representation of numbers using alphabets known as Katopayadhi. A number was encoded using consonant groups of the Sanskrit alphabet, and vowels were provided as additional latitude to the author in poetic composition. The coding is as follows:-

[ka, ta, pa, ya = 1], [kha, tha, pha, ra = 2], [ga, da, ba, la = 3], [gha, dha, bha, va = 4],
[gna, na, ma, scha = 5], [cha, ta, sha = 6], [chha, tha, sa = 7], [ja, da, ha = 8], [jha, dha = 9], [ksha = 0].

Thus pa pa is 11, ma ra is 52. Words kapa, tapo, pipa, and yupa all mean the same
that is 11. It was upto the author to choose one that fit the meaning of the verse well.
If we replace each letter of the hymn by corresponding number from the table according to Katopayadhi, we will get 3141… etc

101%

From a strictly mathematical viewpoint:



What Equals 100%? What does it mean to give MORE than 100%?

Ever wonder about those people who say they are giving more than 100%?

We have all been in situations where someone wants you to GIVE OVER
100%.

How about ACHIEVING 101%?



What equals 100% in life?



Here's a little mathematical formula that might help answer these
questions:


If:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z



Is represented as:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.


If:


H-A-R-D-W-O-R- K

8+1+18+4+23+15+18+11 = 98%


And:

K-N-O-W-L-E-D-G-E

11+14+15+23+12+5+4+7+5 = 96%


But:

A-T-T-I-T-U-D-E

1+20+20+9+20+21+4+5 = 100%


THEN, look how far the love of God will take you:


L-O-V-E-O-F-G-O-D

12+15+22+5+15+6+7+15+4 = 101%


Therefore, one can conclude with mathematical certainty that:

While Hard Work and Knowledge will get you close, and Attitude will
get you there, It's the Love of God that will put you over the top!

BEAUTY OF MATHS

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Brilliant, isn't it?

And look at this symmetry:

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321

SHORT CUT TO FIND SQUARES FROM50 TO 60

With out doing actual multiplication another interesting & shortcut method is there to find 50² to 60²

50²= 5²+0,0² =2500(here write 0²=00)

51²= 5²+1 ,1² =2601

52²= 5²+2 ,2²=2704

53²= 5²+3 , 3²=2809

54²= 5²+4 ,4²=2916

55²= 5²+5 ,5² =3025

56²= 5²+6 ,6² = 3136

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FINDING SQUARES FROM 21 TO 30

In the last post you learned how to find squares from 11

11² =11+1 ,1² =121

……………………….

To day let us find 21² to 30²

21² = 2X(21+1) ,1² =441

22² = 2X(22+2) ,2² =484

23² = 2X(23+3) ,3² = 529

24² = 2X(24+4) ,4² = 56,16 =576(carry 1 & add it to56)

25² = 2X(25+5) ,5² = 60 ,25 =625 (carry 2 & add it to 60)

…………………………………………………………….

………………………………………………………………….

Similarly

31² = 3(31+1) ,1² =961

32² = 3(32+2) ,2² =1024

………………………………

………………………………….

SHORTCUT TO FIND SQUARES FROM 11

11² =11X11

without doing actual multiplication we can do it in a simple way.

11² = 11+1, 1² =121

12² =12+2, 2² =144

13² = 13+3, 3² =169

14² = 14+4, 4² =18,16 =196 (carry 1 &add it to18)

15² =15+5, 5² =20,25 =225 (carry 2 & add it to 20)

16² =16+6, 6² =22,36 =256 (carry 3 &add it to 22)

………………………………………………………………

…………………………………………………………………..

SHORTCUTS IN MULTIPLICATION

Multiplication of two numbers whose tens digits are same and sum of the unit digits is 10.

example: 97x93
84x86
72x78

Multiply the ten's digit with its next integer and write the product of unit digits next to it
97x93= (9x10),7x3 =9021
84x86= (8x9),4x6 =7224
72x78= (7x8),2x8 =5616
This rule is also applicable for three digit numbers whose sum of unit digits is 10 and the remaining digits are same.
113x117= (11x12),3x7 =13221
128x122= (12x13),8x2=15616
The same rule is applicable to find the squares of numbers whose unit digit end with 5.
square of 15 = 15x15 =1x2,5x5 = 225
square of 25 = 25x25 = 2x3, 5x5 = 625
square of 35 = 35x35 = 3x4, 5x5 = 1225
square of 45 = 45x45 = 4x5, 5x5 = 2025

square of 125 =12x13,5x5=15625

SHORTCUT FOR MULTIPLICATION OF11

SHORTCUT FOR MULTIPLICATION OF11

Consider 11 x 35

Take 35 and separate the digits

Add 3+5. Put the 8 in between 3&5.

We get 385

Therefore 11x35=385

……………………………….

If the number being multiplied has digits that add up to more then 9, you simply carry over to the first digit. For example:

Consider 11 x 57

Take 57 and separate the number

Add 5&7=12

add 1 to the first digit 5, it gives 6.

and put the 2 in the middle. You end up with 627

Therefore 11x57=627.

……………………………………

MULTIPLICATION OF NUMBERS CLOSE TO10^3(=1000)

This method is very easy when compared with general multiplication, but useful only when the numbers are close to powers of 10.

Ex 1) 998x987

• here 998 is 2 less than 1000& 987 is 13 less than 1000.
• multiply 2&13. And write it as 026
• now take 998-13 or987-2 which is equal to 985 (cross subtraction)
  

• therefore 998x987=985026

998........2
X 987........13
--------------------
985 026
here 985=998-13 or 987-2(cross subtraction)
026=2X13
Therefore 998x987= 985026

Ex:2) 1007x1013

• here 1007 is 7 more than 1000&1013 is 13 more than 1000
• multiply 7&13 and write it as 091
• now take 1007+13 or 1013+7 (cross addition) which is equal to1020.
• therefore 1007x1013=1020091

1007................7
X 1013..............13
---------------------------------
1020 091

Therefore 1007X1013 =1020091

MULTIPLICATION OF NUMBERS CLOSE TO 100

EX :1) 98x97
98 is 2 less than 100& 97 is 3 less than 100.
now multiply 2&3
write 2x3=06
and then take 98-3 or 97-2 which is equal to 95
therefore ans is 9506.

98.............2
x 97...............3
-----------------
95 06
here 95= 98-3 or 97-2 (cross subtraction)
06=2x3

so 98x97=9506

ANOTHER EXAMPLE: 108X109
Here 108 is 8 more than 100&109 is 9 more than100
now multiply 8&9
and write it as 72
now take 108+9 or109+8.which is =117
THEREFORE 108x109=11772

108.........8
x 109..........9
.....................................
117 72

here 117=108+9 or 109+8
72=8x9

THEREFORE 108X109= 11772

MULTIPLICATION OF NUMBERS CLOSE TO 10

A)MULTIPLICATION OF NUMBERS CLOSE TO 10.

EX: 1 9X8 9 is 1 less than 10& 8 is 2 less than 10. now multiply 1&2
write in this way

9...........1
x8...........2
-------------
7 2 Here 7= 9-2 or 8-1 (cross subtraction)
2=1x2
therefore 9x8=72.

EX:2 12X14 12 is 2 more than 10 &14 is 4 more than 10

12..........2
x 14..........4
---------------
16 8 here 8=2x4 and 16=12+4 or 14+2(cross addition)

there fore 12x14=168

HOW TO FIND APPROXIMATE%

EXAMPLE: WHAT % OF 1512 IS 683?

IN GENERAL WE WRITE x% OF 1512=683
SO X /100 .1512=683
X= 683 X 100/1512
HERE CALCULATION PART IS VERY DIFFICULT
SO EASY METHOD IS......
IN 683/1512 TAKE 10% OF DENOMINATOR THAT IS151.2 ,SEE IT DIVIDES THE NUMERATOR HOW MANY TIMES. HERE IT DIVIDES THE NUMERATOR 4 TIMES SO ANSWER IS IN FORTIES( i.e ANS IS BETWEEN 40%TO 50%
THIS KIND OF SHORT CUTS ARE VERY USEFUL FOR GMAT, CAT &OTHER COMPETITIVE EXAMS.

IF THERE IS ONLY ONE OPTION BETWEEN 40% &50% THEN IT IS THE CORRECT ANSWER. IF MORE THAN ONE OPTION BETWEEN 40% & 50% ,THEN WE TAKE 1% OF DENOMINATOR AND SEE IT DIVIDES THE NUMERATOR H0W MANY TIMES.IN THE ABOVE EXAMPLE
10% OF DENOMINATOR IS 151.2 SAY APPROXIMATELY 151 DIVIDES THE NUMERATOR 4 TIMES. 151X4=604. AND THE REMAINDER IS 79 .NOW 1% OF DENOMINATOR (=15.12 SAY APPROXIMATELY 15 DIVIDES THE REMAINDER 5 TIMES. SO 45% IS THE ANSWER.